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Non-experimental research: What it is, overview & advantages

Non-experimental research is the type of research that lacks an independent variable. Instead, the researcher observes the context in which the phenomenon occurs and analyzes it to obtain information.

Unlike experimental research , where the variables are held constant, non-experimental research happens during the study when the researcher cannot control, manipulate or alter the subjects but relies on interpretation or observations to conclude.

This means that the method must not rely on correlations, surveys , or case studies and cannot demonstrate an actual cause and effect relationship.

Characteristics of non-experimental research

Some of the essential characteristics of non-experimental research are necessary for the final results. Let’s talk about them to identify the most critical parts of them.

Most studies are based on events that occurred previously and are analyzed later.
In this method, controlled experiments are not performed for reasons such as ethics or morality.
No study samples are created; on the contrary, the samples or participants already exist and develop in their environment.
The researcher does not intervene directly in the environment of the sample.
This method studies the phenomena exactly as they occurred.

Types of non-experimental research

Non-experimental research can take the following forms:

Cross-sectional research : Cross-sectional research is used to observe and analyze the exact time of the research to cover various study groups or samples. This type of research is divided into:

Descriptive: When values are observed where one or more variables are presented.
Causal: It is responsible for explaining the reasons and relationship that exists between variables in a given time.

Longitudinal research: In a longitudinal study , researchers aim to analyze the changes and development of the relationships between variables over time. Longitudinal research can be divided into:

Trend: When they study the changes faced by the study group in general.
Group evolution: When the study group is a smaller sample.
Panel: It is in charge of analyzing individual and group changes to discover the factor that produces them.

LEARN ABOUT: Quasi-experimental Research

When to use non-experimental research

Non-experimental research can be applied in the following ways:

When the research question may be about one variable rather than a statistical relationship about two variables.
There is a non-causal statistical relationship between variables in the research question.
The research question has a causal research relationship, but the independent variable cannot be manipulated.
In exploratory or broad research where a particular experience is confronted.

Advantages and disadvantages

Some advantages of non-experimental research are:

It is very flexible during the research process
The cause of the phenomenon is known, and the effect it has is investigated.
The researcher can define the characteristics of the study group.

Among the disadvantages of non-experimental research are:

The groups are not representative of the entire population.
Errors in the methodology may occur, leading to research biases .

Non-experimental research is based on the observation of phenomena in their natural environment. In this way, they can be studied later to reach a conclusion.

Difference between experimental and non-experimental research

Experimental research involves changing variables and randomly assigning conditions to participants. As it can determine the cause, experimental research designs are used for research in medicine, biology, and social science.

Experimental research designs have strict standards for control and establishing validity. Although they may need many resources, they can lead to very interesting results.

Non-experimental research, on the other hand, is usually descriptive or correlational without any explicit changes done by the researcher. You simply describe the situation as it is, or describe a relationship between variables. Without any control, it is difficult to determine causal effects. The validity remains a concern in this type of research. However, it’s’ more regarding the measurements instead of the effects.

LEARN MORE: Descriptive Research vs Correlational Research

Whether you should choose experimental research or non-experimental research design depends on your goals and resources. If you need any help with how to conduct research and collect relevant data, or have queries regarding the best approach for your research goals, contact us today! You can create an account with our survey software and avail of 88+ features including dashboard and reporting for free.

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What is non-experimental research: Definition, types & examples

What is non-experimental research: Definition, types & examples

Defne Çobanoğlu

The experimentation method is very useful for getting information on a specific subject. However, when experimenting is not possible or practical, there is another way of collecting data for those interested. It's a non-experimental way, to say the least.

In this article, we have gathered information on non-experimental research, clearly defined what it is and when one should use it, and listed the types of non-experimental research. We also gave some useful examples to paint a better picture. Let us get started.

What is non-experimental research?

Non-experimental research is a type of research design that is based on observation and measuring instead of experimentation with randomly assigned participants.

What characterizes this research design is the fact that it lacks the manipulation of independent variables . Because of this fact, the non-experimental research is based on naturally occurring conditions, and there is no involvement of external interventions. Therefore, the researchers doing this method must not rely heavily on interviews, surveys , or case studies.

When to use non-experimental research?

An experiment is done when a researcher is investigating the relationship between one or two phenomena and has a theory or hypothesis on the relationship between two variables that are involved. The researcher can carry out an experiment when it is ethical, possible, and feasible to do one.

However, when an experiment can not be done because of a limitation, then they decide to opt for a non-experimental research design . Non-experimental research is considered preferable in some conditions, including:

When the manipulation of the independent variable is not possible because of ethical or practical concerns
When the subjects of an experimental design can not be randomly assigned to treatments.
When the research question is too extensive or it relates to a general experience.
When researchers want to do a starter research before investing in more extensive research.
When the research question is about the statistical relationship between variables , but in a noncausal context.
Characteristics of non-experimental research

Non-experimental research has some characteristics that clearly define the framework of this research method. They provide a clear distinction between experimental design and non-experimental design. Let us see some of them:

Non-experimental research does not involve the manipulation of variables .
The aim of this research type is to explore the factors as they naturally occur .
This method is used when experimentation is not possible because of ethical or practical reasons .
Instead of creating a sample or participant group, the existing groups or natural thresholds are used during the research.
This research method is not about finding causality between two variables.
Most studies are done on past events or historical occurrences to make sense of specific research questions.
Types of non-experimental research

Non-experimental research types

What makes research non-experimental research is the fact that the researcher does not manipulate the factors, does not randomly assign the participants, and observes the existing groups. But this research method can also be divided into different types. These types are:

Correlational research:

In correlation studies, the researcher does not manipulate the variables and is not interested in controlling the extraneous variables. They only observe and assess the relationship between them. For example, a researcher examines students’ study hours every day and their overall academic performance. The positive correlation this between study hours and academic performance suggests a statistical association.

Quasi-experimental research:

In quasi-experimental research, the researcher does not randomly assign the participants into two groups. Because you can not deliberately deprive someone of treatment, the researcher uses natural thresholds or dividing points . For example, examining students from two different high schools with different education methods.

Cross-sectional research:

In cross-sectional research, the researcher studies and compares a portion of a population at the same time . It does not involve random assignment or any outside manipulation. For example, a study on smokers and non-smokers in a specific area.

Observational research:

In observational research, the researcher once again does not manipulate any aspect of the study, and their main focus is observation of the participants . For example, a researcher examining a group of children playing in a playground would be a good example.

Non-experimental research examples

Non-experimental research is a good way of collecting information and exploring relationships between variables. It can be used in numerous fields, from social sciences, economics, psychology, education, and market research. When gathering information using secondary research is not enough and an experiment can not be done, this method can bring out new information.

Non-experimental research example #1

Imagine a researcher who wants to see the connection between mobile phone usage before bedtime and the amount of sleep adults get in a night . They can gather a group of individuals to observe and present them with some questions asking about the details of their day, frequency and duration of phone usage, quality of sleep, etc . And observe them by analyzing the findings.

Non-experimental research example #2

Imagine a researcher who wants to explore the correlation between job satisfaction levels among employees and what are the factors that affect this . The researcher can gather all the information they get about the employees’ ages, sexes, positions in the company, working patterns, demographic information, etc .

The research provides the researcher with all the information to make an analysis to identify correlations and patterns. Then, it is possible for researchers and administrators to make informed predictions.

Frequently asked questions about non-experimental research

When not to use non-experimental research?

There are some situations where non-experimental research is not suitable or the best choice. For example, the aim of non-experimental research is not about finding causality therefore, if the researcher wants to explore the relationship between two variables, then this method is not for them. Also, if the control over the variables is extremely important to the test of a theory, then experimentation is a more appropriate option.

What is the difference between experimental and non-experimental research?

Experimental research is an example of primary research where the researcher takes control of all the variables, randomly assigns the participants into different groups, and studies them in a pre-determined environment to test a hypothesis.

On the contrary, non-experimental research does not intervene in any way and only observes and studies the participants in their natural environments to make sense of a phenomenon

What makes a quasi-experiment a non-experiment?

The same as true experimentation, quasi-experiment research also aims to explore a cause-and-effect relationship between independent and dependent variables. However, in quasi-experimental research, the participants are not randomly selected. They are assigned to groups based on non-random criteria .

Is a survey a non-experimental study?

Yes, as the main purpose of a survey or questionnaire is to collect information from participants without outside interference, it makes the survey a non-experimental study. Surveys are used by researchers when experimentation is not possible because of ethical reasons, but first-hand data is needed

What is non-experimental data?

Non-experimental data is data collected by researchers via using non-experimental methods such as observations, interpretation, and interactions. Non-experimental data could both be qualitative or quantitative, depending on the situation.

Advantages of non-experimental research

Non-experimental research has its positive sides that a researcher should have in mind when going through a study. They can start their research by going through the advantages. These advantages are:

It is used to observe and analyze past events .
This method is more affordable than a true experiment .
As the researcher can adapt the methods during the study, this research type is more flexible than an experimental study.
This method allows the researchers to answer specific questions .

Disadvantages of non-experimental research

Even though non-experimental research has its advantages, it also has some disadvantages a researcher should be mindful of. Here are some of them:

The findings of non-experimental research can not be generalized to the whole population. Therefore, it has low external validity .
This research is used to explore only a single variable .
Non-experimental research designs are prone to researcher bias and may not produce neutral results.
Final words

A non-experimental study differs from an experimental study in that there is no intervention or change of internal or extraneous elements. It is a smart way to collect information without the limitations of experimentation. These limitations could be about ethical or practical problems. When you can not do proper experimentation, your other option is to study existing conditions and groups to draw conclusions. This is a non-experimental design .

In this article, we have gathered information on non-experimental research to shed light on the details of this research method. If you are thinking of doing a study, make sure to have this information in mind. And lastly, do not forget to visit our articles on other research methods and so much more!

Defne is a content writer at forms.app. She is also a translator specializing in literary translation. Defne loves reading, writing, and translating professionally and as a hobby. Her expertise lies in survey research, research methodologies, content writing, and translation.

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6.1 Overview of Non-Experimental Research

Learning objectives.

Define non-experimental research, distinguish it clearly from experimental research, and give several examples.
Explain when a researcher might choose to conduct non-experimental research as opposed to experimental research.

What Is Non-Experimental Research?

Non-experimental research is research that lacks the manipulation of an independent variable. Rather than manipulating an independent variable, researchers conducting non-experimental research simply measure variables as they naturally occur (in the lab or real world).

Most researchers in psychology consider the distinction between experimental and non-experimental research to be an extremely important one. This is because although experimental research can provide strong evidence that changes in an independent variable cause differences in a dependent variable, non-experimental research generally cannot. As we will see, however, this inability to make causal conclusions does not mean that non-experimental research is less important than experimental research.

When to Use Non-Experimental Research

As we saw in the last chapter , experimental research is appropriate when the researcher has a specific research question or hypothesis about a causal relationship between two variables—and it is possible, feasible, and ethical to manipulate the independent variable. It stands to reason, therefore, that non-experimental research is appropriate—even necessary—when these conditions are not met. There are many times in which non-experimental research is preferred, including when:

the research question or hypothesis relates to a single variable rather than a statistical relationship between two variables (e.g., How accurate are people’s first impressions?).
the research question pertains to a non-causal statistical relationship between variables (e.g., is there a correlation between verbal intelligence and mathematical intelligence?).
the research question is about a causal relationship, but the independent variable cannot be manipulated or participants cannot be randomly assigned to conditions or orders of conditions for practical or ethical reasons (e.g., does damage to a person’s hippocampus impair the formation of long-term memory traces?).
the research question is broad and exploratory, or is about what it is like to have a particular experience (e.g., what is it like to be a working mother diagnosed with depression?).

Again, the choice between the experimental and non-experimental approaches is generally dictated by the nature of the research question. Recall the three goals of science are to describe, to predict, and to explain. If the goal is to explain and the research question pertains to causal relationships, then the experimental approach is typically preferred. If the goal is to describe or to predict, a non-experimental approach will suffice. But the two approaches can also be used to address the same research question in complementary ways. For example, Similarly, after his original study, Milgram conducted experiments to explore the factors that affect obedience. He manipulated several independent variables, such as the distance between the experimenter and the participant, the participant and the confederate, and the location of the study (Milgram, 1974) [1] .

Types of Non-Experimental Research

Non-experimental research falls into three broad categories: cross-sectional research, correlational research, and observational research.

First, cross-sectional research involves comparing two or more pre-existing groups of people. What makes this approach non-experimental is that there is no manipulation of an independent variable and no random assignment of participants to groups. Imagine, for example, that a researcher administers the Rosenberg Self-Esteem Scale to 50 American college students and 50 Japanese college students. Although this “feels” like a between-subjects experiment, it is a cross-sectional study because the researcher did not manipulate the students’ nationalities. As another example, if we wanted to compare the memory test performance of a group of cannabis users with a group of non-users, this would be considered a cross-sectional study because for ethical and practical reasons we would not be able to randomly assign participants to the cannabis user and non-user groups. Rather we would need to compare these pre-existing groups which could introduce a selection bias (the groups may differ in other ways that affect their responses on the dependent variable). For instance, cannabis users are more likely to use more alcohol and other drugs and these differences may account for differences in the dependent variable across groups, rather than cannabis use per se.

