benefits of single subject research design

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Advantages and disadvantages of using a single-subject research design.

Most empirical research relies on using the scientific method to conduct large studies that use many participants in a control group and an experimental group. The purpose is to determine the effect of some experimental factor by introducing it to the experimental group, but not to the control group, and seeing what, if any, effect the experimental factor has. However, in some cases researchers will use an alternative method called single-subject research design.

Single-Subject Methodology

Single Subject Research Designs (SSRDs) work by designing an experiment where, instead of a control group of subjects and an experimental group of subjects whose results are compared to one another, the control and experimental measurements come from a single subject. Researchers measure the metric of interest before introducing the experimental factor for a control measurement, and measure the metric of interest after introducing the experimental factor for the experimental measure. While studies may include more than one subject, each subject is treated as a unique experiment instead of one trial in a larger experiment.

Self-Controlling

An advantage of using an SSRD is that, instead of comparing the percentage of people that responded to an experimental factor to the percentage of people that did not, the study examines how an individual subject, with his own unique characteristics, responds to the experimental factor. This is particularly useful when studying specific subsets of a population, rather than the population as a whole.

Finding Subjects

In an experimental group versus control group study, the researcher has to find a large number of participants to act as subjects. This is necessary for the data from the experiment to yield statistically relevant results. This requires the time and resources to not only gather the participants, but to run trials of the experiment on all the subjects to gather all the data. An SSRD allows researchers to quickly design and run their study without having to find so many participants.

Empirical Value

While the fact that the researcher does not use a large number of participants has its advantages, it also has a downside: Because the experimental trials are run on only one subject, it is difficult to empirically show with the experiment's data that the findings will generalize out to larger populations. All the trial can show is what happened with the individual subject, whereas traditional research designs that use large numbers of participants are specifically designed to show if a result is statistically valid for the general population.

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• NASP Communiqué; "Using Single-Subject Research in the Practice of School Psychology"; Michelle Marchant et al.; September 2006

Micah McDunnigan has been writing on politics and technology since 2007. He has written technology pieces and political op-eds for a variety of student organizations and blogs. McDunnigan earned a Bachelor of Arts in international relations from the University of California, Davis.

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10.1 Overview of Single-Subject Research

Learning objectives.

• Explain what single-subject research is, including how it differs from other types of psychological research.
• Explain what case studies are, including some of their strengths and weaknesses.
• Explain who uses single-subject research and why.

What Is Single-Subject Research?

Single-subject research is a type of quantitative research that involves studying in detail the behavior of each of a small number of participants. Note that the term single-subject does not mean that only one participant is studied; it is more typical for there to be somewhere between two and 10 participants. (This is why single-subject research designs are sometimes called small- n designs, where n is the statistical symbol for the sample size.) Single-subject research can be contrasted with group research , which typically involves studying large numbers of participants and examining their behavior primarily in terms of group means, standard deviations, and so on. The majority of this book is devoted to understanding group research, which is the most common approach in psychology. But single-subject research is an important alternative, and it is the primary approach in some areas of psychology.

Before continuing, it is important to distinguish single-subject research from two other approaches, both of which involve studying in detail a small number of participants. One is qualitative research, which focuses on understanding people’s subjective experience by collecting relatively unstructured data (e.g., detailed interviews) and analyzing those data using narrative rather than quantitative techniques. Single-subject research, in contrast, focuses on understanding objective behavior through experimental manipulation and control, collecting highly structured data, and analyzing those data quantitatively.

It is also important to distinguish single-subject research from case studies. A case study is a detailed description of an individual, which can include both qualitative and quantitative analyses. (Case studies that include only qualitative analyses can be considered a type of qualitative research.) The history of psychology is filled with influential cases studies, such as Sigmund Freud’s description of “Anna O.” (see Note 10.5 “The Case of “Anna O.”” ) and John Watson and Rosalie Rayner’s description of Little Albert (Watson & Rayner, 1920), who learned to fear a white rat—along with other furry objects—when the researchers made a loud noise while he was playing with the rat. Case studies can be useful for suggesting new research questions and for illustrating general principles. They can also help researchers understand rare phenomena, such as the effects of damage to a specific part of the human brain. As a general rule, however, case studies cannot substitute for carefully designed group or single-subject research studies. One reason is that case studies usually do not allow researchers to determine whether specific events are causally related, or even related at all. For example, if a patient is described in a case study as having been sexually abused as a child and then as having developed an eating disorder as a teenager, there is no way to determine whether these two events had anything to do with each other. A second reason is that an individual case can always be unusual in some way and therefore be unrepresentative of people more generally. Thus case studies have serious problems with both internal and external validity.

The Case of “Anna O.”

Sigmund Freud used the case of a young woman he called “Anna O.” to illustrate many principles of his theory of psychoanalysis (Freud, 1961). (Her real name was Bertha Pappenheim, and she was an early feminist who went on to make important contributions to the field of social work.) Anna had come to Freud’s colleague Josef Breuer around 1880 with a variety of odd physical and psychological symptoms. One of them was that for several weeks she was unable to drink any fluids. According to Freud,

She would take up the glass of water that she longed for, but as soon as it touched her lips she would push it away like someone suffering from hydrophobia.…She lived only on fruit, such as melons, etc., so as to lessen her tormenting thirst (p. 9).

But according to Freud, a breakthrough came one day while Anna was under hypnosis.

[S]he grumbled about her English “lady-companion,” whom she did not care for, and went on to describe, with every sign of disgust, how she had once gone into this lady’s room and how her little dog—horrid creature!—had drunk out of a glass there. The patient had said nothing, as she had wanted to be polite. After giving further energetic expression to the anger she had held back, she asked for something to drink, drank a large quantity of water without any difficulty, and awoke from her hypnosis with the glass at her lips; and thereupon the disturbance vanished, never to return.

Freud’s interpretation was that Anna had repressed the memory of this incident along with the emotion that it triggered and that this was what had caused her inability to drink. Furthermore, her recollection of the incident, along with her expression of the emotion she had repressed, caused the symptom to go away.

As an illustration of Freud’s theory, the case study of Anna O. is quite effective. As evidence for the theory, however, it is essentially worthless. The description provides no way of knowing whether Anna had really repressed the memory of the dog drinking from the glass, whether this repression had caused her inability to drink, or whether recalling this “trauma” relieved the symptom. It is also unclear from this case study how typical or atypical Anna’s experience was.

Figure 10.2

“Anna O.” was the subject of a famous case study used by Freud to illustrate the principles of psychoanalysis.

Wikimedia Commons – public domain.

Assumptions of Single-Subject Research

Again, single-subject research involves studying a small number of participants and focusing intensively on the behavior of each one. But why take this approach instead of the group approach? There are several important assumptions underlying single-subject research, and it will help to consider them now.

First and foremost is the assumption that it is important to focus intensively on the behavior of individual participants. One reason for this is that group research can hide individual differences and generate results that do not represent the behavior of any individual. For example, a treatment that has a positive effect for half the people exposed to it but a negative effect for the other half would, on average, appear to have no effect at all. Single-subject research, however, would likely reveal these individual differences. A second reason to focus intensively on individuals is that sometimes it is the behavior of a particular individual that is primarily of interest. A school psychologist, for example, might be interested in changing the behavior of a particular disruptive student. Although previous published research (both single-subject and group research) is likely to provide some guidance on how to do this, conducting a study on this student would be more direct and probably more effective.

A second assumption of single-subject research is that it is important to discover causal relationships through the manipulation of an independent variable, the careful measurement of a dependent variable, and the control of extraneous variables. For this reason, single-subject research is often considered a type of experimental research with good internal validity. Recall, for example, that Hall and his colleagues measured their dependent variable (studying) many times—first under a no-treatment control condition, then under a treatment condition (positive teacher attention), and then again under the control condition. Because there was a clear increase in studying when the treatment was introduced, a decrease when it was removed, and an increase when it was reintroduced, there is little doubt that the treatment was the cause of the improvement.

A third assumption of single-subject research is that it is important to study strong and consistent effects that have biological or social importance. Applied researchers, in particular, are interested in treatments that have substantial effects on important behaviors and that can be implemented reliably in the real-world contexts in which they occur. This is sometimes referred to as social validity (Wolf, 1976). The study by Hall and his colleagues, for example, had good social validity because it showed strong and consistent effects of positive teacher attention on a behavior that is of obvious importance to teachers, parents, and students. Furthermore, the teachers found the treatment easy to implement, even in their often chaotic elementary school classrooms.

Who Uses Single-Subject Research?

Single-subject research has been around as long as the field of psychology itself. In the late 1800s, one of psychology’s founders, Wilhelm Wundt, studied sensation and consciousness by focusing intensively on each of a small number of research participants. Herman Ebbinghaus’s research on memory and Ivan Pavlov’s research on classical conditioning are other early examples, both of which are still described in almost every introductory psychology textbook.