Cross-sectional designs are commonly used by developmental psychologists who study aging and by researchers interested in sex differences. Using this design, developmental psychologists compare groups of people of different ages (e.g., young adults spanning from 18-25 years of age versus older adults spanning 60-75 years of age) on various dependent variables (e.g., memory, depression, life satisfaction). Of course, the primary limitation of using this design to study the effects of aging is that differences between the groups other than age may account for differences in the dependent variable. For instance, differences between the groups may reflect the generation that people come from (a cohort effect) rather than a direct effect of age. For this reason, longitudinal studies in which one group of people is followed as they age offer a superior means of studying the effects of aging. Once again, cross-sectional designs are also commonly used to study sex differences. Since researchers cannot practically or ethically manipulate the sex of their participants they must rely on cross-sectional designs to compare groups of men and women on different outcomes (e.g., verbal ability, substance use, depression). Using these designs researchers have discovered that men are more likely than women to suffer from substance abuse problems while women are more likely than men to suffer from depression. But, using this design it is unclear what is causing these differences. So, using this design it is unclear whether these differences are due to environmental factors like socialization or biological factors like hormones?

When researchers use a participant characteristic to create groups (nationality, cannabis use, age, sex), the independent variable is usually referred to as an experimenter-selected independent variable (as opposed to the experimenter-manipulated independent variables used in experimental research). Figure 6.1 shows data from a hypothetical study on the relationship between whether people make a daily list of things to do (a “to-do list”) and stress. Notice that it is unclear whether this is an experiment or a cross-sectional study because it is unclear whether the independent variable was manipulated by the researcher or simply selected by the researcher. If the researcher randomly assigned some participants to make daily to-do lists and others not to, then the independent variable was experimenter-manipulated and it is a true experiment. If the researcher simply asked participants whether they made daily to-do lists or not, then the independent variable it is experimenter-selected and the study is cross-sectional. The distinction is important because if the study was an experiment, then it could be concluded that making the daily to-do lists reduced participants’ stress. But if it was a cross-sectional study, it could only be concluded that these variables are statistically related. Perhaps being stressed has a negative effect on people’s ability to plan ahead. Or perhaps people who are more conscientious are more likely to make to-do lists and less likely to be stressed. The crucial point is that what defines a study as experimental or cross-sectional l is not the variables being studied, nor whether the variables are quantitative or categorical, nor the type of graph or statistics used to analyze the data. It is how the study is conducted.

Figure 6.1 Results of a Hypothetical Study on Whether People Who Make Daily To-Do Lists Experience Less Stress Than People Who Do Not Make Such Lists

Second, the most common type of non-experimental research conducted in Psychology is correlational research. Correlational research is considered non-experimental because it focuses on the statistical relationship between two variables but does not include the manipulation of an independent variable. More specifically, in correlational research , the researcher measures two continuous variables with little or no attempt to control extraneous variables and then assesses the relationship between them. As an example, a researcher interested in the relationship between self-esteem and school achievement could collect data on students’ self-esteem and their GPAs to see if the two variables are statistically related. Correlational research is very similar to cross-sectional research, and sometimes these terms are used interchangeably. The distinction that will be made in this book is that, rather than comparing two or more pre-existing groups of people as is done with cross-sectional research, correlational research involves correlating two continuous variables (groups are not formed and compared).

Third, observational research is non-experimental because it focuses on making observations of behavior in a natural or laboratory setting without manipulating anything. Milgram’s original obedience study was non-experimental in this way. He was primarily interested in the extent to which participants obeyed the researcher when he told them to shock the confederate and he observed all participants performing the same task under the same conditions. The study by Loftus and Pickrell described at the beginning of this chapter is also a good example of observational research. The variable was whether participants “remembered” having experienced mildly traumatic childhood events (e.g., getting lost in a shopping mall) that they had not actually experienced but that the researchers asked them about repeatedly. In this particular study, nearly a third of the participants “remembered” at least one event. (As with Milgram’s original study, this study inspired several later experiments on the factors that affect false memories.

The types of research we have discussed so far are all quantitative, referring to the fact that the data consist of numbers that are analyzed using statistical techniques. But as you will learn in this chapter, many observational research studies are more qualitative in nature. In qualitative research , the data are usually nonnumerical and therefore cannot be analyzed using statistical techniques. Rosenhan’s observational study of the experience of people in a psychiatric ward was primarily qualitative. The data were the notes taken by the “pseudopatients”—the people pretending to have heard voices—along with their hospital records. Rosenhan’s analysis consists mainly of a written description of the experiences of the pseudopatients, supported by several concrete examples. To illustrate the hospital staff’s tendency to “depersonalize” their patients, he noted, “Upon being admitted, I and other pseudopatients took the initial physical examinations in a semi-public room, where staff members went about their own business as if we were not there” (Rosenhan, 1973, p. 256) [2] . Qualitative data has a separate set of analysis tools depending on the research question. For example, thematic analysis would focus on themes that emerge in the data or conversation analysis would focus on the way the words were said in an interview or focus group.

Internal Validity Revisited

Recall that internal validity is the extent to which the design of a study supports the conclusion that changes in the independent variable caused any observed differences in the dependent variable. Figure 6.2 shows how experimental, quasi-experimental, and non-experimental (correlational) research vary in terms of internal validity. Experimental research tends to be highest in internal validity because the use of manipulation (of the independent variable) and control (of extraneous variables) help to rule out alternative explanations for the observed relationships. If the average score on the dependent variable in an experiment differs across conditions, it is quite likely that the independent variable is responsible for that difference. Non-experimental (correlational) research is lowest in internal validity because these designs fail to use manipulation or control. Quasi-experimental research (which will be described in more detail in a subsequent chapter) is in the middle because it contains some, but not all, of the features of a true experiment. For instance, it may fail to use random assignment to assign participants to groups or fail to use counterbalancing to control for potential order effects. Imagine, for example, that a researcher finds two similar schools, starts an anti-bullying program in one, and then finds fewer bullying incidents in that “treatment school” than in the “control school.” While a comparison is being made with a control condition, the lack of random assignment of children to schools could still mean that students in the treatment school differed from students in the control school in some other way that could explain the difference in bullying (e.g., there may be a selection effect).

Figure 7.1 Internal Validity of Correlational, Quasi-Experimental, and Experimental Studies. Experiments are generally high in internal validity, quasi-experiments lower, and correlational studies lower still.

Figure 6.2 Internal Validity of Correlation, Quasi-Experimental, and Experimental Studies. Experiments are generally high in internal validity, quasi-experiments lower, and correlation studies lower still.

Notice also in Figure 6.2 that there is some overlap in the internal validity of experiments, quasi-experiments, and correlational studies. For example, a poorly designed experiment that includes many confounding variables can be lower in internal validity than a well-designed quasi-experiment with no obvious confounding variables. Internal validity is also only one of several validities that one might consider, as noted in Chapter 5.

Key Takeaways

Non-experimental research is research that lacks the manipulation of an independent variable.
There are two broad types of non-experimental research. Correlational research that focuses on statistical relationships between variables that are measured but not manipulated, and observational research in which participants are observed and their behavior is recorded without the researcher interfering or manipulating any variables.
In general, experimental research is high in internal validity, correlational research is low in internal validity, and quasi-experimental research is in between.
A researcher conducts detailed interviews with unmarried teenage fathers to learn about how they feel and what they think about their role as fathers and summarizes their feelings in a written narrative.
A researcher measures the impulsivity of a large sample of drivers and looks at the statistical relationship between this variable and the number of traffic tickets the drivers have received.
A researcher randomly assigns patients with low back pain either to a treatment involving hypnosis or to a treatment involving exercise. She then measures their level of low back pain after 3 months.
A college instructor gives weekly quizzes to students in one section of his course but no weekly quizzes to students in another section to see whether this has an effect on their test performance.
Milgram, S. (1974). Obedience to authority: An experimental view . New York, NY: Harper & Row. ↵
Rosenhan, D. L. (1973). On being sane in insane places. Science, 179 , 250–258. ↵

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Experimental Vs Non-Experimental Research: 15 Key Differences

There is a general misconception around research that once the research is non-experimental, then it is non-scientific, making it more important to understand what experimental and experimental research entails. Experimental research is the most common type of research, which a lot of people refer to as scientific research.

Non experimental research, on the other hand, is easily used to classify research that is not experimental. It clearly differs from experimental research, and as such has different use cases.

In this article, we will be explaining these differences in detail so as to ensure proper identification during the research process.

What is Experimental Research?

Experimental research is the type of research that uses a scientific approach towards manipulating one or more control variables of the research subject(s) and measuring the effect of this manipulation on the subject. It is known for the fact that it allows the manipulation of control variables.

This research method is widely used in various physical and social science fields, even though it may be quite difficult to execute. Within the information field, they are much more common in information systems research than in library and information management research.

Experimental research is usually undertaken when the goal of the research is to trace cause-and-effect relationships between defined variables. However, the type of experimental research chosen has a significant influence on the results of the experiment.

Therefore bringing us to the different types of experimental research. There are 3 main types of experimental research, namely; pre-experimental, quasi-experimental, and true experimental research.

Pre-experimental Research

Pre-experimental research is the simplest form of research, and is carried out by observing a group or groups of dependent variables after the treatment of an independent variable which is presumed to cause change on the group(s). It is further divided into three types.

One-shot case study research
One-group pretest-posttest research
Static-group comparison

Quasi-experimental Research

The Quasi type of experimental research is similar to true experimental research, but uses carefully selected rather than randomized subjects. The following are examples of quasi-experimental research:

Time series
No equivalent control group design
Counterbalanced design.

True Experimental Research

True experimental research is the most accurate type, and may simply be called experimental research. It manipulates a control group towards a group of randomly selected subjects and records the effect of this manipulation.

True experimental research can be further classified into the following groups:

The posttest-only control group
The pretest-posttest control group
Solomon four-group

Pros of True Experimental Research

Researchers can have control over variables.
It can be combined with other research methods.
The research process is usually well structured.
It provides specific conclusions.
The results of experimental research can be easily duplicated.

Cons of True Experimental Research

It is highly prone to human error.
Exerting control over extraneous variables may lead to the personal bias of the researcher.
It is time-consuming.
It is expensive.
Manipulating control variables may have ethical implications.
It produces artificial results.

What is Non-Experimental Research?

Non-experimental research is the type of research that does not involve the manipulation of control or independent variable. In non-experimental research, researchers measure variables as they naturally occur without any further manipulation.

This type of research is used when the researcher has no specific research question about a causal relationship between 2 different variables, and manipulation of the independent variable is impossible. They are also used when:

subjects cannot be randomly assigned to conditions.
the research subject is about a causal relationship but the independent variable cannot be manipulated.
the research is broad and exploratory
the research pertains to a non-causal relationship between variables.
limited information can be accessed about the research subject.

There are 3 main types of non-experimental research , namely; cross-sectional research, correlation research, and observational research.

Cross-sectional Research

Cross-sectional research involves the comparison of two or more pre-existing groups of people under the same criteria. This approach is classified as non-experimental because the groups are not randomly selected and the independent variable is not manipulated.

For example, an academic institution may want to reward its first-class students with a scholarship for their academic excellence. Therefore, each faculty places students in the eligible and ineligible group according to their class of degree.

In this case, the student’s class of degree cannot be manipulated to qualify him or her for a scholarship because it is an unethical thing to do. Therefore, the placement is cross-sectional.

Correlational Research

Correlational type of research compares the statistical relationship between two variables .Correlational research is classified as non-experimental because it does not manipulate the independent variables.

For example, a researcher may wish to investigate the relationship between the class of family students come from and their grades in school. A questionnaire may be given to students to know the average income of their family, then compare it with CGPAs.

The researcher will discover whether these two factors are positively correlated, negatively corrected, or have zero correlation at the end of the research.

Observational Research

Observational research focuses on observing the behavior of a research subject in a natural or laboratory setting. It is classified as non-experimental because it does not involve the manipulation of independent variables.

A good example of observational research is an investigation of the crowd effect or psychology in a particular group of people. Imagine a situation where there are 2 ATMs at a place, and only one of the ATMs is filled with a queue, while the other is abandoned.

The crowd effect infers that the majority of newcomers will also abandon the other ATM.

You will notice that each of these non-experimental research is descriptive in nature. It then suffices to say that descriptive research is an example of non-experimental research.

Pros of Observational Research

The research process is very close to a real-life situation.
It does not allow for the manipulation of variables due to ethical reasons.
Human characteristics are not subject to experimental manipulation.

Cons of Observational Research

The groups may be dissimilar and nonhomogeneous because they are not randomly selected, affecting the authenticity and generalizability of the study results.
The results obtained cannot be absolutely clear and error-free.

What Are The Differences Between Experimental and Non-Experimental Research?

Definitions

Experimental research is the type of research that uses a scientific approach towards manipulating one or more control variables and measuring their defect on the dependent variables, while non-experimental research is the type of research that does not involve the manipulation of control variables.

The main distinction in these 2 types of research is their attitude towards the manipulation of control variables. Experimental allows for the manipulation of control variables while non-experimental research doesn’t.

Examples of experimental research are laboratory experiments that involve mixing different chemical elements together to see the effect of one element on the other while non-experimental research examples are investigations into the characteristics of different chemical elements.

Consider a researcher carrying out a laboratory test to determine the effect of adding Nitrogen gas to Hydrogen gas. It may be discovered that using the Haber process, one can create Nitrogen gas.

Non-experimental research may further be carried out on Ammonia, to determine its characteristics, behaviour, and nature.

There are 3 types of experimental research, namely; experimental research, quasi-experimental research, and true experimental research. Although also 3 in number, non-experimental research can be classified into cross-sectional research, correlational research, and observational research.

The different types of experimental research are further divided into different parts, while non-experimental research types are not further divided. Clearly, these divisions are not the same in experimental and non-experimental research.

Characteristics

Experimental research is usually quantitative, controlled, and multivariable. Non-experimental research can be both quantitative and qualitative , has an uncontrolled variable, and also a cross-sectional research problem.