In the middle of the 20th century, B. F. Skinner clarified many of the assumptions underlying single-subject research and refined many of its techniques (Skinner, 1938). He and other researchers then used it to describe how rewards, punishments, and other external factors affect behavior over time. This work was carried out primarily using nonhuman subjects—mostly rats and pigeons. This approach, which Skinner called the experimental analysis of behavior —remains an important subfield of psychology and continues to rely almost exclusively on single-subject research. For excellent examples of this work, look at any issue of the Journal of the Experimental Analysis of Behavior . By the 1960s, many researchers were interested in using this approach to conduct applied research primarily with humans—a subfield now called applied behavior analysis (Baer, Wolf, & Risley, 1968). Applied behavior analysis plays an especially important role in contemporary research on developmental disabilities, education, organizational behavior, and health, among many other areas. Excellent examples of this work (including the study by Hall and his colleagues) can be found in the Journal of Applied Behavior Analysis .

Although most contemporary single-subject research is conducted from the behavioral perspective, it can in principle be used to address questions framed in terms of any theoretical perspective. For example, a studying technique based on cognitive principles of learning and memory could be evaluated by testing it on individual high school students using the single-subject approach. The single-subject approach can also be used by clinicians who take any theoretical perspective—behavioral, cognitive, psychodynamic, or humanistic—to study processes of therapeutic change with individual clients and to document their clients’ improvement (Kazdin, 1982).

Key Takeaways

• Single-subject research—which involves testing a small number of participants and focusing intensively on the behavior of each individual—is an important alternative to group research in psychology.
• Single-subject studies must be distinguished from case studies, in which an individual case is described in detail. Case studies can be useful for generating new research questions, for studying rare phenomena, and for illustrating general principles. However, they cannot substitute for carefully controlled experimental or correlational studies because they are low in internal and external validity.
• Single-subject research has been around since the beginning of the field of psychology. Today it is most strongly associated with the behavioral theoretical perspective, but it can in principle be used to study behavior from any perspective.
• Practice: Find and read a published article in psychology that reports new single-subject research. (A good source of articles published in the Journal of Applied Behavior Analysis can be found at http://seab.envmed.rochester.edu/jaba/jabaMostPop-2011.html .) Write a short summary of the study.

Practice: Find and read a published case study in psychology. (Use case study as a key term in a PsycINFO search.) Then do the following:

• Describe one problem related to internal validity.
• Describe one problem related to external validity.
• Generate one hypothesis suggested by the case study that might be interesting to test in a systematic single-subject or group study.

Baer, D. M., Wolf, M. M., & Risley, T. R. (1968). Some current dimensions of applied behavior analysis. Journal of Applied Behavior Analysis , 1 , 91–97.

Freud, S. (1961). Five lectures on psycho-analysis . New York, NY: Norton.

Kazdin, A. E. (1982). Single-case research designs: Methods for clinical and applied settings . New York, NY: Oxford University Press.

Skinner, B. F. (1938). The behavior of organisms: An experimental analysis . New York, NY: Appleton-Century-Crofts.

Watson, J. B., & Rayner, R. (1920). Conditioned emotional reactions. Journal of Experimental Psychology , 3 , 1–14.

Wolf, M. (1976). Social validity: The case for subjective measurement or how applied behavior analysis is finding its heart. Journal of Applied Behavior Analysis, 11 , 203–214.

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.

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Neag School of Education

Educational Research Basics by Del Siegle

Single subject research.

“ Single subject research (also known as single case experiments) is popular in the fields of special education and counseling. This research design is useful when the researcher is attempting to change the behavior of an individual or a small group of individuals and wishes to document that change. Unlike true experiments where the researcher randomly assigns participants to a control and treatment group, in single subject research the participant serves as both the control and treatment group. The researcher uses line graphs to show the effects of a particular intervention or treatment.  An important factor of single subject research is that only one variable is changed at a time. Single subject research designs are “weak when it comes to external validity….Studies involving single-subject designs that show a particular treatment to be effective in changing behavior must rely on replication–across individuals rather than groups–if such results are be found worthy of generalization” (Fraenkel & Wallen, 2006, p. 318).

Suppose a researcher wished to investigate the effect of praise on reducing disruptive behavior over many days. First she would need to establish a baseline of how frequently the disruptions occurred. She would measure how many disruptions occurred each day for several days. In the example below, the target student was disruptive seven times on the first day, six times on the second day, and seven times on the third day. Note how the sequence of time is depicted on the x-axis (horizontal axis) and the dependent variable (outcome variable) is depicted on the y-axis (vertical axis).

Once a baseline of behavior has been established (when a consistent pattern emerges with at least three data points), the intervention begins. The researcher continues to plot the frequency of behavior while implementing the intervention of praise.

In this example, we can see that the frequency of disruptions decreased once praise began. The design in this example is known as an A-B design. The baseline period is referred to as A and the intervention period is identified as B.

Another design is the A-B-A design. An A-B-A design (also known as a reversal design) involves discontinuing the intervention and returning to a nontreatment condition.

Sometimes an individual’s behavior is so severe that the researcher cannot wait to establish a baseline and must begin with an intervention. In this case, a B-A-B design is used. The intervention is implemented immediately (before establishing a baseline). This is followed by a measurement without the intervention and then a repeat of the intervention.

Multiple-Baseline Design

Sometimes, a researcher may be interested in addressing several issues for one student or a single issue for several students. In this case, a multiple-baseline design is used.

“In a multiple baseline across subjects design, the researcher introduces the intervention to different persons at different times. The significance of this is that if a behavior changes only after the intervention is presented, and this behavior change is seen successively in each subject’s data, the effects can more likely be credited to the intervention itself as opposed to other variables. Multiple-baseline designs do not require the intervention to be withdrawn. Instead, each subject’s own data are compared between intervention and nonintervention behaviors, resulting in each subject acting as his or her own control (Kazdin, 1982). An added benefit of this design, and all single-case designs, is the immediacy of the data. Instead of waiting until postintervention to take measures on the behavior, single-case research prescribes continuous data collection and visual monitoring of that data displayed graphically, allowing for immediate instructional decision-making. Students, therefore, do not linger in an intervention that is not working for them, making the graphic display of single-case research combined with differentiated instruction responsive to the needs of students.” (Geisler, Hessler, Gardner, & Lovelace, 2009)

Regardless of the research design, the line graphs used to illustrate the data contain a set of common elements.

Generally, in single subject research we count the number of times something occurs in a given time period and see if it occurs more or less often in that time period after implementing an intervention. For example, we might measure how many baskets someone makes while shooting for 2 minutes. We would repeat that at least three times to get our baseline. Next, we would test some intervention. We might play music while shooting, give encouragement while shooting, or video the person while shooting to see if our intervention influenced the number of shots made. After the 3 baseline measurements (3 sets of 2 minute shooting), we would measure several more times (sets of 2 minute shooting) after the intervention and plot the time points (number of baskets made in 2 minutes for each of the measured time points). This works well for behaviors that are distinct and can be counted.

Sometimes behaviors come and go over time (such as being off task in a classroom or not listening during a coaching session). The way we can record these is to select a period of time (say 5 minutes) and mark down every 10 seconds whether our participant is on task. We make a minimum of three sets of 5 minute observations for a baseline, implement an intervention, and then make more sets of 5 minute observations with the intervention in place. We use this method rather than counting how many times someone is off task because one could continually be off task and that would only be a count of 1 since the person was continually off task. Someone who might be off task twice for 15 second would be off task twice for a score of 2. However, the second person is certainly not off task twice as much as the first person. Therefore, recording whether the person is off task at 10-second intervals gives a more accurate picture. The person continually off task would have a score of 30 (off task at every second interval for 5 minutes) and the person off task twice for a short time would have a score of 2 (off task only during 2 of the 10 second interval measures.

I also have additional information about how to record single-subject research data .

I hope this helps you better understand single subject research.

I have created a PowerPoint on Single Subject Research , which also available below as a video.

I have also created instructions for creating single-subject research design graphs with Excel .

Fraenkel, J. R., & Wallen, N. E. (2006). How to design and evaluate research in education (6th ed.). Boston, MA: McGraw Hill.

Geisler, J. L., Hessler, T., Gardner, R., III, & Lovelace, T. S. (2009). Differentiated writing interventions for high-achieving urban African American elementary students. Journal of Advanced Academics, 20, 214–247.

Del Siegle, Ph.D. University of Connecticut [email protected] www.delsiegle.info

Revised 02/02/2024

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Chapter 10: Single-Subject Research

Single-Subject Research Designs

Learning Objectives

• Describe the basic elements of a single-subject research design.
• Design simple single-subject studies using reversal and multiple-baseline designs.
• Explain how single-subject research designs address the issue of internal validity.
• Interpret the results of simple single-subject studies based on the visual inspection of graphed data.

General Features of Single-Subject Designs

Before looking at any specific single-subject research designs, it will be helpful to consider some features that are common to most of them. Many of these features are illustrated in Figure 10.2, which shows the results of a generic single-subject study. First, the dependent variable (represented on the  y -axis of the graph) is measured repeatedly over time (represented by the  x -axis) at regular intervals. Second, the study is divided into distinct phases, and the participant is tested under one condition per phase. The conditions are often designated by capital letters: A, B, C, and so on. Thus Figure 10.2 represents a design in which the participant was tested first in one condition (A), then tested in another condition (B), and finally retested in the original condition (A). (This is called a reversal design and will be discussed in more detail shortly.)

Another important aspect of single-subject research is that the change from one condition to the next does not usually occur after a fixed amount of time or number of observations. Instead, it depends on the participant’s behaviour. Specifically, the researcher waits until the participant’s behaviour in one condition becomes fairly consistent from observation to observation before changing conditions. This is sometimes referred to as the steady state strategy  (Sidman, 1960) [1] . The idea is that when the dependent variable has reached a steady state, then any change across conditions will be relatively easy to detect. Recall that we encountered this same principle when discussing experimental research more generally. The effect of an independent variable is easier to detect when the “noise” in the data is minimized.

Reversal Designs

The most basic single-subject research design is the  reversal design , also called the  ABA design . During the first phase, A, a  baseline  is established for the dependent variable. This is the level of responding before any treatment is introduced, and therefore the baseline phase is a kind of control condition. When steady state responding is reached, phase B begins as the researcher introduces the treatment. There may be a period of adjustment to the treatment during which the behaviour of interest becomes more variable and begins to increase or decrease. Again, the researcher waits until that dependent variable reaches a steady state so that it is clear whether and how much it has changed. Finally, the researcher removes the treatment and again waits until the dependent variable reaches a steady state. This basic reversal design can also be extended with the reintroduction of the treatment (ABAB), another return to baseline (ABABA), and so on.

The study by Hall and his colleagues was an ABAB reversal design. Figure 10.3 approximates the data for Robbie. The percentage of time he spent studying (the dependent variable) was low during the first baseline phase, increased during the first treatment phase until it leveled off, decreased during the second baseline phase, and again increased during the second treatment phase.

Why is the reversal—the removal of the treatment—considered to be necessary in this type of design? Why use an ABA design, for example, rather than a simpler AB design? Notice that an AB design is essentially an interrupted time-series design applied to an individual participant. Recall that one problem with that design is that if the dependent variable changes after the treatment is introduced, it is not always clear that the treatment was responsible for the change. It is possible that something else changed at around the same time and that this extraneous variable is responsible for the change in the dependent variable. But if the dependent variable changes with the introduction of the treatment and then changes  back  with the removal of the treatment (assuming that the treatment does not create a permanent effect), it is much clearer that the treatment (and removal of the treatment) is the cause. In other words, the reversal greatly increases the internal validity of the study.

There are close relatives of the basic reversal design that allow for the evaluation of more than one treatment. In a  multiple-treatment reversal design , a baseline phase is followed by separate phases in which different treatments are introduced. For example, a researcher might establish a baseline of studying behaviour for a disruptive student (A), then introduce a treatment involving positive attention from the teacher (B), and then switch to a treatment involving mild punishment for not studying (C). The participant could then be returned to a baseline phase before reintroducing each treatment—perhaps in the reverse order as a way of controlling for carryover effects. This particular multiple-treatment reversal design could also be referred to as an ABCACB design.

In an  alternating treatments design , two or more treatments are alternated relatively quickly on a regular schedule. For example, positive attention for studying could be used one day and mild punishment for not studying the next, and so on. Or one treatment could be implemented in the morning and another in the afternoon. The alternating treatments design can be a quick and effective way of comparing treatments, but only when the treatments are fast acting.

Multiple-Baseline Designs

There are two potential problems with the reversal design—both of which have to do with the removal of the treatment. One is that if a treatment is working, it may be unethical to remove it. For example, if a treatment seemed to reduce the incidence of self-injury in a developmentally disabled child, it would be unethical to remove that treatment just to show that the incidence of self-injury increases. The second problem is that the dependent variable may not return to baseline when the treatment is removed. For example, when positive attention for studying is removed, a student might continue to study at an increased rate. This could mean that the positive attention had a lasting effect on the student’s studying, which of course would be good. But it could also mean that the positive attention was not really the cause of the increased studying in the first place. Perhaps something else happened at about the same time as the treatment—for example, the student’s parents might have started rewarding him for good grades.

One solution to these problems is to use a  multiple-baseline design , which is represented in Figure 10.4. In one version of the design, a baseline is established for each of several participants, and the treatment is then introduced for each one. In essence, each participant is tested in an AB design. The key to this design is that the treatment is introduced at a different  time  for each participant. The idea is that if the dependent variable changes when the treatment is introduced for one participant, it might be a coincidence. But if the dependent variable changes when the treatment is introduced for multiple participants—especially when the treatment is introduced at different times for the different participants—then it is extremely unlikely to be a coincidence.

As an example, consider a study by Scott Ross and Robert Horner (Ross & Horner, 2009) [2] . They were interested in how a school-wide bullying prevention program affected the bullying behaviour of particular problem students. At each of three different schools, the researchers studied two students who had regularly engaged in bullying. During the baseline phase, they observed the students for 10-minute periods each day during lunch recess and counted the number of aggressive behaviours they exhibited toward their peers. (The researchers used handheld computers to help record the data.) After 2 weeks, they implemented the program at one school. After 2 more weeks, they implemented it at the second school. And after 2 more weeks, they implemented it at the third school. They found that the number of aggressive behaviours exhibited by each student dropped shortly after the program was implemented at his or her school. Notice that if the researchers had only studied one school or if they had introduced the treatment at the same time at all three schools, then it would be unclear whether the reduction in aggressive behaviours was due to the bullying program or something else that happened at about the same time it was introduced (e.g., a holiday, a television program, a change in the weather). But with their multiple-baseline design, this kind of coincidence would have to happen three separate times—a very unlikely occurrence—to explain their results.

In another version of the multiple-baseline design, multiple baselines are established for the same participant but for different dependent variables, and the treatment is introduced at a different time for each dependent variable. Imagine, for example, a study on the effect of setting clear goals on the productivity of an office worker who has two primary tasks: making sales calls and writing reports. Baselines for both tasks could be established. For example, the researcher could measure the number of sales calls made and reports written by the worker each week for several weeks. Then the goal-setting treatment could be introduced for one of these tasks, and at a later time the same treatment could be introduced for the other task. The logic is the same as before. If productivity increases on one task after the treatment is introduced, it is unclear whether the treatment caused the increase. But if productivity increases on both tasks after the treatment is introduced—especially when the treatment is introduced at two different times—then it seems much clearer that the treatment was responsible.

In yet a third version of the multiple-baseline design, multiple baselines are established for the same participant but in different settings. For example, a baseline might be established for the amount of time a child spends reading during his free time at school and during his free time at home. Then a treatment such as positive attention might be introduced first at school and later at home. Again, if the dependent variable changes after the treatment is introduced in each setting, then this gives the researcher confidence that the treatment is, in fact, responsible for the change.

Data Analysis in Single-Subject Research

In addition to its focus on individual participants, single-subject research differs from group research in the way the data are typically analyzed. As we have seen throughout the book, group research involves combining data across participants. Group data are described using statistics such as means, standard deviations, Pearson’s  r , and so on to detect general patterns. Finally, inferential statistics are used to help decide whether the result for the sample is likely to generalize to the population. Single-subject research, by contrast, relies heavily on a very different approach called  visual inspection . This means plotting individual participants’ data as shown throughout this chapter, looking carefully at those data, and making judgments about whether and to what extent the independent variable had an effect on the dependent variable. Inferential statistics are typically not used.

In visually inspecting their data, single-subject researchers take several factors into account. One of them is changes in the  level  of the dependent variable from condition to condition. If the dependent variable is much higher or much lower in one condition than another, this suggests that the treatment had an effect. A second factor is  trend , which refers to gradual increases or decreases in the dependent variable across observations. If the dependent variable begins increasing or decreasing with a change in conditions, then again this suggests that the treatment had an effect. It can be especially telling when a trend changes directions—for example, when an unwanted behaviour is increasing during baseline but then begins to decrease with the introduction of the treatment. A third factor is  latency , which is the time it takes for the dependent variable to begin changing after a change in conditions. In general, if a change in the dependent variable begins shortly after a change in conditions, this suggests that the treatment was responsible.

In the top panel of Figure 10.5, there are fairly obvious changes in the level and trend of the dependent variable from condition to condition. Furthermore, the latencies of these changes are short; the change happens immediately. This pattern of results strongly suggests that the treatment was responsible for the changes in the dependent variable. In the bottom panel of Figure 10.5, however, the changes in level are fairly small. And although there appears to be an increasing trend in the treatment condition, it looks as though it might be a continuation of a trend that had already begun during baseline. This pattern of results strongly suggests that the treatment was not responsible for any changes in the dependent variable—at least not to the extent that single-subject researchers typically hope to see.