The characteristics of experimental research are the direct opposite of that of non-experimental research. The most distinct characteristic element is the ability to control or manipulate independent variables in experimental research and not in non-experimental research.

In experimental research, a level of control is usually exerted on extraneous variables, therefore tampering with the natural research setting. Experimental research settings are usually more natural with no tampering with the extraneous variables.

Data Collection/Tools

The data used during experimental research is collected through observational study, simulations, and surveys while non-experimental data is collected through observations, surveys, and case studies. The main distinction between these data collection tools is case studies and simulations.

Even at that, similar tools are used differently. For example, an observational study may be used during a laboratory experiment that tests how the effect of a control variable manifests over a period of time in experimental research.

However, when used in non-experimental research, data is collected based on the researcher’s discretion and not through a clear scientific reaction. In this case, we see a difference in the level of objectivity.

The goal of experimental research is to measure the causes and effects of variables present in research, while non-experimental research provides very little to no information about causal agents.

Experimental research answers the question of why something is happening. This is quite different in non-experimental research, as they are more descriptive in nature with the end goal being to describe what .

Experimental research is mostly used to make scientific innovations and find major solutions to problems while non-experimental research is used to define subject characteristics, measure data trends, compare situations and validate existing conditions.

For example, if experimental research results in an innovative discovery or solution, non-experimental research will be conducted to validate this discovery. This research is done for a period of time in order to properly study the subject of research.

Experimental research process is usually well structured and as such produces results with very little to no errors, while non-experimental research helps to create real-life related experiments. There are a lot more advantages of experimental and non-experimental research , with the absence of each of these advantages in the other leaving it at a disadvantage.

For example, the lack of a random selection process in non-experimental research leads to the inability to arrive at a generalizable result. Similarly, the ability to manipulate control variables in experimental research may lead to the personal bias of the researcher.

Disadvantage

Experimental research is highly prone to human error while the major disadvantage of non-experimental research is that the results obtained cannot be absolutely clear and error-free. In the long run, the error obtained due to human error may affect the results of the experimental research.

Some other disadvantages of experimental research include the following; extraneous variables cannot always be controlled, human responses can be difficult to measure, and participants may also cause bias.

In experimental research, researchers can control and manipulate control variables, while in non-experimental research, researchers cannot manipulate these variables. This cannot be done due to ethical reasons.

For example, when promoting employees due to how well they did in their annual performance review, it will be unethical to manipulate the results of the performance review (independent variable). That way, we can get impartial results of those who deserve a promotion and those who don’t.

Experimental researchers may also decide to eliminate extraneous variables so as to have enough control over the research process. Once again, this is something that cannot be done in non-experimental research because it relates more to real-life situations.

Experimental research is carried out in an unnatural setting because most of the factors that influence the setting are controlled while the non-experimental research setting remains natural and uncontrolled. One of the things usually tampered with during research is extraneous variables.

In a bid to get a perfect and well-structured research process and results, researchers sometimes eliminate extraneous variables. Although sometimes seen as insignificant, the elimination of these variables may affect the research results.

Consider the optimization problem whose aim is to minimize the cost of production of a car, with the constraints being the number of workers and the number of hours they spend working per day.

In this problem, extraneous variables like machine failure rates or accidents are eliminated. In the long run, these things may occur and may invalidate the result.

Cause-Effect Relationship

The relationship between cause and effect is established in experimental research while it cannot be established in non-experimental research. Rather than establish a cause-effect relationship, non-experimental research focuses on providing descriptive results.

Although it acknowledges the causal variable and its effect on the dependent variables, it does not measure how or the extent to which these dependent variables change. It, however, observes these changes, compares the changes in 2 variables, and describes them.

Experimental research does not compare variables while non-experimental research does. It compares 2 variables and describes the relationship between them.

The relationship between these variables can be positively correlated, negatively correlated or not correlated at all. For example, consider a case whereby the subject of research is a drum, and the control or independent variable is the drumstick.

Experimental research will measure the effect of hitting the drumstick on the drum, where the result of this research will be sound. That is, when you hit a drumstick on a drum, it makes a sound.

Non-experimental research, on the other hand, will investigate the correlation between how hard the drum is hit and the loudness of the sound that comes out. That is, if the sound will be higher with a harder bang, lower with a harder bang, or will remain the same no matter how hard we hit the drum.

Quantitativeness

Experimental research is a quantitative research method while non-experimental research can be both quantitative and qualitative depending on the time and the situation where it is been used. An example of a non-experimental quantitative research method is correlational research .

Researchers use it to correlate two or more variables using mathematical analysis methods. The original patterns, relationships, and trends between variables are observed, then the impact of one of these variables on the other is recorded along with how it changes the relationship between the two variables.

Observational research is an example of non-experimental research, which is classified as a qualitative research method.

Cross-section

Experimental research is usually single-sectional while non-experimental research is cross-sectional. That is, when evaluating the research subjects in experimental research, each group is evaluated as an entity.

For example, let us consider a medical research process investigating the prevalence of breast cancer in a certain community. In this community, we will find people of different ages, ethnicities, and social backgrounds.

If a significant amount of women from a particular age are found to be more prone to have the disease, the researcher can conduct further studies to understand the reason behind it. A further study into this will be experimental and the subject won’t be a cross-sectional group.

A lot of researchers consider the distinction between experimental and non-experimental research to be an extremely important one. This is partly due to the fact that experimental research can accommodate the manipulation of independent variables, which is something non-experimental research can not.

Therefore, as a researcher who is interested in using any one of experimental and non-experimental research, it is important to understand the distinction between these two. This helps in deciding which method is better for carrying out particular research.

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Chapter 7: Nonexperimental Research

Overview of Nonexperimental Research

Learning Objectives

Define nonexperimental research, distinguish it clearly from experimental research, and give several examples.
Explain when a researcher might choose to conduct nonexperimental research as opposed to experimental research.

What Is Nonexperimental Research?

Nonexperimental research is research that lacks the manipulation of an independent variable, random assignment of participants to conditions or orders of conditions, or both.

In a sense, it is unfair to define this large and diverse set of approaches collectively by what they are not . But doing so reflects the fact that most researchers in psychology consider the distinction between experimental and nonexperimental research to be an extremely important one. This distinction is because although experimental research can provide strong evidence that changes in an independent variable cause differences in a dependent variable, nonexperimental research generally cannot. As we will see, however, this inability does not mean that nonexperimental research is less important than experimental research or inferior to it in any general sense.

When to Use Nonexperimental Research

As we saw in Chapter 6 , experimental research is appropriate when the researcher has a specific research question or hypothesis about a causal relationship between two variables—and it is possible, feasible, and ethical to manipulate the independent variable and randomly assign participants to conditions or to orders of conditions. It stands to reason, therefore, that nonexperimental research is appropriate—even necessary—when these conditions are not met. There are many ways in which preferring nonexperimental research can be the case.

The research question or hypothesis can be about a single variable rather than a statistical relationship between two variables (e.g., How accurate are people’s first impressions?).
The research question can be about a noncausal statistical relationship between variables (e.g., Is there a correlation between verbal intelligence and mathematical intelligence?).
The research question can be about a causal relationship, but the independent variable cannot be manipulated or participants cannot be randomly assigned to conditions or orders of conditions (e.g., Does damage to a person’s hippocampus impair the formation of long-term memory traces?).
The research question can be broad and exploratory, or it can be about what it is like to have a particular experience (e.g., What is it like to be a working mother diagnosed with depression?).

Again, the choice between the experimental and nonexperimental approaches is generally dictated by the nature of the research question. If it is about a causal relationship and involves an independent variable that can be manipulated, the experimental approach is typically preferred. Otherwise, the nonexperimental approach is preferred. But the two approaches can also be used to address the same research question in complementary ways. For example, nonexperimental studies establishing that there is a relationship between watching violent television and aggressive behaviour have been complemented by experimental studies confirming that the relationship is a causal one (Bushman & Huesmann, 2001) [1] . Similarly, after his original study, Milgram conducted experiments to explore the factors that affect obedience. He manipulated several independent variables, such as the distance between the experimenter and the participant, the participant and the confederate, and the location of the study (Milgram, 1974) [2] .

Types of Nonexperimental Research

Nonexperimental research falls into three broad categories: single-variable research, correlational and quasi-experimental research, and qualitative research. First, research can be nonexperimental because it focuses on a single variable rather than a statistical relationship between two variables. Although there is no widely shared term for this kind of research, we will call it single-variable research . Milgram’s original obedience study was nonexperimental in this way. He was primarily interested in one variable—the extent to which participants obeyed the researcher when he told them to shock the confederate—and he observed all participants performing the same task under the same conditions. The study by Loftus and Pickrell described at the beginning of this chapter is also a good example of single-variable research. The variable was whether participants “remembered” having experienced mildly traumatic childhood events (e.g., getting lost in a shopping mall) that they had not actually experienced but that the research asked them about repeatedly. In this particular study, nearly a third of the participants “remembered” at least one event. (As with Milgram’s original study, this study inspired several later experiments on the factors that affect false memories.)

As these examples make clear, single-variable research can answer interesting and important questions. What it cannot do, however, is answer questions about statistical relationships between variables. This detail is a point that beginning researchers sometimes miss. Imagine, for example, a group of research methods students interested in the relationship between children’s being the victim of bullying and the children’s self-esteem. The first thing that is likely to occur to these researchers is to obtain a sample of middle-school students who have been bullied and then to measure their self-esteem. But this design would be a single-variable study with self-esteem as the only variable. Although it would tell the researchers something about the self-esteem of children who have been bullied, it would not tell them what they really want to know, which is how the self-esteem of children who have been bullied compares with the self-esteem of children who have not. Is it lower? Is it the same? Could it even be higher? To answer this question, their sample would also have to include middle-school students who have not been bullied thereby introducing another variable.

Research can also be nonexperimental because it focuses on a statistical relationship between two variables but does not include the manipulation of an independent variable, random assignment of participants to conditions or orders of conditions, or both. This kind of research takes two basic forms: correlational research and quasi-experimental research. In correlational research , the researcher measures the two variables of interest with little or no attempt to control extraneous variables and then assesses the relationship between them. A research methods student who finds out whether each of several middle-school students has been bullied and then measures each student’s self-esteem is conducting correlational research. In quasi-experimental research , the researcher manipulates an independent variable but does not randomly assign participants to conditions or orders of conditions. For example, a researcher might start an antibullying program (a kind of treatment) at one school and compare the incidence of bullying at that school with the incidence at a similar school that has no antibullying program.

The final way in which research can be nonexperimental is that it can be qualitative. The types of research we have discussed so far are all quantitative, referring to the fact that the data consist of numbers that are analyzed using statistical techniques. In qualitative research , the data are usually nonnumerical and therefore cannot be analyzed using statistical techniques. Rosenhan’s study of the experience of people in a psychiatric ward was primarily qualitative. The data were the notes taken by the “pseudopatients”—the people pretending to have heard voices—along with their hospital records. Rosenhan’s analysis consists mainly of a written description of the experiences of the pseudopatients, supported by several concrete examples. To illustrate the hospital staff’s tendency to “depersonalize” their patients, he noted, “Upon being admitted, I and other pseudopatients took the initial physical examinations in a semipublic room, where staff members went about their own business as if we were not there” (Rosenhan, 1973, p. 256). [3] Qualitative data has a separate set of analysis tools depending on the research question. For example, thematic analysis would focus on themes that emerge in the data or conversation analysis would focus on the way the words were said in an interview or focus group.

Internal Validity Revisited

Recall that internal validity is the extent to which the design of a study supports the conclusion that changes in the independent variable caused any observed differences in the dependent variable. Figure 7.1 shows how experimental, quasi-experimental, and correlational research vary in terms of internal validity. Experimental research tends to be highest because it addresses the directionality and third-variable problems through manipulation and the control of extraneous variables through random assignment. If the average score on the dependent variable in an experiment differs across conditions, it is quite likely that the independent variable is responsible for that difference. Correlational research is lowest because it fails to address either problem. If the average score on the dependent variable differs across levels of the independent variable, it could be that the independent variable is responsible, but there are other interpretations. In some situations, the direction of causality could be reversed. In others, there could be a third variable that is causing differences in both the independent and dependent variables. Quasi-experimental research is in the middle because the manipulation of the independent variable addresses some problems, but the lack of random assignment and experimental control fails to address others. Imagine, for example, that a researcher finds two similar schools, starts an antibullying program in one, and then finds fewer bullying incidents in that “treatment school” than in the “control school.” There is no directionality problem because clearly the number of bullying incidents did not determine which school got the program. However, the lack of random assignment of children to schools could still mean that students in the treatment school differed from students in the control school in some other way that could explain the difference in bullying.

Notice also in Figure 7.1 that there is some overlap in the internal validity of experiments, quasi-experiments, and correlational studies. For example, a poorly designed experiment that includes many confounding variables can be lower in internal validity than a well designed quasi-experiment with no obvious confounding variables. Internal validity is also only one of several validities that one might consider, as noted in Chapter 5.

Key Takeaways

Nonexperimental research is research that lacks the manipulation of an independent variable, control of extraneous variables through random assignment, or both.
There are three broad types of nonexperimental research. Single-variable research focuses on a single variable rather than a relationship between variables. Correlational and quasi-experimental research focus on a statistical relationship but lack manipulation or random assignment. Qualitative research focuses on broader research questions, typically involves collecting large amounts of data from a small number of participants, and analyses the data nonstatistically.
In general, experimental research is high in internal validity, correlational research is low in internal validity, and quasi-experimental research is in between.

Discussion: For each of the following studies, decide which type of research design it is and explain why.