The results of single-subject research can also be analyzed using statistical procedures—and this is becoming more common. There are many different approaches, and single-subject researchers continue to debate which are the most useful. One approach parallels what is typically done in group research. The mean and standard deviation of each participant’s responses under each condition are computed and compared, and inferential statistical tests such as the  t  test or analysis of variance are applied (Fisch, 2001) [3] . (Note that averaging  across  participants is less common.) Another approach is to compute the  percentage of nonoverlapping data  (PND) for each participant (Scruggs & Mastropieri, 2001) [4] . This is the percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition. In the study of Hall and his colleagues, for example, all measures of Robbie’s study time in the first treatment condition were greater than the highest measure in the first baseline, for a PND of 100%. The greater the percentage of nonoverlapping data, the stronger the treatment effect. Still, formal statistical approaches to data analysis in single-subject research are generally considered a supplement to visual inspection, not a replacement for it.

Key Takeaways

• Single-subject research designs typically involve measuring the dependent variable repeatedly over time and changing conditions (e.g., from baseline to treatment) when the dependent variable has reached a steady state. This approach allows the researcher to see whether changes in the independent variable are causing changes in the dependent variable.
• In a reversal design, the participant is tested in a baseline condition, then tested in a treatment condition, and then returned to baseline. If the dependent variable changes with the introduction of the treatment and then changes back with the return to baseline, this provides strong evidence of a treatment effect.
• In a multiple-baseline design, baselines are established for different participants, different dependent variables, or different settings—and the treatment is introduced at a different time on each baseline. If the introduction of the treatment is followed by a change in the dependent variable on each baseline, this provides strong evidence of a treatment effect.
• Single-subject researchers typically analyze their data by graphing them and making judgments about whether the independent variable is affecting the dependent variable based on level, trend, and latency.
• Does positive attention from a parent increase a child’s toothbrushing behaviour?
• Does self-testing while studying improve a student’s performance on weekly spelling tests?
• Does regular exercise help relieve depression?
• Practice: Create a graph that displays the hypothetical results for the study you designed in Exercise 1. Write a paragraph in which you describe what the results show. Be sure to comment on level, trend, and latency.

Long Descriptions

Figure 10.3 long description: Line graph showing the results of a study with an ABAB reversal design. The dependent variable was low during first baseline phase; increased during the first treatment; decreased during the second baseline, but was still higher than during the first baseline; and was highest during the second treatment phase. [Return to Figure 10.3]

Figure 10.4 long description: Three line graphs showing the results of a generic multiple-baseline study, in which different baselines are established and treatment is introduced to participants at different times.

For Baseline 1, treatment is introduced one-quarter of the way into the study. The dependent variable ranges between 12 and 16 units during the baseline, but drops down to 10 units with treatment and mostly decreases until the end of the study, ranging between 4 and 10 units.

For Baseline 2, treatment is introduced halfway through the study. The dependent variable ranges between 10 and 15 units during the baseline, then has a sharp decrease to 7 units when treatment is introduced. However, the dependent variable increases to 12 units soon after the drop and ranges between 8 and 10 units until the end of the study.

For Baseline 3, treatment is introduced three-quarters of the way into the study. The dependent variable ranges between 12 and 16 units for the most part during the baseline, with one drop down to 10 units. When treatment is introduced, the dependent variable drops down to 10 units and then ranges between 8 and 9 units until the end of the study. [Return to Figure 10.4]

Figure 10.5 long description: Two graphs showing the results of a generic single-subject study with an ABA design. In the first graph, under condition A, level is high and the trend is increasing. Under condition B, level is much lower than under condition A and the trend is decreasing. Under condition A again, level is about as high as the first time and the trend is increasing. For each change, latency is short, suggesting that the treatment is the reason for the change.

In the second graph, under condition A, level is relatively low and the trend is increasing. Under condition B, level is a little higher than during condition A and the trend is increasing slightly. Under condition A again, level is a little lower than during condition B and the trend is decreasing slightly. It is difficult to determine the latency of these changes, since each change is rather minute, which suggests that the treatment is ineffective. [Return to Figure 10.5]

• Sidman, M. (1960). Tactics of scientific research: Evaluating experimental data in psychology . Boston, MA: Authors Cooperative. ↵
• Ross, S. W., & Horner, R. H. (2009). Bully prevention in positive behaviour support. Journal of Applied Behaviour Analysis, 42 , 747–759. ↵
• Fisch, G. S. (2001). Evaluating data from behavioural analysis: Visual inspection or statistical models.  Behavioural Processes, 54 , 137–154. ↵
• Scruggs, T. E., & Mastropieri, M. A. (2001). How to summarize single-participant research: Ideas and applications.  Exceptionality, 9 , 227–244. ↵

The researcher waits until the participant’s behaviour in one condition becomes fairly consistent from observation to observation before changing conditions. This way, any change across conditions will be easy to detect.

A study method in which the researcher gathers data on a baseline state, introduces the treatment and continues observation until a steady state is reached, and finally removes the treatment and observes the participant until they return to a steady state.

The level of responding before any treatment is introduced and therefore acts as a kind of control condition.

A baseline phase is followed by separate phases in which different treatments are introduced.

Two or more treatments are alternated relatively quickly on a regular schedule.

A baseline is established for several participants and the treatment is then introduced to each participant at a different time.

The plotting of individual participants’ data, examining the data, and making judgements about whether and to what extent the independent variable had an effect on the dependent variable.

Whether the data is higher or lower based on a visual inspection of the data; a change in the level implies the treatment introduced had an effect.

The gradual increases or decreases in the dependent variable across observations.

The time it takes for the dependent variable to begin changing after a change in conditions.

The percentage of responses in the treatment condition that are more extreme than the most extreme response in a relevant control condition.

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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Single Subject Research

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In this chapter, we describe basic and expert competencies for the use of single subject designs. Basic competencies include repeated observation of behavioral phenomenon of interest, the participant serving as his or her own control, and utilizing measurement and visual analysis strategies that allow one to determine whether change occurs over time. Expert competencies include basic competencies plus repeated demonstration of experimental effect and altering only one variable at a time when introducing treatment. Through the use of numerous examples, we illustrate how single subject research designs lend themselves well to various aspects of research, including the stage of theory development (Level 1 research) and more formal and systematic tests of said theories (Level II and Level III research). We also describe how basic and expert competencies of single subject designs can be incorporated into clinical practice to evaluate effects of intervention. The reader will learn how single subject designs are unique approaches to scientific inquiry due to several features, including repeated observation of the dependent variable(s), replication of treatment effects, intrasubject and intersubject comparisons, visual analysis of individual participant data, and systematic manipulation of independent variable(s). This chapter will likely be useful for clinicians and researchers alike who are interested in answering questions about clinical phenomena in a manner that meets the requirements of the scientific method.

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Freeman, K.A., Lim, M. (2010). Single Subject Research. In: Thomas, J.C., Hersen, M. (eds) Handbook of Clinical Psychology Competencies. Springer, New York, NY. https://doi.org/10.1007/978-0-387-09757-2_15

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In This Article Expand or collapse the "in this article" section Single-Subject Research Design

Introduction, general overviews.

• Basics of Single-Subject Research Design
• Data Collection
• Visual Analysis
• Statistical Analysis
• Meta-analysis and Single-Subject Designs

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Single-Subject Research Design by Timothy J. Lewis , Nicholas Gage LAST REVIEWED: 19 November 2019 LAST MODIFIED: 25 June 2013 DOI: 10.1093/obo/9780199756810-0103

Single-subject research, at times referred to as single-case research, is a quantitative approach to examine functional relationships between baseline and experimental conditions over time within individual subjects. The central features of single-subject research include collecting repeated measures of behavior through direct observation across several sessions, comparing rates or amount of behavior between baseline or typical conditions to an intervention condition, and repeating baseline and intervention phases to note a functional relationship between the introduction and withdrawal of the intervention or independent variable (IV) and the subject’s behavior or dependent variable (DV). Collected observational data are converted to a standard metric and plotted in a line graph and visually analyzed to note variations in trend, level, and variability of the data across baseline and intervention conditions.

First described by Murray Sidman in 1960 ( Sidman 1960 ) to study behavioral principles within psychology and then later expanded to become a central element of applied behavior analysis ( Baer, et al. 1968 ; Baer, et al. 1987 ; Cooper, et al. 2007 ), single-subject research is used across several disciplines including special and general education, social work, communication sciences, and rehabilitative therapies. Horner and colleagues report that more than forty-five scholarly journals accept and publish single-subject research studies ( Horner, et al. 2005 ). See also Campbell and Stanley 1963 , Kazdin and Tuma 1982 , and Kratochwill and Levin 1992 .

Baer, Donald M., Montrose M. Wolf, and Todd R. Risley. 1968. Some current dimensions of applied behavior analysis . Journal of Applied Behavior Analysis 1.1: 91–97.

DOI: 10.1901/jaba.1968.1-91

A seminal article in the field of applied behavior analysis, this article operationally defines the essential features of applied behavior analysis and the experimental conditions under which applied behavior analysis principles can and should be studied.

Baer, Donald M., Montrose M. Wolf, and Todd R. Risley. 1987. Some still-current dimensions of applied behavior analysis . Journal of Applied Behavior Analysis 20.4: 313–327.

DOI: 10.1901/jaba.1987.20-313

A follow-up to the seminal Baer, et al. 1968 , this article provides the foundation for the applied behavior analysis field by outlining the general premise of applied behavior analytic research, which is the foundation of single-subject designs. The paper articulates that analysis of an effect in behavior analytic research, particularly single-subject research, should focus on practical significance that can be observed.

Campbell, Donald T., and Julian C. Stanley. 1963. Experimental and quasi-experimental designs for research . Boston: Houghton Mifflin.

A seminal text on conducting behavioral research, Campbell and Stanley provide a chapter on single-subject designs and the framework for what has become the standard in threats to internal and external validity and how each design accounts for these.

Cooper, John O., Timothy E. Heron, and William L. Heward. 2007. Applied behavior analysis . 2d ed. Upper Saddle River, NJ: Pearson/Merrill-Prentice Hall.

This textbook provides an overview of single-subject research designs and, importantly, details how to assess behavior change using visual analysis in clinical/applied and research contexts within an applied behavior analysis context.

Horner, Robert H., Edward G. Carr, James Halle, Gail McGee, Samuel Odom, and Mark Wolery. 2005. The use of single-subject research to identify evidence-based practices in special education . Exceptional Children 71.2: 165–179.

This article outlines the essential features within and across single-subject research studies to ascertain a minimal level of evidence to brand the practice under investigation “evidence-based.”

Kazdin, Alan E., and A. Hussain Tuma, eds. 1982. Single-case research designs . New Directions for Methodology of Behavioral Science 13. San Francisco: Jossey-Bass.

This edited text provides a rationale and the basic logic of single-subject research within the context of traditional psychological and clinical research. Although dated with respect to current issues and design variations, the text provides an historical context and establishes the roots of single-subject research.

Kratochwill, Thomas R., and Joel R. Levin, eds. 1992. Single-case research design and analysis: New directions for psychology and education . Hillsdale, NJ: Lawrence Erlbaum.

This text provides a series of chapters setting the stage for contemporary issues related to single-subject research including limitations of visual analysis, effect size, statistical analysis, and the appropriateness of meta-analyses across single-subject research. The book ends with a chapter on the current state of the art at the time and recommended future directions.

Sidman, Murray. 1960. Tactics of scientific research: Evaluating experimental data in psychology . New York: Basic Books.

A seminal text that laid the foundation for single-subject research within behavioral psychology.

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Opinion article, the benefits of single-subject research designs and multi-methodological approaches for neuroscience research.

• Department of Behavior Analysis, College of Health and Public Service, University of North Texas, Denton, TX, United States

1. Introduction

The scientific method is neither singular nor fixed; it is an evolving, plural set of processes. It develops and improves through time as methodology rises to meet new challenges ( Lakatos, 1978 ; Hull, 1988 ; Kuhn and Hacking, 2012 ). “It would be wrong to assume that one must stay with a research programme until it has exhausted all its heuristic power, that one must not introduce a rival programme before everybody agrees that the point of degeneration has probably been reached” ( Lakatos, 1978 ). These insights apply not least to experimental design approaches.

For better and for worse, no experimental design comes without limitation. We must accept that the realities of the world cannot be simplistically verified against universal standard procedures; we are free instead to explore how the progressive evolution of experimental design enables new advancement. This paper proposes support for a shift of focus in the methodology of experimental research in neuroscience toward an increased utilization of single-subject experimental designs. I will highlight several supports for this suggestion. Most importantly, single-subject methods can complement group methodologies in two ways: by addressing important points of internal validity and by enabling the inductive process characteristic of quality early research. The power of these approaches has already been somewhat established by key historical neuroscience experiments. Additionally, the individuated nature of subject matter in behavioral neuroscience makes the single-subject approach particularly powerful, and single-subject phases in a research program can decrease time and resource costs in relation to scientific gains.

2. Complimentary research designs

Though the completely randomized group design is considered by many to be the gold standard of evidence ( Meldrum, 2000 ), its limitations as well as ethical and logistical execution difficulties have been noted: e.g., blindness to group heterogeneity, problematic application to individual cases, and experimental weakness in the context of other often-neglected aspects of study design such as group size, randomization, and bias ( Kravitz et al., 2004 ; Grossman and Mackenzie, 2005 ; Williams, 2010 ; Button et al., 2013 ). Thus, the concept of a “gold standard” results not from the uniform superiority of a method, but from an implicit valuing of its relative strengths compared to other designs, all things being equal (even though such things as context, randomization, group size, bias, heterogeneity, etc. are rarely equal). There is an alternative to this approach. Utilizing a wider array of methods across studies can help compensate for the limitations of each and provide flexibility in the face of unequal contexts. In a multi-methodological approach, different experimental designs can be evaluated in terms of complementarity rather than absolute strength. If one experimental design is limited in a particular way, adding another approach that is stronger in that aspect (but perhaps limited in another) can provide a more complete picture. This tactic also implicitly acknowledges that scientific rigor does not proceed only from the single study; replication, systematic replication, and convergent evidence may proceed from a progression of methods.

I suggest adding greater utilization of single-subject design to the already traditionally utilized between-subject and within-subject group designs in neuroscience to achieve this complementarity. The advantages and limitations of these designs are somewhat symmetrical. Overall, single-subject experiments carry with them more finely-focused internal validity because the same subject (together with their array of individual characteristics) serves in both the experimental and control conditions. Unlike in typical within-subject group comparisons, the repetition of comparisons in single-subject designs control for other confounding variables, rendering n = 1 into a true experiment. While an unreplicated single-subject experiment by itself cannot establish external validity, systematic replication of single-subject experiments over the relevant range of individual differences can. On the other hand, group designs cannot demonstrate an effect on an individual level, but within-individual group studies can characterize the generality of effects across large populations in a single properly sampled study, and may be particularly suited to analyzing combined effects of multiple variables ( Kazdin, 1981 ). Single subject and group approaches can also be hybridized to fit a study's goals ( Kazdin, 2011 ). In the following sections, I will describe aspects of each approach that illustrate how the addition of single-subject methodology to neuroscience could be of use. I do not mean to exhaustively describe either methodology, which would be outside the scope of this paper.

2.1. Group designs

Group experimental designs 1 interrogate the effect of an independent variable (IV) by applying that variable to a group of people, other organisms, or other biological units (e.g., neurons) and usually—but not always—comparing an aggregated population measure to that of one or more control groups. These designs require data from multiple individuals (people, animals, cells, etc.). Group experiments with between-group comparisons often assign these individuals to conditions (experimental or control) randomly. Other group experiments (such as a randomized block design) assign individuals to conditions systematically to explicitly balance the groups according to particular pre-considered individual factors. In both cases, the assumption is that if alternative variables influence the dependent variable (DV), they are unlikely to do so differentially across groups. Group experiments with within-subject comparisons expose each individual to both experimental and control conditions at different times and compare the grouped measures between conditions; this approach assures that the groups are truly identical since the same individuals are included in both conditions.

Because they involve multiple individuals, some group designs can provide important information about the generality of an effect across the included population, especially in the case of within-subject group designs. Unfortunately, some often-misused aspects of group designs tend to temper this advantage. For example, restricted inclusion criteria are often necessary to produce clear results. When desired generality involves only such a restricted population (e.g., only acute stroke patients, or only layer IV glutamatergic cortical neurons), this practice carries no disadvantage. However, if the study aims to identify more widely applicable processes, stringent inclusion criteria can produce cleaner but overly conditional results, limiting external validity ( Henrich et al., 2010 ). Further, the analysis approach taken in many group designs that narrowly examines changes in central tendency (such as the mean) of groups can limit the assessment of generality within the sampled population since averaging will wash out heterogeneity of effects. Other aspects of rigor in group designs can also affect external validity (e.g., Kravitz et al., 2004 ; Grossman and Mackenzie, 2005 ; Williams, 2010 ; Button et al., 2013 ).

Another limitation of group design logic is the practical difficulty of balancing individual differences between groups. In the case of between-group comparisons, these difficulties arise from selection bias, mortality, etc. Even well controlled studies can still produce probabilistically imbalanced groups, especially in the small sample sizes often used in neuroscience research ( Button et al., 2013 ). Deliberately balanced groups or post-hoc statistical control may help, but the former introduces a potential problem with true randomization, and the latter is weaker than true experimental control. Within-subject group comparisons implement both experimental and control conditions for each individual in a group and therefore better control for individual differences, however these designs still do not experimentally establish effects within the individual since single manipulations of experimental conditions can be confounded with other changes on an individual level.