A researcher conducts detailed interviews with unmarried teenage fathers to learn about how they feel and what they think about their role as fathers and summarizes their feelings in a written narrative.
A researcher measures the impulsivity of a large sample of drivers and looks at the statistical relationship between this variable and the number of traffic tickets the drivers have received.
A researcher randomly assigns patients with low back pain either to a treatment involving hypnosis or to a treatment involving exercise. She then measures their level of low back pain after 3 months.
A college instructor gives weekly quizzes to students in one section of his course but no weekly quizzes to students in another section to see whether this has an effect on their test performance.
Bushman, B. J., & Huesmann, L. R. (2001). Effects of televised violence on aggression. In D. Singer & J. Singer (Eds.), Handbook of children and the media (pp. 223–254). Thousand Oaks, CA: Sage. ↵
Milgram, S. (1974). Obedience to authority: An experimental view . New York, NY: Harper & Row. ↵
Rosenhan, D. L. (1973). On being sane in insane places. Science, 179 , 250–258. ↵

Research that lacks the manipulation of an independent variable, random assignment of participants to conditions or orders of conditions, or both.

Research that focuses on a single variable rather than a statistical relationship between two variables.

The researcher measures the two variables of interest with little or no attempt to control extraneous variables and then assesses the relationship between them.

The researcher manipulates an independent variable but does not randomly assign participants to conditions or orders of conditions.

Research Methods in Psychology - 2nd Canadian Edition Copyright © 2015 by Paul C. Price, Rajiv Jhangiani, & I-Chant A. Chiang is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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7.1 Overview of Nonexperimental Research

Learning objectives.

Define nonexperimental research, distinguish it clearly from experimental research, and give several examples.
Explain when a researcher might choose to conduct nonexperimental research as opposed to experimental research.

What Is Nonexperimental Research?

Nonexperimental research is research that lacks the manipulation of an independent variable, random assignment of participants to conditions or orders of conditions, or both.

In a sense, it is unfair to define this large and diverse set of approaches collectively by what they are not . But doing so reflects the fact that most researchers in psychology consider the distinction between experimental and nonexperimental research to be an extremely important one. This is because while experimental research can provide strong evidence that changes in an independent variable cause differences in a dependent variable, nonexperimental research generally cannot. As we will see, however, this does not mean that nonexperimental research is less important than experimental research or inferior to it in any general sense.

When to Use Nonexperimental Research

As we saw in Chapter 6 “Experimental Research” , experimental research is appropriate when the researcher has a specific research question or hypothesis about a causal relationship between two variables—and it is possible, feasible, and ethical to manipulate the independent variable and randomly assign participants to conditions or to orders of conditions. It stands to reason, therefore, that nonexperimental research is appropriate—even necessary—when these conditions are not met. There are many ways in which this can be the case.

The research question or hypothesis can be about a single variable rather than a statistical relationship between two variables (e.g., How accurate are people’s first impressions?).
The research question can be about a noncausal statistical relationship between variables (e.g., Is there a correlation between verbal intelligence and mathematical intelligence?).
The research question can be about a causal relationship, but the independent variable cannot be manipulated or participants cannot be randomly assigned to conditions or orders of conditions (e.g., Does damage to a person’s hippocampus impair the formation of long-term memory traces?).
The research question can be broad and exploratory, or it can be about what it is like to have a particular experience (e.g., What is it like to be a working mother diagnosed with depression?).

Again, the choice between the experimental and nonexperimental approaches is generally dictated by the nature of the research question. If it is about a causal relationship and involves an independent variable that can be manipulated, the experimental approach is typically preferred. Otherwise, the nonexperimental approach is preferred. But the two approaches can also be used to address the same research question in complementary ways. For example, nonexperimental studies establishing that there is a relationship between watching violent television and aggressive behavior have been complemented by experimental studies confirming that the relationship is a causal one (Bushman & Huesmann, 2001). Similarly, after his original study, Milgram conducted experiments to explore the factors that affect obedience. He manipulated several independent variables, such as the distance between the experimenter and the participant, the participant and the confederate, and the location of the study (Milgram, 1974).

Types of Nonexperimental Research

As these examples make clear, single-variable research can answer interesting and important questions. What it cannot do, however, is answer questions about statistical relationships between variables. This is a point that beginning researchers sometimes miss. Imagine, for example, a group of research methods students interested in the relationship between children’s being the victim of bullying and the children’s self-esteem. The first thing that is likely to occur to these researchers is to obtain a sample of middle-school students who have been bullied and then to measure their self-esteem. But this would be a single-variable study with self-esteem as the only variable. Although it would tell the researchers something about the self-esteem of children who have been bullied, it would not tell them what they really want to know, which is how the self-esteem of children who have been bullied compares with the self-esteem of children who have not. Is it lower? Is it the same? Could it even be higher? To answer this question, their sample would also have to include middle-school students who have not been bullied.

The final way in which research can be nonexperimental is that it can be qualitative. The types of research we have discussed so far are all quantitative, referring to the fact that the data consist of numbers that are analyzed using statistical techniques. In qualitative research , the data are usually nonnumerical and are analyzed using nonstatistical techniques. Rosenhan’s study of the experience of people in a psychiatric ward was primarily qualitative. The data were the notes taken by the “pseudopatients”—the people pretending to have heard voices—along with their hospital records. Rosenhan’s analysis consists mainly of a written description of the experiences of the pseudopatients, supported by several concrete examples. To illustrate the hospital staff’s tendency to “depersonalize” their patients, he noted, “Upon being admitted, I and other pseudopatients took the initial physical examinations in a semipublic room, where staff members went about their own business as if we were not there” (Rosenhan, 1973, p. 256).

Internal Validity Revisited

Recall that internal validity is the extent to which the design of a study supports the conclusion that changes in the independent variable caused any observed differences in the dependent variable. Figure 7.1 shows how experimental, quasi-experimental, and correlational research vary in terms of internal validity. Experimental research tends to be highest because it addresses the directionality and third-variable problems through manipulation and the control of extraneous variables through random assignment. If the average score on the dependent variable in an experiment differs across conditions, it is quite likely that the independent variable is responsible for that difference. Correlational research is lowest because it fails to address either problem. If the average score on the dependent variable differs across levels of the independent variable, it could be that the independent variable is responsible, but there are other interpretations. In some situations, the direction of causality could be reversed. In others, there could be a third variable that is causing differences in both the independent and dependent variables. Quasi-experimental research is in the middle because the manipulation of the independent variable addresses some problems, but the lack of random assignment and experimental control fails to address others. Imagine, for example, that a researcher finds two similar schools, starts an antibullying program in one, and then finds fewer bullying incidents in that “treatment school” than in the “control school.” There is no directionality problem because clearly the number of bullying incidents did not determine which school got the program. However, the lack of random assignment of children to schools could still mean that students in the treatment school differed from students in the control school in some other way that could explain the difference in bullying.

Experiments are generally high in internal validity, quasi-experiments lower, and correlational studies lower still.

Key Takeaways

Nonexperimental research is research that lacks the manipulation of an independent variable, control of extraneous variables through random assignment, or both.
There are three broad types of nonexperimental research. Single-variable research focuses on a single variable rather than a relationship between variables. Correlational and quasi-experimental research focus on a statistical relationship but lack manipulation or random assignment. Qualitative research focuses on broader research questions, typically involves collecting large amounts of data from a small number of participants, and analyzes the data nonstatistically.
In general, experimental research is high in internal validity, correlational research is low in internal validity, and quasi-experimental research is in between.

Discussion: For each of the following studies, decide which type of research design it is and explain why.

A researcher conducts detailed interviews with unmarried teenage fathers to learn about how they feel and what they think about their role as fathers and summarizes their feelings in a written narrative.
A researcher measures the impulsivity of a large sample of drivers and looks at the statistical relationship between this variable and the number of traffic tickets the drivers have received.
A researcher randomly assigns patients with low back pain either to a treatment involving hypnosis or to a treatment involving exercise. She then measures their level of low back pain after 3 months.
A college instructor gives weekly quizzes to students in one section of his course but no weekly quizzes to students in another section to see whether this has an effect on their test performance.

Bushman, B. J., & Huesmann, L. R. (2001). Effects of televised violence on aggression. In D. Singer & J. Singer (Eds.), Handbook of children and the media (pp. 223–254). Thousand Oaks, CA: Sage.

Milgram, S. (1974). Obedience to authority: An experimental view . New York, NY: Harper & Row.

Rosenhan, D. L. (1973). On being sane in insane places. Science, 179 , 250–258.

Research Methods in Psychology Copyright © 2016 by University of Minnesota is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

Overview of Non-Experimental Research

Rajiv S. Jhangiani; I-Chant A. Chiang; Carrie Cuttler; and Dana C. Leighton

Learning Objectives

Define non-experimental research, distinguish it clearly from experimental research, and give several examples.
Explain when a researcher might choose to conduct non-experimental research as opposed to experimental research.

What Is Non-Experimental Research?

When to Use Non-Experimental Research

the research question or hypothesis relates to a single variable rather than a statistical relationship between two variables (e.g., how accurate are people’s first impressions?).
the research question pertains to a non-causal statistical relationship between variables (e.g., is there a correlation between verbal intelligence and mathematical intelligence?).
the research question is about a causal relationship, but the independent variable cannot be manipulated or participants cannot be randomly assigned to conditions or orders of conditions for practical or ethical reasons (e.g., does damage to a person’s hippocampus impair the formation of long-term memory traces?).
the research question is broad and exploratory, or is about what it is like to have a particular experience (e.g., what is it like to be a working mother diagnosed with depression?).

Again, the choice between the experimental and non-experimental approaches is generally dictated by the nature of the research question. Recall the three goals of science are to describe, to predict, and to explain. If the goal is to explain and the research question pertains to causal relationships, then the experimental approach is typically preferred. If the goal is to describe or to predict, a non-experimental approach is appropriate. But the two approaches can also be used to address the same research question in complementary ways. For example, in Milgram’s original (non-experimental) obedience study, he was primarily interested in one variable—the extent to which participants obeyed the researcher when he told them to shock the confederate—and he observed all participants performing the same task under the same conditions. However, Milgram subsequently conducted experiments to explore the factors that affect obedience. He manipulated several independent variables, such as the distance between the experimenter and the participant, the participant and the confederate, and the location of the study (Milgram, 1974) [1] .

Types of Non-Experimental Research

Non-experimental research falls into two broad categories: correlational research and observational research.

The most common type of non-experimental research conducted in psychology is correlational research. Correlational research is considered non-experimental because it focuses on the statistical relationship between two variables but does not include the manipulation of an independent variable. More specifically, in correlational research , the researcher measures two variables with little or no attempt to control extraneous variables and then assesses the relationship between them. As an example, a researcher interested in the relationship between self-esteem and school achievement could collect data on students’ self-esteem and their GPAs to see if the two variables are statistically related.

Observational research is non-experimental because it focuses on making observations of behavior in a natural or laboratory setting without manipulating anything. Milgram’s original obedience study was non-experimental in this way. He was primarily interested in the extent to which participants obeyed the researcher when he told them to shock the confederate and he observed all participants performing the same task under the same conditions. The study by Loftus and Pickrell described at the beginning of this chapter is also a good example of observational research. The variable was whether participants “remembered” having experienced mildly traumatic childhood events (e.g., getting lost in a shopping mall) that they had not actually experienced but that the researchers asked them about repeatedly. In this particular study, nearly a third of the participants “remembered” at least one event. (As with Milgram’s original study, this study inspired several later experiments on the factors that affect false memories).

Cross-Sectional, Longitudinal, and Cross-Sequential Studies

When psychologists wish to study change over time (for example, when developmental psychologists wish to study aging) they usually take one of three non-experimental approaches: cross-sectional, longitudinal, or cross-sequential. Cross-sectional studies involve comparing two or more pre-existing groups of people (e.g., children at different stages of development). What makes this approach non-experimental is that there is no manipulation of an independent variable and no random assignment of participants to groups. Using this design, developmental psychologists compare groups of people of different ages (e.g., young adults spanning from 18-25 years of age versus older adults spanning 60-75 years of age) on various dependent variables (e.g., memory, depression, life satisfaction). Of course, the primary limitation of using this design to study the effects of aging is that differences between the groups other than age may account for differences in the dependent variable. For instance, differences between the groups may reflect the generation that people come from (a cohort effect ) rather than a direct effect of age. For this reason, longitudinal studies , in which one group of people is followed over time as they age, offer a superior means of studying the effects of aging. However, longitudinal studies are by definition more time consuming and so require a much greater investment on the part of the researcher and the participants. A third approach, known as cross-sequential studies , combines elements of both cross-sectional and longitudinal studies. Rather than measuring differences between people in different age groups or following the same people over a long period of time, researchers adopting this approach choose a smaller period of time during which they follow people in different age groups. For example, they might measure changes over a ten year period among participants who at the start of the study fall into the following age groups: 20 years old, 30 years old, 40 years old, 50 years old, and 60 years old. This design is advantageous because the researcher reaps the immediate benefits of being able to compare the age groups after the first assessment. Further, by following the different age groups over time they can subsequently determine whether the original differences they found across the age groups are due to true age effects or cohort effects.