The typical focus on parameters such as the mean in the analysis of group designs can also threaten internal as well as external validity, particularly if the experimental question concerns biological or behavioral variables that are highly individually contextualized or developmentally variant. 2 This problem extends from the fact that aggregate measures across populations do not necessarily reflect any of the underlying individuals (e.g., Williams, 2010 ); for example, average brain functional mapping tends not to apply to individual brains ( Brett et al., 2002 ; Dworetsky et al., 2021 ; Fedorenko, 2021 ; Hanson, 2022 ). This kind of problem is particularly amplified in the study of human behavior and brain sciences, which both tend to be highly idiosyncratic. In these cases, aggregated measures can mask key heterogeneity including contradictory effects of IVs. This can complicate the application of results to individuals: an issue especially relevant in clinical research ( Sidman, 1960 ; Williams, 2010 ). Relatedly, the estimation of population-based effect size provides scant information with which to estimate effects and relevance for an individual. Post-hoc statistical analysis may help to tease out these issues, but verification still requires new experimentation. True generality of a scientific insight requires not only that effects occur with reasonable replicability across individuals, but that a reasonable range of conditions that would alter the effect can be predicted: a difficult point to discern in group studies. Thus, while group designs carry advantages insofar as they can be used to characterize effects across a whole population in a single experiment, those advantages can be and often are subverted. Perhaps counter-intuitively, single-subject approaches can be ideal for methodically discovering the common processes that underlie diversity within a population, which have made it particularly powerful in producing generalizable results (see next section).

2.2. Single-subject designs

Single-subject designs compare experimental to control conditions repeatedly over time within the same individual. Like group designs with within-subject comparisons, single-subject designs can control for individual differences, which remain constant. However, single-subject designs take individual control to a new level. Since other confounding changes may coincide with a single change in the IV, single-subject designs also require multiple implementations of the same manipulation so that the comparison can be repeated within the individual, controlling for the coincidental confounds of a single condition change. Additionally, single-subject designs measure multiple data points through time within each condition before any experimental change occurs to assess pre-existing variation and trends in comparisons with the subsequent condition. Of course, a single-subject experiment without inter-individual replication has no generality—systematic replications across relevant individual characteristics and contexts are generally required to establish external validity. However, the typical group design also often requires similar replication to establish the same validity, and unlike group designs single-subject studies are also capable of rigorously interrogating even the rarest of effects.

Because single-subject experiments deal well with individual effects, they are often used in clinical and closely applied disciplines, e.g., education ( Alnahdi, 2015 ), rehabilitation and therapy ( Tankersley et al., 2006 ), speech and language ( Byiers et al., 2012 ), implementation science ( Miller et al., 2020 ), neuropsychology ( Perdices and Tate, 2009 ), biomedicine ( Janosky et al., 2009 ), and behavior analysis ( Perone, 1991 ). However, the single-subject design is not limited to clinical applications or to the study of rare effects; it can also be used for the study of generalizable individual processes via systematic replication. Serial replications often enable detailed distillation of both common and uncommon relevant factors across individuals, making the approach particularly powerful for identifying generalizable processes that account for within-population diversity (although this process can be challenging even on the single-subject level; see Kazdin, 1981 ). Single-subject methodology has historically established some of the most generalizable findings in psychology including the principles of Pavlovian and operant conditioning ( Iversen, 2013 ). Establishing this generalizability requires a research program rather than a single study, however since each replication (and comparisons between them) can potentially add information about important contextual variables, systematic progression toward generality can be more efficient than in one-shot group studies.

Single-subject designs are sometimes confused with within-subject group comparisons or n-of-1 case studies, neither of which usually include multiple implementations of each condition for any one individual. N-of-1 case studies sometimes make no manipulation at all or may make a single comparison (as with an embedded AB design or pre-post observation), which can at best serve as a quasi-experiment ( Kazdin and Tuma, 1982 ). A single subject design, in contrast, will include many repeated condition changes and collect multiple data points inside each condition (as in the ABABABAB design as well as many others, see Perone, 1991 ). As is the case for group designs, the quality of evidence in a single-subject experiment increases with the number of instances in which the experimental condition is compared to a control condition; the more comparisons occur, the less likely it is that an alternative explanation will have tracked with the manipulation. A strong single-subject design will require a minimum of three IV implementations for the same individual (i.e., ABABAB, with multiple data points for each A and each B), and a robust effect will require many more.

Because single-subject designs implement conditions across time, they are susceptible to some important limitations including sequence, maturation, and exposure effects. The need to consider within-condition stability, serial dependence in data sets, reversibility, carryover effects, and long experimental time courses can also complicate these designs. Still, manipulations common in neuroscience research is often amenable to these challenges ( Soto, 2020 ). Single-subject designs for phenomena that are not reversable (such as skill acquisition) can also be studied using approaches such as the within-subject multiple baseline. Multiple baselines experiments across behaviors, across cell populations, or across homotopic brain regions may be reasonable if independence can be established ( Soto, 2020 ). A variety of single-subject methods are available that can help to address the unique strengths and limitations in single-subject methodology; the reader is encouraged to explore the variety of designs that cannot be enumerated in the scope of the current paper ( Horner and Baer, 1978 ; Hains and Baer, 1989 ; Perone, 1991 ; Holcombe et al., 1994 ; Edgington, 1996 ; Kratochwill et al., 2010 ; Ward-Horner and Sturmey, 2010 ).

2.3. A note about statistical methods

Issues relating to statistical analysis are commonly erroneously conflated with group experimental design per se . Problems with the frequentist statistical approach commonly used in group designs has greatly impacted its efficacy; frequentist statistical methods carry limitations that have been treated thoroughly elsewhere [e.g., the generic problems with null-hypothesis statistical testing NHST ( Branch, 2014 ), the inappropriate use of frequentist statistics contrary to their best use and design ( Moen et al., 2016 ; Wasserstein and Lazar, 2016 ), and the inappropriate reliance on p -values ( Wasserstein and Lazar, 2016 )]. I do not expand on these issues in my summary of group design because such critiques need not apply to all between-group comparisons. The use and applicability of analysis techniques are separable from the experimental utility of group designs in general, which are not limited to inferential statistics. Group experiments can also be analyzed using alternative, less problematic statistical approaches such as the probability of replication statistic or P-rep ( Killeen, 2015 ) and Bayesian approaches ( Berry and Stangl, 2018 ). Well-considered statistical best practices for various forms of group analysis (e.g., Moen et al., 2016 ) can help a researcher to address limitations.

The conflation of statistical methods with group designs has also led to the misconception that single-subject designs cannot be analyzed statistically. Most scientists have less familiarity with statistical analyses appropriate for use in single-subject designs and the serially-dependent data sets that they produce. While pronounced effects uncovered in single-subject experiments can often be clearly detected using appropriate visual analysis, rigorous statistical methods applicable to single-subject designs are also available (e.g., Parker and Brossart, 2003 ; Scruggs and Mastropieri, 2013 ).

3. Single-subject design and the inductive process

The advantages highlighted above suggest not only compatibility between single-subject and group approaches, but a potential advantage conferred by an order of operations between methods. Early in the research process, inductive inference based on single-subject manipulations are ideal to generate likely and testable abstractions ( Russell, 1962 ). Using single-subject approaches for this inductive phase requires fewer resources compared to fully powered group approaches and can be more rigorous than small-n group pilots. An effect can be isolated in one individual, then systematically replicated across relevant differences and contexts until it fails to replicate, at which time explanatory variables can be adjusted until replicated results are produced. The altered experiment can then be analyzed in comparison to previous experiments to form a more general understanding that can be tested in a new series of experiments. After sufficient systematic replication, hybrid and group designs can assess the extent to which inductively and contextually informed abstractions generalize across the widest relevant populations.

4. Precedent of within-subject methods

Although within-subject group experiments are common in human neuroscience and psychology, e.g., Greenwald (1976) and Crockett and Fehr (2014) , full-fledged single-subject designs are virtually unknown in many subfields. Still, high-impact neuroscience experiments have occasionally either implicitly or deliberately implemented within-subject reversals, demonstrating the power of these approaches to advance the science. To name just a few high-impact examples, Hodgkin et al. (1952) classic work on voltage clamping utilizing the giant squid neuron involved multiple parametric IV implementations on single neurons. The discovery of circadian rhythms in humans also involved systematic single-subject experiments comparing circadian patterns at various light intensities, light-dark schedules, and control contexts, which allowed investigators to establish that outside entrainment overrode the cycle-altering effects of different light intensities ( Aschoff, 1965 ). This fruitful precedent of single-subject-like experiments at the very foundation of historical neuroscience together with the well-established efficacy of single-subject design in other fields imply that the wider adoption of the full methodology can succeed.

5. Single-subject design and individuality in neuroscience

As suggested earlier in this paper, individual variation dominates the scene in behavioral and brain sciences and constitutes a basic part of the evolutionary selection processes that shaped them. In human neuroscience, individual developmental and experience-dependent variation are of particular importance. Human brains are so individuated that functional units across individuals cannot be discerned via typical anatomical landmarks, and even between-group designs often need to utilize individuated or normalized measures ( Brett et al., 2002 ; Dworetsky et al., 2021 ; Fedorenko, 2021 ; Hanson, 2022 ). A shift toward including rigorous single-subject research therefore holds particular promise for the field. For example, systematically replicated individual analyses of functional brain networks and their dynamics may more easily lead to generalizable ideas about how they develop and change, and these purportedly general processes could in turn be tested across individual contexts.