The types of research we have discussed so far are all quantitative, referring to the fact that the data consist of numbers that are analyzed using statistical techniques. But as you will learn in this chapter, many observational research studies are more qualitative in nature. In qualitative research , the data are usually nonnumerical and therefore cannot be analyzed using statistical techniques. Rosenhan’s observational study of the experience of people in psychiatric wards was primarily qualitative. The data were the notes taken by the “pseudopatients”—the people pretending to have heard voices—along with their hospital records. Rosenhan’s analysis consists mainly of a written description of the experiences of the pseudopatients, supported by several concrete examples. To illustrate the hospital staff’s tendency to “depersonalize” their patients, he noted, “Upon being admitted, I and other pseudopatients took the initial physical examinations in a semi-public room, where staff members went about their own business as if we were not there” (Rosenhan, 1973, p. 256) [2] . Qualitative data has a separate set of analysis tools depending on the research question. For example, thematic analysis would focus on themes that emerge in the data or conversation analysis would focus on the way the words were said in an interview or focus group.

Internal Validity Revisited

Recall that internal validity is the extent to which the design of a study supports the conclusion that changes in the independent variable caused any observed differences in the dependent variable. Figure 6.1 shows how experimental, quasi-experimental, and non-experimental (correlational) research vary in terms of internal validity. Experimental research tends to be highest in internal validity because the use of manipulation (of the independent variable) and control (of extraneous variables) help to rule out alternative explanations for the observed relationships. If the average score on the dependent variable in an experiment differs across conditions, it is quite likely that the independent variable is responsible for that difference. Non-experimental (correlational) research is lowest in internal validity because these designs fail to use manipulation or control. Quasi-experimental research (which will be described in more detail in a subsequent chapter) falls in the middle because it contains some, but not all, of the features of a true experiment. For instance, it may fail to use random assignment to assign participants to groups or fail to use counterbalancing to control for potential order effects. Imagine, for example, that a researcher finds two similar schools, starts an anti-bullying program in one, and then finds fewer bullying incidents in that “treatment school” than in the “control school.” While a comparison is being made with a control condition, the inability to randomly assign children to schools could still mean that students in the treatment school differed from students in the control school in some other way that could explain the difference in bullying (e.g., there may be a selection effect).

Figure 6.1 Internal Validity of Correlational, Quasi-Experimental, and Experimental Studies. Experiments are generally high in internal validity, quasi-experiments lower, and correlational studies lower still.

Notice also in Figure 6.1 that there is some overlap in the internal validity of experiments, quasi-experiments, and correlational (non-experimental) studies. For example, a poorly designed experiment that includes many confounding variables can be lower in internal validity than a well-designed quasi-experiment with no obvious confounding variables. Internal validity is also only one of several validities that one might consider, as noted in Chapter 5.

Milgram, S. (1974). Obedience to authority: An experimental view . New York, NY: Harper & Row. ↵
Rosenhan, D. L. (1973). On being sane in insane places. Science, 179 , 250–258. ↵

A research that lacks the manipulation of an independent variable.

Research that is non-experimental because it focuses on the statistical relationship between two variables but does not include the manipulation of an independent variable.

Research that is non-experimental because it focuses on recording systemic observations of behavior in a natural or laboratory setting without manipulating anything.

Studies that involve comparing two or more pre-existing groups of people (e.g., children at different stages of development).

Differences between the groups may reflect the generation that people come from rather than a direct effect of age.

Studies in which one group of people are followed over time as they age.

Studies in which researchers follow people in different age groups in a smaller period of time.

Overview of Non-Experimental Research Copyright © by Rajiv S. Jhangiani; I-Chant A. Chiang; Carrie Cuttler; and Dana C. Leighton is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Chapter 6: Data Collection Strategies

6.2 Nonexperimental Research

Nonexperimental research is research that lacks manipulation of an independent variable and/or random assignment of participants to conditions. While the distinction between experimental and nonexperimental research is considered important, it does not mean that nonexperimental research is less important or inferior to experimental research (Price, Jhangiani & Chiang, 2015).

When to Use Nonexperimental Research

Often it is not possible, feasible, and/or ethical to manipulate the independent variable, nor to randomly assign participants to conditions or to orders of conditions. In such cases, nonexperimental research is more appropriate and often necessary. Price, et al. (2015) provide the following examples that demonstrate when the research question is better answered with non-experimental methods:

The research question or hypothesis contains a single variable rather than a statistical relationship between two variables (e.g., How accurate are people’s first impressions?).
The research question involves a non-causal statistical relationship between variables (e.g., is there a correlation between verbal intelligence and mathematical intelligence?).
The research question involves a causal relationship, but the independent variable cannot be manipulated, or participants cannot be randomly assigned to conditions or orders of conditions (e.g., Does damage to a person’s hippocampus impair the formation of long-term memory traces?).
The research question is broad and exploratory, or explores a particular experience (e.g., what is it like to be a working mother diagnosed with depression?).

As demonstrated above, it is the nature of the research question that guides the choice between experimental and non-experimental approaches. However, this is not to suggest that a research project cannot contain elements of both an experiment and a non-experiment. For example, nonexperimental studies that establish a relationship between two variables can be explored further in an experimental study to confirm or refute the causal nature of the relationship (Price, Jhangiani & Chiang, 2015).

Types of Nonexperimental Research

In social sciences it is often the case that a true experimental approach is inappropriate and unethical. For example, conducting a true experiment may require the researcher to deny needed treatment to a patient, which is clearly an ethical issue. Furthermore, it might not be equitable or ethical to provide a large financial or other reward to members of an experimental group, as can occur in a true experiment.

There are three types of non-experimental research: cross-sectional, correlational, and observational. In the following sections we explore each of three types of nonexperimental research.

Research Methods for the Social Sciences: An Introduction Copyright © 2020 by Valerie Sheppard is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Non-Experimental Research

What do the following classic studies have in common?

Stanley Milgram found that about two thirds of his research participants were willing to administer dangerous shocks to another person just because they were told to by an authority figure (Milgram, 1963) [1] .
Elizabeth Loftus and Jacqueline Pickrell showed that it is relatively easy to “implant” false memories in people by repeatedly asking them about childhood events that did not actually happen to them (Loftus & Pickrell, 1995) [2] .
John Cacioppo and Richard Petty evaluated the validity of their Need for Cognition Scale—a measure of the extent to which people like and value thinking—by comparing the scores of university professors with those of factory workers (Cacioppo & Petty, 1982) [3] .
David Rosenhan found that confederates who went to psychiatric hospitals claiming to have heard voices saying things like “empty” and “thud” were labeled as schizophrenic by the hospital staff and kept there even though they behaved normally in all other ways (Rosenhan, 1973) [4] .

The answer for purposes of this chapter is that they are not experiments. In this chapter, we look more closely at non-experimental research. We begin with a general definition of non-experimental research, along with a discussion of when and why non-experimental research is more appropriate than experimental research. We then look separately at two important types of non-experimental research: correlational research and observational research.

Milgram, S. (1963). Behavioral study of obedience. Journal of Abnormal and Social Psychology, 67 , 371–378. ↵
Loftus, E. F., & Pickrell, J. E. (1995). The formation of false memories. Psychiatric Annals, 25 , 720–725. ↵
Cacioppo, J. T., & Petty, R. E. (1982). The need for cognition. Journal of Personality and Social Psychology, 42 , 116–131. ↵
Rosenhan, D. L. (1973). On being sane in insane places. Science, 179 , 250–258. ↵

Research Methods in Psychology Copyright © 2019 by Rajiv S. Jhangiani, I-Chant A. Chiang, Carrie Cuttler, & Dana C. Leighton is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Non-Experimental Research: Overview & Advantages

In traditional experimental research, variables are carefully controlled by researchers in a lab setting. In non-experimental study, there are no variables the observer can directly control.

Non-Experimental Research

Non-experimental research gets its name from the fact that there is no independent variable involved in testing. Researchers instead look to take past events and re-examine them; analyzing them for new information and coming to new or supporting conclusions.

In traditional experimental research, variables are carefully controlled by researchers in a lab setting. In non-experimental study, there are no variables the observer can directly control. Instead, researchers are tasked with parsing through established context to come up with their own interpretation of the events. While non-experimental research is limited in use, there are a few key areas where a researcher may find using this kind of methodology is beneficial.

Characteristics of Non-Experimental Research

These key characteristics of non-experimental research set it apart from other common methods:

The vast majority of these studies are conducted using prior events and past experiences.
This method is not concerned with establishing links between variables.
The research collected does not directly influence the events that are being studied.
This type of testing does not influence or impact the phenomena being studied.

Types of Non-Experimental Research

There are three primary forms of non-experimental research. They are:

Single-Variable Research

Single-variable research involves locating one variable and attempting to discern new meaning from these events. Instead of trying to discern a relationship between two variables, this type of study aims to ganer a deeper understanding of a particular issue - often so that further testing can be completed.

One example of a single-variable research project could involve looking at how high the average person can jump. In this case, researchers would invite participants to make 3 attempts to jump up into the air as high as they could from a standing position; researchers would then average out the 3 attempts into one number. In this case, researchers are not looking to connect the variable jump height with any other piece of information. All the study is concerned about is measuring the average of an individual’s jumps.

Correlational and Quasi-Experimental

Correlational research involves measuring two or more variables of interest while maintaining little or no control over the variables themselves. In the quasi-experimental method, researchers change an independent variable - but will not recruit or control the participants involved in the experiment. An example would be a researcher who starts a campaign urging people to stop smoking in one city - and then comparing those results to cities without a no-smoking program.

Qualitative Research

The qualitative research method seeks to answer complex questions, and involves written documentation of experiences and events. Unlike the quantitative research method, which is concerned with facts and hard data, the qualitative method can be used to gather insights for a breadth of vital topics.

Advantages of Non-Experimental Research

Non-experimental designs can open a number of advantageous research opportunities. The benefits include:

Non-experimental research can be used to analyze events that have happened in the past.
The versatility of the model can be used to observe many unique phenomena.
This method of research is far more affordable than the experimental kind.

Disadvantages of Non-Experimental Research

The limitations of non-experimental research are:

These limited samples do not represent the larger population.
The research can only be used to observe a single variable.
Researcher bias or error in the methodology can lead to inaccurate results.

These disadvantages can be mitigated by applying the non-experimental method to the correct situations.

Disadvantages of Non-Experimental Research

How it is different from experimental research

Experimental research often involves taking two or more variables (independent and dependent) and attempting to develop a causal relationship between them. Experimental designs will be tightly controlled by researchers, and the tests themselves will often be far more intricate and expansive than non-experimental ones.

When to use Non-Experimental Research

Non-experimental research is best suited for situations where you want to observe events that have already happened; or you are only interested in gathering information about one isolated variable.

Experimental designs are far more common in the fields of science: medicine, biology, psychology, and so forth. Non-experimental design often sees use in business, politics, history, and general academia.

Determining when you should use either experimental or non-experimental methods boil down to the purpose of your research.

If the situation calls for direct intervention, then experimental methods offer researchers more tools for changing and measuring independent variables.

The best place to use non-experimental research design is when the question at hand can be answered without altering the independent variable.

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Quantitative Research Designs: Non-Experimental vs. Experimental

While there are many types of quantitative research designs, they generally fall under one of three umbrellas: experimental research, quasi-experimental research, and non-experimental research.

Experimental research designs are what many people think of when they think of research; they typically involve the manipulation of variables and random assignment of participants to conditions. A traditional experiment may involve the comparison of a control group to an experimental group who receives a treatment (i.e., a variable is manipulated). When done correctly, experimental designs can provide evidence for cause and effect. Because of their ability to determine causation, experimental designs are the gold-standard for research in medicine, biology, and so on. However, such designs can also be used in the “soft sciences,” like social science. Experimental research has strict standards for control within the research design and for establishing validity. These designs may also be very resource and labor intensive. Additionally, it can be hard to justify the generalizability of the results in a very tightly controlled or artificial experimental setting. However, if done well, experimental research methods can lead to some very convincing and interesting results.

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Non-experimental research, on the other hand, can be just as interesting, but you cannot draw the same conclusions from it as you can with experimental research. Non-experimental research is usually descriptive or correlational, which means that you are either describing a situation or phenomenon simply as it stands, or you are describing a relationship between two or more variables, all without any interference from the researcher. This means that you do not manipulate any variables (e.g., change the conditions that an experimental group undergoes) or randomly assign participants to a control or treatment group. Without this level of control, you cannot determine any causal effects. While validity is still a concern in non-experimental research, the concerns are more about the validity of the measurements, rather than the validity of the effects.

Finally, a quasi-experimental design is a combination of the two designs described above. For quasi-experimental designs you still can manipulate a variable in the experimental group, but there is no random assignment into groups. Quasi-experimental designs are the most common when the researcher uses a convenience sample to recruit participants. For example, let’s say you were interested in studying the effect of stress on student test scores at the school that you work for. You teach two separate classes so you decide to just use each class as a different group. Class A becomes the experimental group who experiences the stressor manipulation and class B becomes the control group. Because you are sampling from two different pre-existing groups, without any random assignment, this would be known as a quasi-experimental design. These types of designs are very useful for when you want to find a causal relationship between variables but cannot randomly assign people to groups for practical or ethical reasons, such as working with a population of clinically depressed people or looking for gender differences (we can’t randomly assign people to be clinically depressed or to be a different gender). While these types of studies sometimes have higher external validity than a true experimental design, since they involve real world interventions and group rather than a laboratory setting, because of the lack of random assignment in these groups, the generalizability of the study is severely limited.

So, how do you choose between these designs? This will depend on your topic, your available resources, and desired goal. For example, do you want to see if a particular intervention relieves feelings of anxiety? The most convincing results for that would come from a true experimental design with random sampling and random assignment to groups. Ultimately, this is a decision that should be made in close collaboration with your advisor. Therefore, I recommend discussing the pros and cons of each type of research, what it might mean for your personal dissertation process, and what is required of each design before making a decision.

Take the Course: Experimental and Quasi-Experimental Research Design

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Please note you do not have access to teaching notes, nonexperimental research: strengths, weaknesses and issues of precision.

European Journal of Training and Development

ISSN : 2046-9012

Article publication date: 6 September 2016

Nonexperimental research, defined as any kind of quantitative or qualitative research that is not an experiment, is the predominate kind of research design used in the social sciences. How to unambiguously and correctly present the results of nonexperimental research, however, remains decidedly unclear and possibly detrimental to applied disciplines such as human resource development. To clarify issues about the accurate reporting and generalization of nonexperimental research results, this paper aims to present information about the relative strength of research designs, followed by the strengths and weaknesses of nonexperimental research. Further, some possible ways to more precisely report nonexperimental findings without using causal language are explored. Next, the researcher takes the position that the results of nonexperimental research can be used cautiously, yet appropriately, for making practice recommendations. Finally, some closing thoughts about nonexperimental research and the appropriate use of causal language are presented.

Design/methodology/approach

A review of the extant social science literature was consulted to inform this paper.

Nonexperimental research, when reported accurately, makes a tremendous contribution because it can be used for conducting research when experimentation is not feasible or desired. It can be used also to make tentative recommendations for practice.

Originality/value

This article presents useful means to more accurately report nonexperimental findings through avoiding causal language. Ways to link nonexperimental results to making practice recommendations are explored.

Research design
Experimental design
Causal inference
Nonexperimental
Social science research
Triangulation

Reio, T.G. (2016), "Nonexperimental research: strengths, weaknesses and issues of precision", European Journal of Training and Development , Vol. 40 No. 8/9, pp. 676-690. https://doi.org/10.1108/EJTD-07-2015-0058

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Published: 15 September 2024

Unified framework for open quantum dynamics with memory

Felix Ivander 1 ,
Lachlan P. Lindoy 2 &
Joonho Lee ORCID: orcid.org/0000-0002-9667-1081 3 , 4

Nature Communications volume 15 , Article number: 8087 ( 2024 ) Cite this article

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Quantum mechanics
Theoretical physics

The dynamics of quantum systems coupled to baths are typically studied using the Nakajima-Zwanzig memory kernel ( \({{{\bf{{{{\mathcal{K}}}}}}}}\) ) or the influence functions ( I ), particularly when memory effects are present. Despite their significance, formal connections between the two have not been explicitly known. We establish their connections by examining the system propagator for a N -level system linearly coupled to Gaussian baths with various types of system-bath coupling. For a certain class of problems, we devised a non-perturbative, diagrammatic approach to construct \({{{\bf{{{{\mathcal{K}}}}}}}}\) from I for (driven) systems interacting with Gaussian baths, bypassing conventional projection-free dynamics inputs. Our work provides a way to interpret approximate path integral methods in terms of approximate memory kernels. Moreover, it offers a Hamiltonian learning procedure to extract the bath spectral density from reduced system trajectories, opening new avenues in quantum sensing and engineering. The insights we provide advance our understanding of non-Markovian dynamics and will serve as a stepping stone for future theoretical and experimental developments in this area.

Accurate Lindblad-form master equation for weakly damped quantum systems across all regimes

Stochastic Schrödinger equation derivation of non-Markovian two-time correlation functions

Witness of non-Markovian dynamics based on Bhattacharyya quantum distance

Introduction.

Most existing quantum systems inevitably interact with the surrounding environment, often making a straightforward application of Schrödinger’s equation impractical 1 . The main challenge in modeling these “open” quantum systems is the large Hilbert space dimension because the environment is much larger than the system of interest. Addressing this challenge is important in many disciplines, including solid state and condensed matter physics 2 , 3 , 4 , chemical physics and quantum biology 5 , 6 , 7 , 8 , quantum optics 9 , 10 , 11 , 12 , and quantum information science 13 , 14 , 15 . In this work, we provide a unified framework for studying non-Markovian open quantum systems, which will help to facilitate a better understanding of open quantum dynamics and the development of numerical methods.

Various numerically exact methods have been developed to describe non-Markovian open quantum dynamics. Two of the most commonly used approaches are (1) the Feynman–Vernon influence functional path integral (INFPI) 16 based techniques, including the quasiadiabatic path-integral method of Makri and Makarov and its variants 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , hierarchical equations of motion (HEOM) methods 7 , 27 , 28 , and time-evolving matrix product operator and related process tensor-based approaches 29 , 30 , 31 , 32 , 33 , 34 and (2) the Nakajima–Zwanzig generalized quantum master equation (GQME) techniques 1 , 35 , 36 , 37 . The INFPI formulation employs the influence functional ( \({{\mathcal{I}}}\) ) that encodes the time-nonlocal influence of the baths on the system. In the GQME formalism, the analogous object to \({{{\mathcal{I}}}}\) is the memory kernel ( \({{{\bf{{{{\mathcal{K}}}}}}}}\) ), which describes the entire complexity of the bath influence on the reduced system dynamics. It is natural to intuit that \({{{\mathcal{I}}}}\) and \({{{\bf{{{{\mathcal{K}}}}}}}}\) are closely connected and are presumably identical in their information content. Despite this, to the best of our knowledge, analytic and explicit relationships between the two have yet to be shown.

There have been several works that loosely connect these two frameworks. For instance, there is a body of work on numerically computing \({{{\bf{{{{\mathcal{K}}}}}}}}\) with projection-free inputs using short-time system trajectories based on INFPI or other exact quantum dynamics methods 38 , 39 , 40 , 41 , 42 . The obtained \({{{\bf{{{{\mathcal{K}}}}}}}}\) is then used to propagate system dynamics for longer times. Another line of work worth noting is the real-time path integral Monte Carlo algorithms for evaluating memory kernels exactly 43 . These works took advantage of the real-time path integral approaches used to evaluate \({{{\mathcal{I}}}}\) 44 to evaluate necessary matrix elements in computing the exact memory kernel. Nonetheless, they did not present any direct analytical relationship between the memory kernel and \({{{\mathcal{I}}}}\) .

In this work, we present a unifying description of these non-Markovian quantum dynamics frameworks. In particular, we establish explicit analytic correspondence between \({{{\mathcal{I}}}}\) and \({{{\bf{{{{\mathcal{K}}}}}}}}\) . We present a visual schematic describing the main idea of our work in Fig. 1 a. Readers interested in the relationship between our work and existing numerical tools are referred to Supplementary Note 3 C.

a An open quantum system, where the environment is characterized by the spectral density J ( ω ), can be described with the generalized quantum master equation (GQME) and the influence functional path integral (INFPI). The former distills environmental correlations through the memory kernels \({{{\mathcal{K}}}}\) while the latter through the influence functionals \({{{\mathcal{I}}}}\) . In this work, we show both are related through Dyck Paths, and that, furthermore, we can use the Dyck construction for extracting J ( ω ) by simply knowing how the quantum system evolves. b Cumulant expansion of memory kernel. Examples through Eq. ( 6 ) for N = 2 and N = 3. Solid arcs of diameter k filled with all possible arcs of diameters smaller than k denote propagator U k . c Dyck path diagrams. Examples for N = 2 and N = 3 and their corresponding influence function diagrams, which composes \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{2}\) and \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{3}\) , respectively. Solid lines denote influence functions I and dashed lines denote \(\tilde{{{{\bf{I}}}}}\) .

General setup

We consider a broad range of system-bath Hamiltonians in which the bath is Gaussian, and the system-bath Hamiltonian is bilinear. The total Hamiltonian is \(\hat{H}={\hat{H}}_{S}+{\sum }_{j}({\hat{H}}_{B,j}+{\sum }_{\alpha }{\hat{H}}_{I,j,\alpha })\) , with subscripts j and α specifying the j th bath and the α th interaction, respectively. While we do not limit the form of \({\hat{H}}_{S}\) in our discussion, we consider a quadratic (i.e., Gaussian) Hamiltonian for the baths, \({\hat{H}}_{B,j}={\sum }_{k}{\omega }_{k,j}{\hat{a}}_{k,j}^{{{\dagger}} }{\hat{a}}_{k,j}\) , where \({\hat{a}}_{k,j}\) can be fermionic or bosonic (it is also possible to treat baths consisting of noninteracting spins in a certain limit, see Supplementary Notes 3 ), and the bilinear interaction Hamiltonian, \({\hat{H}}_{I,j,\alpha }={\hat{S}}_{j,\alpha }\otimes {\hat{B}}_{j,\alpha }\) with \({\hat{S}}_{j,\alpha }\) and \({\hat{B}}_{j,\alpha }\) being the system and bath operators, respectively. We also assume that the initial density matrix is separable between the system and each bath. There are four classes of problems that one may commonly encounter under the setup described:

Class 1: With only single α for all baths j (such cases are henceforth indicated by dropping the subscript α ), \(\{{\hat{S}}_{j}\}\) are all diagonalizable, and furthermore, that \(\{{\hat{S}}_{j}\}\) are all simultaneously diagonalizable. That is, all terms in \(\{{\hat{H}}_{I,j}\}\) commute. The spin-boson model, other models in the same universality class, and Frenkel exciton models for photosynthetic systems belong to this class.

Class 2: No terms in \(\{{\hat{S}}_{j}\}\) commute but each term in \(\{{\hat{S}}_{j}\}\) is diagonalizable. Generalizing the models in Class 1 to multiple nonadditive baths typically leads to this case. Such systems may arise when considering non-adiabatic dynamics of systems involving strong coupling of electronic degrees of freedom coupled to quantized photonic modes 32 .

Class 3: There are common baths for some \({\hat{H}}_{I,j,\alpha }\) and \(\{{\hat{S}}_{j,\alpha }\}\) may or may not commute. Examples of such baths arise when considering decoherence in models of coupled qubits 45 .

Class 4: No terms in \(\{{\hat{S}}_{j}\}\) commute and each term in \(\{{\hat{S}}_{j}\}\) is not diagonalizable. The Anderson impurity model 46 is representative of this category.

We show in all three classes that one can relate \({{{\mathcal{I}}}}\) and \({{{\bf{{{{\mathcal{K}}}}}}}}\) analytically. Furthermore, we show that one can obtain the bath spectral density from the reduced dynamics. Lastly, for Class 1 , we show that a simple diagrammatic structure in the relationship between \({{{\mathcal{I}}}}\) and \({{{\bf{{{{\mathcal{K}}}}}}}}\) can be found, which allows for efficient construction of \({{{\bf{{{{\mathcal{K}}}}}}}}\) without approximations. We provide more details of Class 1 in the main text, and additional details for other classes are available in the Supplementary Notes . Further, for Class 1 models, we extend this analysis to consider driven systems, extending the analysis beyond the time-translationally invariant memory kernels observed for time-independent Hamiltonians.

Path integral formulation

The time evolution of the full system is given by, \({\rho }_{{{{\rm{tot}}}}}(t)={e}^{-i\hat{H}t}{\rho }_{{{{\rm{tot}}}}}(0){e}^{i\hat{H}t}\) . We discretize time and employ a Trotterized propagator,

where \({\hat{H}}_{{{{\rm{env}}}}}=\hat{H}-{\hat{H}}_{S}\) . The initial total density matrix is assumed to be factorized into \({\rho }_{{{{\rm{tot}}}}}(0)=\rho (0)\otimes {({Z}_{j}^{-1}\exp [-{\beta }_{j}{\hat{H}}_{B,j}])}^{\otimes j}\) at inverse temperature β j where \({Z}_{j}={{{\rm{Tr}}}}\exp [-\beta {\hat{H}}_{B,j}]\) . Then, one can show that the dynamics of the reduced system density matrix, \(\rho (N\Delta t)={\rho }_{N}={{{{\rm{Tr}}}}}_{B}\left[{\rho }_{{{{\rm{tot}}}}}(N\Delta t)\right]\) (partial trace over all baths’ degree of freedom), follows

where \({G}_{{x}_{m}^{\pm }{x}_{m+1}^{\pm }}=\langle {x}_{m}^{+}| {e}^{-\frac{i{\hat{H}}_{s}\Delta t}{2}}| {x}_{m+1}^{+}\rangle \langle {x}_{m+1}^{-}| {e}^{\frac{i{\hat{H}}_{s}\Delta t}{2}}| {x}_{m}^{-}\rangle\) .

Restricting ourselves to problems in Class 1 (details for other Classes are available in the Supplementary Notes ), we consider \({\hat{H}}_{I}=\hat{S}\otimes \hat{B}\) where \(\hat{S}\) is a system operator that is diagonal in the computational basis and \(\hat{B}={\sum }_{k}{\lambda }_{k}({\hat{a}}_{k}^{{{\dagger}} }+{\hat{a}}_{k})\) is a bath operator that is linear in the bath creation and annihilation operators (with the subscript α and j dropped for clarity.) The discussion below can be applied to cases with multiple commuting \(\hat{S}\otimes \hat{B}\) since \({{{\mathcal{I}}}}\) take simple product form, see Supplementary Note 1 . We can show that the influence functional, \({{{\mathcal{I}}}}\) , is pairwise separable,

where the influence functions I k are defined in Supplementary Note 1 , and are related to the bath spectral density, \(J(\omega )=\pi {\sum }_{k}{\lambda }_{k}^{2}\delta (\omega -{\omega }_{k})\) . For later use, we note that Eq. ( 2 ) can be simplified into

where U N is the system propagator from t = 0 to t = N Δ t . It is then straightforward to express U N in terms of { I k } 19 , 20 , 21 , 42 , 47 .