6. Time and resource logistics

Group methodology often requires great time and resources in order to produce properly powered experiments. This can lead to problems with rigor, particularly in contexts of limited funding and publish-or-perish job demands ( Bernard, 2016 ; Button, 2016 ). Especially in early stages of research, single-subject methodology enables experimenters to investigate effects more critically and rigorously for each subject, to more quickly answer and refine questions in individuals first before systematically exploring the generality of findings or the importance of context, and to do so in a cost-effective way. Thus, both cost and rigor could be served by conscientiously adding single-subject methodology to the neuroscience toolbelt.

7. Suggestions for neuroscience subfields that could benefit

Cognitive, behavioral, social, and developmental neuroscience each deal with individual variation in which later stages are often dependent on earlier stages and seek to identify generalizable processes that produce variant outcomes: a task for which the single-subject and multi-method approach is ideal. Neurology and clinical neuroscience also stand to benefit from a more rigorous tool for investigating clinical cases or rare phenomena. While I do not mean to suggest that the method's utility should be limited to these subfields, the potential benefit seems particularly pronounced.

8. Discussion

In summary, greater utilization of single-subject research in human neuroscience can complement current methods by balancing the progression toward internal and then external validity and enabling a low-cost and flexible inductive process that can strengthen subsequent between-group studies. These methods have already been incidentally utilized in important neuroscience research, and they could be an even more powerful, thorough, cost-efficient, rigorous, and deliberate ingredient of an ideal approach to studying the generalizable processes that account for the highly individuated human brain and the behavior that it enables.

Author contributions

AB conceived of and wrote this manuscript.

AB was funded by the Beatrice H. Barrett endowment for research on neuro-operant relations.

Acknowledgments

The author would like to thank Daniele Ortu, Ph.D. for helpful comments.

Conflict of interest

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

1. ^ This discussion intentionally excludes assignment to groups based on non-manipulable variables because of the qualitative difference between correlational approaches and true experimental approaches that manipulates the IV. The former carries a very different set of considerations outside the scope of this paper.

2. ^ If the biological process under investigation actually occurs at the population level (e.g. natural selection), the population parameter precisely applies to the question at hand. However, group comparisons are more often used to study processes that function on the individual level.

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Keywords: single-subject, experimental design, neuroscience, within-subject, validity

Citation: Becker A (2023) The benefits of single-subject research designs and multi-methodological approaches for neuroscience research. Front. Hum. Neurosci. 17:1190412. doi: 10.3389/fnhum.2023.1190412

Received: 20 March 2023; Accepted: 27 September 2023; Published: 25 October 2023.

Reviewed by:

Copyright © 2023 Becker. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: April Becker, april.becker@unt.edu

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Chapter 12:  Single-Subject Designs

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Introduction.

• STRUCTURE OF SINGLE-SUBJECT DESIGNS
• THE TARGET BEHAVIOR
• RELIABILITY
• EXPERIMENTAL CONTROL: LIMITATIONS OF THE A-B DESIGN
• WITHDRAWAL DESIGNS
• MULTIPLE BASELINE DESIGNS
• DESIGNS WITH MULTIPLE TREATMENTS
• DATA ANALYSIS IN SINGLE-SUBJECT RESEARCH
• GENERALIZATION OF FINDINGS
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The demands of traditional experimental methods are often seen as barriers to clinical inquiry for several reasons. Because of their rigorous structure, experiments require control groups and large numbers of homogenous subjects, often unavailable in clinical settings. In addition, group studies typically take measurements at only two or three points in time, potentially missing variations in response that occur over time. Finally, the experimental model deals with group averages and generalizations across individuals, which may not allow the researcher to differentiate characteristics of those patients who responded favorably to treatment from those who did not improve. Therefore, although generalizations are important for explaining behavioral phenomena, clinicians understand that group performance is relevant only if it can be used to understand and predict individual performance.

To illustrate this dilemma, consider a study that was done to determine if the occurrence of stuttering would be different if adults read aloud at "usual" or "fast as possible" rates. 1 A group of 20 adults was tested, and no significant difference was seen between the two conditions based on a comparison of group means. However, a closer look at individual results showed that 8 subjects actually decreased their frequency of stuttering, one didn't change, and 11 demonstrated an increase during the faster speaking condition. The group analysis obscured these individual variations. 2 These results could mean that there is no consistent effect, but they may also point to specific subject characteristics that account for the differences.

Single-subject designs ∗ provide an alternative approach that allows us to draw conclusions about the effects of treatment based on the responses of a single patient under controlled conditions. Through a variety of strategies and structures, these designs provide a clinically viable, controlled experimental approach to the study of a single case or several subjects, and the flexibility to observe change under ongoing treatment conditions. Given the focus of evidence-based practice on clinical decision making for individual patients, these designs are especially useful.

Single-subject designs require the same attention to logical design and control as other experimental designs, based on a research hypothesis that indicates the expected relationship between an independent and dependent variable and specific operational definitions that address reliability and validity. The independent variable is the intervention. The dependent variable is the patient response, defined as a target behavior that is observable, quantifiable, and a valid indicator of treatment effectiveness.

Single-subject designs can be used to study comparisons between several treatments, between components of treatments, or between treatment and no-treatment conditions. The purpose of this chapter is to describe a variety of single-subject designs and to explore issues associated with their structure, application and interpretation.

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Single-Case Design, Analysis, and Quality Assessment for Intervention Research

Michele a. lobo.

1 Biomechanics & Movement Science Program, Department of Physical Therapy, University of Delaware, Newark, DE, USA

Mariola Moeyaert

2 Division of Educational Psychology & Methodology, State University of New York at Albany, Albany, NY, USA

Andrea Baraldi Cunha

Iryna babik, background and purpose.

The purpose of this article is to describe single-case studies, and contrast them with case studies and randomized clinical trials. We will highlight current research designs, analysis techniques, and quality appraisal tools relevant for single-case rehabilitation research.

Summary of Key Points

Single-case studies can provide a viable alternative to large group studies such as randomized clinical trials. Single case studies involve repeated measures, and manipulation of and independent variable. They can be designed to have strong internal validity for assessing causal relationships between interventions and outcomes, and external validity for generalizability of results, particularly when the study designs incorporate replication, randomization, and multiple participants. Single case studies should not be confused with case studies/series (ie, case reports), which are reports of clinical management of one patient or a small series of patients.

Recommendations for Clinical Practice

When rigorously designed, single-case studies can be particularly useful experimental designs in a variety of situations, even when researcher resources are limited, studied conditions have low incidences, or when examining effects of novel or expensive interventions. Readers will be directed to examples from the published literature in which these techniques have been discussed, evaluated for quality, and implemented.

Introduction

The purpose of this article is to present current tools and techniques relevant for single-case rehabilitation research. Single-case (SC) studies have been identified by a variety of names, including “n of 1 studies” and “single-subject” studies. The term “single-case study” is preferred over the previously mentioned terms because previous terms suggest these studies include only one participant. In fact, as will be discussed below, for purposes of replication and improved generalizability, the strongest SC studies commonly include more than one participant.

A SC study should not be confused with a “case study/series “ (also called “case report”. In a typical case study/series, a single patient or small series of patients is involved, but there is not a purposeful manipulation of an independent variable, nor are there necessarily repeated measures. Most case studies/series are reported in a narrative way while results of SC studies are presented numerically or graphically. 1 , 2 This article defines SC studies, contrasts them with randomized clinical trials, discusses how they can be used to scientifically test hypotheses, and highlights current research designs, analysis techniques, and quality appraisal tools that may be useful for rehabilitation researchers.

In SC studies, measurements of outcome (dependent variables) are recorded repeatedly for individual participants across time and varying levels of an intervention (independent variables). 1 – 5 These varying levels of intervention are referred to as “phases” with one phase serving as a baseline or comparison, so each participant serves as his/her own control. 2 In contrast to case studies and case series in which participants are observed across time without experimental manipulation of the independent variable, SC studies employ systematic manipulation of the independent variable to allow for hypothesis testing. 1 , 6 As a result, SC studies allow for rigorous experimental evaluation of intervention effects and provide a strong basis for establishing causal inferences. Advances in design and analysis techniques for SC studies observed in recent decades have made SC studies increasingly popular in educational and psychological research. Yet, the authors believe SC studies have been undervalued in rehabilitation research, where randomized clinical trials (RCTs) are typically recommended as the optimal research design to answer questions related to interventions. 7 In reality, there are advantages and disadvantages to both SC studies and RCTs that should be carefully considered in order to select the best design to answer individual research questions. While there are a variety of other research designs that could be utilized in rehabilitation research, only SC studies and RCTs are discussed here because SC studies are the focus of this article and RCTs are the most highly recommended design for intervention studies. 7

When designed and conducted properly, RCTs offer strong evidence that changes in outcomes may be related to provision of an intervention. However, RCTs require monetary, time, and personnel resources that many researchers, especially those in clinical settings, may not have available. 8 RCTs also require access to large numbers of consenting participants that meet strict inclusion and exclusion criteria that can limit variability of the sample and generalizability of results. 9 The requirement for large participant numbers may make RCTs difficult to perform in many settings, such as rural and suburban settings, and for many populations, such as those with diagnoses marked by lower prevalence. 8 To rely exclusively on RCTs has the potential to result in bodies of research that are skewed to address the needs of some individuals while neglecting the needs of others. RCTs aim to include a large number of participants and to use random group assignment to create study groups that are similar to one another in terms of all potential confounding variables, but it is challenging to identify all confounding variables. Finally, the results of RCTs are typically presented in terms of group means and standard deviations that may not represent true performance of any one participant. 10 This can present as a challenge for clinicians aiming to translate and implement these group findings at the level of the individual.