The Nakajima–Zwanzig equation

The Nakajima–Zwanzig equation is a time-non-local formulation of the formally exact GQME. Assuming the time-independence of \({\hat{H}}_{S}\) , the discretized homogeneous Nakajima–Zwanzig equation takes the form

where \({{{\bf{L}}}}\equiv ({{{\bf{1}}}}-\frac{i}{\hslash }{{{{\mathcal{L}}}}}_{S}\Delta t)\) with \({{{{\mathcal{L}}}}}_{S}\bullet \equiv [{\hat{H}}_{S},\bullet ]\) being the bare system Liouvillian and \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{n}\) is the discrete-time memory kernel at time step n . To relate \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) to { I k }, we inspect the reduced dynamics evolution operator U N as defined in Eq. ( 4 ),

With this relation, one can obtain \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) from the reduced propagators { U k }. We observe setting N = 1 yields \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{0}=\frac{1}{\Delta {t}^{2}}({{{{\bf{U}}}}}_{1}-{{{\bf{L}}}})\) , since U 0 is the identity. The memory kernel, \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{0}\) , accounts for the deviation of the system dynamics from its pure dynamics (decoupled from the bath) within a time step. From setting N = 2, we get \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{1}=\frac{1}{\Delta {t}^{2}}({{{{\bf{U}}}}}_{2}-{{{{\bf{U}}}}}_{1}{{{{\bf{U}}}}}_{1})\) . This intuitively shows that \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{1}\) captures the effect of the bath that cannot be captured within \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{0}\) . Similarly, for N = 3, \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{2}=\frac{1}{\Delta {t}^{2}}({{{{\bf{U}}}}}_{3}-{{{{\bf{U}}}}}_{2}{{{{\bf{U}}}}}_{1}-{{{{\bf{U}}}}}_{1}{{{{\bf{U}}}}}_{2}+{{{{\bf{U}}}}}_{1}{{{{\bf{U}}}}}_{1}{{{{\bf{U}}}}}_{1}).\) This set of equations is similar to cumulant expansions, widely used in many-body physics and electronic structure theory 48 , 49 . Instead of dealing with higher-order N -body expectation values, we deal with higher-order N -time memory kernel in this context. The N -time memory kernel \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) is the N -th order cumulant in the cumulant expansion of the system operator. Unsurprisingly, these recursive relations lead to diagrammatic expansions commonly found in cumulant expansions 48 , as shown in Fig. 1 b.

Relationship between \({{{\bf{{{{\mathcal{K}}}}}}}}\) and I

Using this cumulant generation of \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) and by expressing { U k } in terms of { I k }, we obtain a direct relationship between \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) and \({\{{{{{\bf{I}}}}}_{k}\}}_{k=0}^{k=N}\) . Specifically, we have

where we define F = G G (bold-face for denoting matrices) and \({\tilde{I}}_{k,ij}={I}_{k,ij}-1\) . We emphasize that Eqs. ( 7 ) to ( 10 ) are exact up to the Trotter discretization error and valid for any coupling strengths in the models considered in this work. By definition, earlier \({{{{\mathcal{K}}}}}_{N}\) contains shorter memory effects and will thus appear simpler.

This series of equations is a part of the main result of this work, showing explicitly how \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) is diagrammatically constructed in terms of influence functions from I 0 to I N . This construction can easily show the computational effort of computing \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) . We sum over an additional time index for each time step. This gives a computational cost that scales exponentially in time, \({{{\mathcal{O}}}}({N}_{\dim }^{2N})\) where \({N}_{\dim }\) is the dimension of the system Hilbert space. In Supplementary Note 3 E, we present further details on the general algorithm for calculating higher-order memory kernels, exploiting a non-trivial diagrammatic structure to express them in terms of I and \(\tilde{{{{\bf{I}}}}}\) .

It can be inferred from Eqs. ( 8 ) to ( 10 ) that each term in \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) is represented uniquely by each Dyck path 50 , 51 , 52 of order N . Hence, one can construct \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) by generating the respective set of Dyck paths and associating each path with a tensor contraction of influence functions. This is illustrated in Fig. 1 c and further detailed in Supplementary Note 3 E. This observation reveals some new properties of \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) . First, the number of terms in \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) is given by the N -th Catalan’s number 51 , 52 \({C}_{N}=\frac{1}{N+1}\left(\begin{array}{c}2N\\ N\end{array}\right)\) (i.e., \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{4}\) has 14 such terms, \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{5}\) has 42, then 132, 429, 1430, 4862, 16796, 58786, …). We note that Catalan’s number appeared in ref. 47 when analyzing an approximate numerical INFPI method. See Supplementary Note 3 E for more information.

Scrutinizing the relationship of \({{{\bf{{{{\mathcal{K}}}}}}}}\) and I , presented in Supplementary Note 3 E, further, we can observe how \({{{\bf{{{{\mathcal{K}}}}}}}}\) decays asymptotically. As is well-known, for typical condensed phase systems I k , i j → 1 for k → ∞ 17 , 53 . Similarly, because \({\tilde{I}}_{k,ij}\,\ll \,1\) for large k , those terms with larger multiplicities contribute less to \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) and decay exponentially to zero as multiplicity grows. In fact, for condensed phase systems, the decay of I N and \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) is often rapid, which motivated the development of approximate INFPI methods 17 , 18 , 19 , 20 , 53 and other approximate GQME methods 37 , 54 , 55 , 56 .

With our new insight, approximate INFPI methods can be viewed through the lens of the corresponding memory kernel content (and vice versa). As an example, we shall discuss the iterative quasiadiabatic path-integral methods 17 , 18 , 53 . In these methods, I k , i j is set to unity beyond a preset truncation length \({k}_{\max }\) . For simplicity, let us consider \({k}_{\max }=1\) , and hence I k , i j = 1 and \({\tilde{I}}_{k,ij}=0\) for \(k \, > \, {k}_{\max }\) . We now inspect what this approximation entails for \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) . First, no approximation is applied to \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{0}\) and \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{1}\) . Then, in \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{2}\) (Eq. ( 9 )),

Similarly, in \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{3}\) (Eq. ( 10 )), the only surviving contribution is from \({\tilde{I}}_{1,jk}{\tilde{I}}_{1,kn}{\tilde{I}}_{1,np}\) . We hope such a direct connection between approximate methods will inspire the development of more efficient and accurate methods.

The time-translational structure of the INFPI formulation and its Dyck-diagrammatic structure allow for a recursive deduction of I N from \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) , which is the inverse map of Eqs. ( 8 ) to ( 10 ). We first observe that

where we obtained I 0 from \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{0}\) . One can then show that

using \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{1}\) and I 0 . Similarly, inspecting the expression for \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{2}\) gives us

where \({\tilde{I}}_{1,jk}={I}_{1,jk}-1\) as well as I 0, i are obtained from the previous two relations.

Spectral density learning

In Supplementary Note 3 F, we present a general recursive procedure using the Dyck paths and how to obtain the bath spectral density from I k . As a result, we achieve the following mapping from left to right,

A remarkable outcome of this analysis is that one can completely characterize the environment (i.e., J ( ω )), by inspecting the reduced system dynamics. Such a tool is powerful in engineering quantum systems in experiments where we have access to only the reduced system Hamiltonian and reduced system dynamics, but lack information about the environment. Furthermore, this approach provides an alternative to quantum noise spectroscopy 57 , 58 . This type of Hamiltonian learning with access only to subsystem observables has been achieved for other simpler Hamiltonians 59 , 60 . To our knowledge, our work is the first to show this inverse map for the Hamiltonian considered here.

Note that the expression Eq. ( 13 ) can become ill-defined when F is diagonal. This occurs when \({\hat{H}}_{S}\) is diagonal and commutes with \({\hat{H}}_{{{{\rm{env}}}}}\) , constituting a purely dephasing dynamics. In that case, the reduced system dynamics is governed only by the diagonal elements of I . Similarly, \({{{\bf{{{{\mathcal{K}}}}}}}}\) is diagonal, as clearly seen in our Dyck path construction. As a result, the map \({{{\bf{{{{\mathcal{K}}}}}}}}\leftrightarrow {{{\bf{I}}}}\) is no longer bijective in that we cannot obtain off-diagonal elements of I . Regardless, one can still extract J ( ω ) using only the diagonal elements of I via inverse cosine transform. One may worry Eq. ( 14 ) could also become ill-conditioned when its denominator vanishes, but \({\hat{H}}_{S}\) is not diagonal. If that were the case, the propagator U 2 would become zero. Therefore, this condition cannot be satisfied in general. Finally, we remark that generalization to extract the \({{{{\mathcal{I}}}}}_{\alpha }\) of multiple baths through a single central system is possible and straightforward. See Supplementary Note 3 F for more details.

Generalization to driven systems

While analysis up to this point considered general time-independent systems, in many scenarios, e.g., of biological or engineering relevance, particularly for quantum control applications 61 , a time-dependent description of the system is necessary. In such cases, \({{{\bf{{{{\mathcal{K}}}}}}}}\) loses its time-translational properties and should depend on two times. Consequently, Eq. ( 6 ) cannot be applied. To overcome this, we factorize \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N+s,s}\) into time-dependent and time-independent parts. This can be achieved straightforwardly, as follows: one observes upon the inclusion of time-dependence in \({\hat{H}}_{S}\) , the terms that are affected in \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) , Eqs. ( 7 ) to ( 10 ), are only the bare system propagators G and F . We define the remainder as tensors with N number of indices, \({T}_{N;{x}_{s+2},{x}_{s+4},...,{x}_{s+2N}}\) , which includes all the influence of the bath between N- time steps. These tensors only need to be computed once and reused for a later time. Then, one builds the kernels via tensor contraction over two tensors,

where • denotes indices, x s +2 , . . . , x s +2 N , and the tensor \({P}_{{x}_{s},\bullet,{x}_{2N+s}}^{N+1+s,s}\) encapsulates the time-dependence of the system Hamiltonian and is constructed only out of bare system propagators. The tensor, T N ;• , then consists only of influence functions, up to I N . The construction of these tensors is straightforward with T N ;• following the Dyck path construction presented for time-independent system dynamics. On the surface, the T N ;• tensor appears to be related to the process tensor 33 , 34 : T represents K upon the contraction with P , but the process tensor is used to construct U when contracted with P . Subsequently, there is a non-trivial rearrangement of the terms to write K in terms of the process tensor. The simple relationship between T and K in Eq. ( 16 ) is our unique contribution. More detailed analysis and relevant numerical results for open, driven system dynamics are presented in Supplementary Note 3 H.

Numerical verification

While the discussion above applies to a generic system linearly coupled to a Gaussian bath (or multiple such baths if they couple additively), we discuss the spin-boson model for further illustration. The spin-boson model is an archetypal model for studying open quantum systems 62 . The model comprises a two-level system coupled linearly to a bath of harmonic oscillators. Hence, it and its generalizations have been used to understand various quantum phenomena: transport, chemical reactions, diode effect, and phase transitions 63 .

We use \({\hat{H}}_{S}=\epsilon {\sigma }_{z}+\Delta {\sigma }_{x}\) , coupled via σ z to a harmonic bath with spectral density ( ω ≥ 0) 62

where J (− ω ) = − J ( ω ), ξ is the Kondo parameter, and s is the Ohmicity. All reference calculations were performed using the HEOM method 28 , 64 , 65 . Details of the HEOM implementation used here are provided in Supplementary Note 7 .

In Fig. 2 , we investigate a series of spin-boson models corresponding to weak and intermediate coupling to an Ohmic environment ( s = 1) as well as strong coupling to a subohmic environment ( s = 0.5). In panels (a, b), we observe that the decay of \({\tilde{{{{\bf{I}}}}}}_{N}\) is rapid for the Ohmic cases. This translates to a similarly rapid decay for the respective \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) , although one can see that both \({\tilde{I}}_{N}\) and \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) are overall scaled larger in the strong coupling regime. This is to be contrasted with the results for the strongly coupled subohmic environment shown in panel (c). The decay of the \({\tilde{{{{\bf{I}}}}}}_{N}\) is slow, accompanied by a similarly slow decay of \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) . Interestingly, the rates by which both \({\tilde{{{{\bf{I}}}}}}_{N}\) and \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) decay are similar, which we observe to be exponential. We also see perfect agreement between \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) constructed from our Dyck diagrammatic method and those obtained by numerically post-processing exact trajectories via the transfer tensor method 40 . Lastly, we construct \({\tilde{{{{\bf{I}}}}}}_{N}\) from \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) up to N = 16 as exemplified in Eqs. ( 13 ) and ( 14 ) and observe perfect agreement between our \({\tilde{{{{\bf{I}}}}}}_{N}\) and those computed from its known analytic formula.

Operator norm of \({\tilde{{{{\bf{I}}}}}}_{N}\) (Light) and \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) (Dark) as a function of N Δ t . Lines denote \({\tilde{{{{\bf{I}}}}}}_{N}\) computed from analytic expressions and \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) from post-processing exact numerical results via the transfer tensor method 40 . Circles denote \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) from the Dyck diagrammatic method, and crosses are \({\tilde{{{{\bf{I}}}}}}_{N}\) obtained via the inverse map discussed in Eqs. ( 13 ) and ( 14 ). Dashed lines denote the operator norm of the crest term of \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) (the Dyck path diagram with the highest height). Parameters used are: Δ = 1 (other parameters are expressed relative to Δ ), ϵ = 0, β = 5, Δ t = 0.1, ω c = 7.5, and ξ = 0.1 and s = 1 ( a ), ξ = 0.5 and s = 1 ( b ), and ξ = 0.5 and s = 0.5 ( c ).

We note that the term with \({\tilde{{{{\bf{I}}}}}}_{N}\) (multiplicity of 1) contributes the most to the memory kernel, \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) for all parameters considered in our work. We refer to this term as the “crest” term, which corresponds to the Dyck path that goes straight to the top and down straight to the bottom, having the tallest height. We see a small difference between the crest term norm and the full memory kernel norm in Fig. 2 , indicating that the memory kernel is dominated by the crest term. Since the decay of \({\tilde{{{{\bf{I}}}}}}_{N}\) is directly related to the decay of the bath correlation function, one can also make connections between the memory kernel decay and the bath correlation function decay. Nonetheless, for a stronger system-bath coupling (e.g., Fig. 2 b) and for cases with a long-lived memory (e.g., Fig. 2 c), terms other than the crest term contribute non-negligibly, making general analysis of the memory kernel decay challenging.

The cost to numerically compute \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) scales exponentially with N . Nevertheless, it is possible to exploit the decay of \({\tilde{{{{\bf{I}}}}}}_{N}\) , which is rapid for some environments, e.g., ohmic baths, in turn signifying the decay behavior of \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) . This allows truncating the summation in Eq. ( 5 ), enabling dynamical propagation to long times (with linear costs in time) as usually done in small matrix path integral methods 19 , 20 and GQME 40 methods. We show in panels (a1) and (b1) of Fig. 3 that this procedure applied to a problem with a rapidly decaying \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) quickly converges to the exact value with a reasonably low-order. On the other hand, for environments with slowly decaying \({\tilde{{{{\bf{I}}}}}}_{N}\) , the truncation scheme struggles to work effectively. For a strongly coupled subohmic environment, as shown in Fig. 3 c1, one would need truncation orders beyond the current computational capabilities of our implementation (about 16) to converge to the exact value. Nonetheless, this illustrates that our direct construction of \({{{{\bf{{{{\mathcal{K}}}}}}}}}_{N}\) can recover exact dynamics if sufficiently high-order is used. Furthermore, the construction is non-perturbative and can be applied to strong coupling problems. We note that describing quantum phase transitions at T = 0 would require capturing the algebraic decay in I N 29 . Our analysis can, in principle, capture such a slow decay as our approach is exact but will require further optimization in the underlying numerical algorithms for practical applications.

a 1, b 1, c 1 Magnetization (〈 σ z ( t )〉) dynamics predicted using \({{{\bf{{{{\mathcal{K}}}}}}}}\) constructed via Dyck diagrams with increasing truncation orders (from light to darker colors) compared to exact results (see Supplementary Note 6 ). a 2, b 2, c 2 Bath spectral densities extracted through the Dyck diagrammatic method with increasing truncation order (from white to black colors) compared to exact spectral densities (dashed), see Supplementary Note 3 F for more details. These results come from numerically exact trajectories, initiated from linearly independent initial states \({\rho }_{1}(0)=\frac{1}{2}({{{\bf{1}}}}+{\sigma }_{z}),\,{\rho }_{2}(0)=\frac{1}{2}({{{\bf{1}}}}-{\sigma }_{z}),\,{\rho }_{3}(0)=\frac{1}{2}({{{\bf{1}}}}+{\sigma }_{x}),\,{\rho }_{4}(0)=\frac{1}{2}({{{\bf{1}}}}+{\sigma }_{x}+{\sigma }_{y}+{\sigma }_{z})\) . Parameters used are: Δ = 1 (other parameters are expressed relative to Δ ), ϵ = 0, β = 5, Δ t = 0.1 ( a 1, b 1, c 1) or Δ t = 0.05 ( a 2, b 2, c 2), ω c = 7.5, and ξ = 0.1 and s = 1 ( a 1 and a 2), ξ = 0.5 and s = 1 ( b 1 and b 2), or ξ = 0.5 and s = 0.5 ( c 1 and c 2).

Finally, in Fig. 3 a2, b2, c2, we show the extraction of spectral densities J ( ω ) for three distinct environments. The extracted J ( ω ) converges to the analytical value as we obtain the influence functions to higher orders. This shows that we can indeed invert the reduced system dynamics to obtain J ( ω ) given the knowledge of the system Hamiltonian, which ultimately characterizes the entire system-bath Hamiltonian. Nonetheless, the accuracy of the resulting J ( ω ) depends on the highest order of I k we can numerically extract. The cost of extracting I k scales exponentially in k without approximations, so there is naturally a limit to the precision of J ( ω ) in practice. Furthermore, we show how this procedure can extract highly structured spectral densities as well in Supplementary Note 8 and Supplementary Fig. 9 . New opportunities await in using approximately inverted I k and quantifying the error in the resulting J ( ω ).

In this work, we provide analytical analysis along with numerical results that show complete equivalence between the memory kernel ( \({{{\bf{{{{\mathcal{K}}}}}}}}\) ) in the GQME formalism and the influence function ( I ) used in INFPI. Our analysis applies to a broad class of general (driven) systems interacting bilinearly with Gaussian baths. Furthermore, we showed that one can extract the bath spectral density from the reduced system dynamics with the knowledge of the reduced system Hamiltonian \({\hat{H}}_{S}\) . We believe that this unified framework for studying non-Markovian dynamics will facilitate the development of new analytical and numerical methods that combine the strengths of both GQME and INFPI. For example, deep connections between the present work and recent matrix product state (MPS)-based approaches invite ideas that would efficiently extract the environmental spectral density from reduced system dynamics 29 , 31 , 32 , 33 , 34 .

Details pertaining to analytical derivation of results in this work, as well as numerical implementations, are provided in the Supplementary Notes .

Data availability

Data generated in this study is available on GitHub ( https://github.com/JoonhoLee-Group/Unified_Framework_OQ_Code_and_Data ) and Zenodo at ref. 66 .

Code availability

Simulation codes used in this study are available on GitHub ( https://github.com/JoonhoLee-Group/Unified_Framework_OQ_Code_and_Data ) and Zenodo at ref. 66 .

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Acknowledgements

F.I. and J.L. were supported by Harvard University’s startup funds. L.P.L. acknowledges the support of the Engineering and Physical Sciences Research Council [grant EP/Y005090/1]. We thank Nathan Ng, David Reichman, Dvira Segal, and Jonathan Keeling for stimulating discussions, Tom O’Brien for discussions on Hamiltonian learning, and Hieu Dinh for providing a code to generate the Dyck path. Computations were carried out partly on the FASRC cluster supported by the FAS Division of Science Research Computing Group at Harvard University. This work also used the Delta system at the National Center for Supercomputing Applications through allocation CHE230078 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program, which is supported by National Science Foundation grants #2138259, #2138286, #2138307, #2137603, and #2138296.

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Ivander, F., Lindoy, L.P. & Lee, J. Unified framework for open quantum dynamics with memory. Nat Commun 15 , 8087 (2024). https://doi.org/10.1038/s41467-024-52081-3

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Non-experimental research: What it is, Types & Tips
Non-experimental research is the type of research that lacks an independent variable. Instead, the researcher observes the context in which the phenomenon occurs and analyzes it to obtain information. Unlike experimental research, where the variables are held constant, non-experimental research happens during the study when the researcher ...
What is non-experimental research: Definition, types & examples
Non-experimental research does not involve the manipulation of variables.; The aim of this research type is to explore the factors as they naturally occur.; This method is used when experimentation is not possible because of ethical or practical reasons.; Instead of creating a sample or participant group, the existing groups or natural thresholds are used during the research.
6.1 Overview of Non-Experimental Research
Non-experimental research is research that lacks the manipulation of an independent variable. There are two broad types of non-experimental research. Correlational research that focuses on statistical relationships between variables that are measured but not manipulated, and observational research in which participants are observed and their ...
Experimental Vs Non-Experimental Research: 15 Key Differences
Definitions. Experimental research is the type of research that uses a scientific approach towards manipulating one or more control variables and measuring their defect on the dependent variables, while non-experimental research is the type of research that does not involve the manipulation of control variables.
Overview of Nonexperimental Research
Key Takeaways. Nonexperimental research is research that lacks the manipulation of an independent variable, control of extraneous variables through random assignment, or both. There are three broad types of nonexperimental research. Single-variable research focuses on a single variable rather than a relationship between variables.
7.1 Overview of Nonexperimental Research
Key Takeaways. Nonexperimental research is research that lacks the manipulation of an independent variable, control of extraneous variables through random assignment, or both. There are three broad types of nonexperimental research. Single-variable research focuses on a single variable rather than a relationship between variables.
Quantitative Research with Nonexperimental Designs
There are two main types of nonexperimental research designs: comparative design and correlational design. In comparative research, the researcher examines the differences between two or more groups on the phenomenon that is being studied. For example, studying gender difference in learning mathematics is a comparative research.
1.6: Non-Experimental Research
Types of Non-Experimental Research. The most common type of non-experimental research conducted in social sciences is correlational research. Correlational research is considered non-experimental because it focuses on the statistical relationship between two variables but does not include the manipulation of an independent variable.
Overview of Non-Experimental Research
Types of Non-Experimental Research. ... Non-experimental (correlational) research is lowest in internal validity because these designs fail to use manipulation or control. Quasi-experimental research (which will be described in more detail in a subsequent chapter) falls in the middle because it contains some, but not all, of the features of a ...
Overview of Non-Experimental Research
Non-experimental research is research that lacks the manipulation of an independent variable. Rather than manipulating an independent variable, researchers conducting non-experimental research simply measure variables as they naturally occur (in the lab or real world). Most researchers in psychology consider the distinction between experimental ...
6.2 Nonexperimental Research
6.2 Nonexperimental Research Nonexperimental research is research that lacks manipulation of an independent variable and/or random assignment of participants to conditions.While the distinction between experimental and nonexperimental research is considered important, it does not mean that nonexperimental research is less important or inferior to experimental research (Price, Jhangiani ...
Non-Experimental Research
We then look separately at two important types of non-experimental research: correlational research and observational research. Milgram, S. (1963). Behavioral study of obedience. Journal of Abnormal and Social Psychology, 67, 371-378.
Non-Experimental Research: Overview & Advantages
Non-experimental designs can open a number of advantageous research opportunities. The benefits include: Non-experimental research can be used to analyze events that have happened in the past. The versatility of the model can be used to observe many unique phenomena. This method of research is far more affordable than the experimental kind.
PDF Non-experimental study designs: The basics and recent advances
So when we can't randomize…the role of design for non-experimental studies. •Should use the same spirit of design when analyzing non-experimental data, where we just see that some people got the treatment and others the control •Helps articulate 1) the causal question, and 2) the timing of covariates, exposure, and outcomes.
2.5: Experimental and Non-experimental Research
One distinction worth making between two types of non-experimental research is the difference be- tween quasi-experimental research and case studies. The example I discussed earlier - in which we wanted to examine incidence of lung cancer among smokers and non-smokers, without trying to control who smokes and who doesn't - is a quasi ...
Overview of Non-Experimental Research
Non-experimental research is research that lacks the manipulation of an independent variable. Rather than manipulating an independent variable, researchers conducting non-experimental research simply measure variables as they naturally occur (in the lab or real world). Most researchers in psychology consider the distinction between experimental ...
Quantitative Research Designs: Non-Experimental vs. Experimental
Without this level of control, you cannot determine any causal effects. While validity is still a concern in non-experimental research, the concerns are more about the validity of the measurements, rather than the validity of the effects. Finally, a quasi-experimental design is a combination of the two designs described above.
Experimental vs. Non-Experimental Research
Types of Non-Experimental Research. The following are the most common non-experimental research designs: Cross-sectional research designs observe and analyze pre-existing groups with defined ...
Nonexperimental research: strengths, weaknesses and issues of precision
Nonexperimental research, defined as any kind of quantitative or qualitative research that is not an experiment, is the predominate kind of research design used in the social sciences. How to unambiguously and correctly present the results of nonexperimental research, however, remains decidedly unclear and possibly detrimental to applied ...
Comparison and analysis of properties of V-type HV-LSPMSM with non
Comparison and analysis of properties of V-type HV-LSPMSM with non-magnetic and magnetic-wedges, Qiuyue Xie, Qiuling Deng, Bing Ren, Yichang Zhong, Jinsheng Ou ... (FEM) are verified, it provides an experimental basis for further research on the effect of relative permeability variation on motor performance. The effects of nonmagnetic-wedges ...
Unified framework for open quantum dynamics with memory
The insights we provide advance our understanding of non-Markovian dynamics and will serve as a stepping stone for future theoretical and experimental developments in this area.

Non-experimental research: What it is, overview & advantages

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6.1 Overview of Non-Experimental Research

What Is Non-Experimental Research?

When to Use Non-Experimental Research

Types of Non-Experimental Research

Internal Validity Revisited

Key Takeaways

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What is Experimental Research?

Pre-experimental Research

Quasi-experimental Research

True Experimental Research

Pros of True Experimental Research

Cons of True Experimental Research

What is Non-Experimental Research?

Cross-sectional Research

Correlational Research

Observational Research

Pros of Observational Research

Cons of Observational Research

What Are The Differences Between Experimental and Non-Experimental Research?

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Overview of Nonexperimental Research

What Is Nonexperimental Research?

When to Use Nonexperimental Research

Types of Nonexperimental Research

Internal Validity Revisited

Share This Book

7.1 Overview of Nonexperimental Research

What Is Nonexperimental Research?

When to Use Nonexperimental Research

Types of Nonexperimental Research

Internal Validity Revisited

Key Takeaways

Overview of Non-Experimental Research

Learning Objectives

What Is Non-Experimental Research?

When to Use Non-Experimental Research

Types of Non-Experimental Research

Cross-Sectional, Longitudinal, and Cross-Sequential Studies

Internal Validity Revisited

Share This Book

6.2 Nonexperimental Research

When to Use Nonexperimental Research

Types of Nonexperimental Research

Share This Book

Non-Experimental Research

Share This Book