SC studies can provide a scientifically rigorous alternative to RCTs for experimentally determining the effectiveness of interventions. 1 , 2 SC studies can assess a variety of research questions, settings, cases, independent variables, and outcomes. 11 There are many benefits to SC studies that make them appealing for intervention research. SC studies may require fewer resources than RCTs and can be performed in settings and with populations that do not allow for large numbers of participants. 1 , 2 In SC studies, each participant serves as his/her own comparison, thus controlling for many confounding variables that can impact outcome in rehabilitation research, such as gender, age, socioeconomic level, cognition, home environment, and concurrent interventions. 2 , 11 Results can be analyzed and presented to determine whether interventions resulted in changes at the level of the individual, the level at which rehabilitation professionals intervene. 2 , 12 When properly designed and executed, SC studies can demonstrate strong internal validity to determine the likelihood of a causal relationship between the intervention and outcomes and external validity to generalize the findings to broader settings and populations. 2 , 12 , 13

Single Case Research Designs for Intervention Research

There are a variety of SC designs that can be used to study the effectiveness of interventions. Here we discuss: 1) AB designs, 2) reversal designs, 3) multiple baseline designs, and 4) alternating treatment designs, as well as ways replication and randomization techniques can be used to improve internal validity of all of these designs. 1 – 3 , 12 – 14

The simplest of these designs is the AB Design 15 ( Figure 1 ). This design involves repeated measurement of outcome variables throughout a baseline control/comparison phase (A ) and then throughout an intervention phase (B). When possible, it is recommended that a stable level and/or rate of change in performance be observed within the baseline phase before transitioning into the intervention phase. 2 As with all SC designs, it is also recommended that there be a minimum of five data points in each phase. 1 , 2 There is no randomization or replication of the baseline or intervention phases in the basic AB design. 2 Therefore, AB designs have problems with internal validity and generalizability of results. 12 They are weak in establishing causality because changes in outcome variables could be related to a variety of other factors, including maturation, experience, learning, and practice effects. 2 , 12 Sample data from a single case AB study performed to assess the impact of Floor Play intervention on social interaction and communication skills for a child with autism 15 are shown in Figure 1 .

An example of results from a single-case AB study conducted on one participant with autism; two weeks of observation (baseline phase A) were followed by seven weeks of Floor Time Play (intervention phase B). The outcome measure Circles of Communications (reciprocal communication with two participants responding to each other verbally or nonverbally) served as a behavioral indicator of the child’s social interaction and communication skills (higher scores indicating better performance). A statistically significant improvement in Circles of Communication was found during the intervention phase as compared to the baseline. Note that although a stable baseline is recommended for SC studies, it is not always possible to satisfy this requirement, as you will see in Figures 1 – 4 . Data were extracted from Dionne and Martini (2011) 15 utilizing Rohatgi’s WebPlotDigitizer software. 78

If an intervention does not have carry-over effects, it is recommended to use a Reversal Design . 2 For example, a reversal A 1 BA 2 design 16 ( Figure 2 ) includes alternation of the baseline and intervention phases, whereas a reversal A 1 B 1 A 2 B 2 design 17 ( Figure 3 ) consists of alternation of two baseline (A 1 , A 2 ) and two intervention (B 1 , B 2 ) phases. Incorporating at least four phases in the reversal design (i.e., A 1 B 1 A 2 B 2 or A 1 B 1 A 2 B 2 A 3 B 3 …) allows for a stronger determination of a causal relationship between the intervention and outcome variables, because the relationship can be demonstrated across at least three different points in time – change in outcome from A 1 to B 1 , from B 1 to A 2 , and from A 2 to B 2 . 18 Before using this design, however, researchers must determine that it is safe and ethical to withdraw the intervention, especially in cases where the intervention is effective and necessary. 12

An example of results from a single-case A 1 BA 2 study conducted on eight participants with stable multiple sclerosis (data on three participants were used for this example). Four weeks of observation (baseline phase A 1 ) were followed by eight weeks of core stability training (intervention phase B), then another four weeks of observation (baseline phase A 2 ). Forward functional reach test (the maximal distance the participant can reach forward or lateral beyond arm’s length, maintaining a fixed base of support in the standing position; higher scores indicating better performance) significantly improved during intervention for Participants 1 and 3 without further improvement observed following withdrawal of the intervention (during baseline phase A 2 ). Data were extracted from Freeman et al. (2010) 16 utilizing Rohatgi’s WebPlotDigitizer software. 78

An example of results from a single-case A 1 B 1 A 2 B 2 study conducted on two participants with severe unilateral neglect after a right-hemisphere stroke. Two weeks of conventional treatment (baseline phases A 1, A 2 ) alternated with two weeks of visuo-spatio-motor cueing (intervention phases B 1 , B 2 ). Performance was assessed in two tests of lateral neglect, the Bells Cancellation Test (Figure A; lower scores indicating better performance) and the Line Bisection Test (Figure B; higher scores indicating better performance). There was a statistically significant intervention-related improvement in participants’ performance on the Line Bisection Test, but not on the Bells Test. Data were extracted from Samuel at al. (2000) 17 utilizing Rohatgi’s WebPlotDigitizer software. 78

A recent study used an ABA reversal SC study to determine the effectiveness of core stability training in 8 participants with multiple sclerosis. 16 During the first four weekly data collections, the researchers ensured a stable baseline, which was followed by eight weekly intervention data points, and concluded with four weekly withdrawal data points. Intervention significantly improved participants’ walking and reaching performance ( Figure 2 ). 16 This A 1 BA 2 design could have been strengthened by the addition of a second intervention phase for replication (A 1 B 1 A 2 B 2 ). For instance, a single-case A 1 B 1 A 2 B 2 withdrawal design aimed to assess the efficacy of rehabilitation using visuo-spatio-motor cueing for two participants with severe unilateral neglect after a severe right-hemisphere stroke. 17 Each phase included 8 data points. Statistically significant intervention-related improvement was observed, suggesting that visuo-spatio-motor cueing might be promising for treating individuals with very severe neglect ( Figure 3 ). 17

The reversal design can also incorporate a cross over design where each participant experiences more than one type of intervention. For instance, a B 1 C 1 B 2 C 2 design could be used to study the effects of two different interventions (B and C) on outcome measures. Challenges with including more than one intervention involve potential carry-over effects from earlier interventions and order effects that may impact the measured effectiveness of the interventions. 2 , 12 Including multiple participants and randomizing the order of intervention phase presentations are tools to help control for these types of effects. 19

When an intervention permanently changes an individual’s ability, a return to baseline performance is not feasible and reversal designs are not appropriate. Multiple Baseline Designs (MBDs) are useful in these situations ( Figure 4 ). 20 MBDs feature staggered introduction of the intervention across time: each participant is randomly assigned to one of at least 3 experimental conditions characterized by the length of the baseline phase. 21 These studies involve more than one participant, thus functioning as SC studies with replication across participants. Staggered introduction of the intervention allows for separation of intervention effects from those of maturation, experience, learning, and practice. For example, a multiple baseline SC study was used to investigate the effect of an anti-spasticity baclofen medication on stiffness in five adult males with spinal cord injury. 20 The subjects were randomly assigned to receive 5–9 baseline data points with a placebo treatment prior to the initiation of the intervention phase with the medication. Both participants and assessors were blind to the experimental condition. The results suggested that baclofen might not be a universal treatment choice for all individuals with spasticity resulting from a traumatic spinal cord injury ( Figure 4 ). 20

An example of results from a single-case multiple baseline study conducted on five participants with spasticity due to traumatic spinal cord injury. Total duration of data collection was nine weeks. The first participant was switched from placebo treatment (baseline) to baclofen treatment (intervention) after five data collection sessions, whereas each consecutive participant was switched to baclofen intervention at the subsequent sessions through the ninth session. There was no statistically significant effect of baclofen on viscous stiffness at the ankle joint. Data were extracted from Hinderer at al. (1990) 20 utilizing Rohatgi’s WebPlotDigitizer software. 78

The impact of two or more interventions can also be assessed via Alternating Treatment Designs (ATDs) . In ATDs, after establishing the baseline, the experimenter exposes subjects to different intervention conditions administered in close proximity for equal intervals ( Figure 5 ). 22 ATDs are prone to “carry-over effects” when the effects of one intervention influence the observed outcomes of another intervention. 1 As a result, such designs introduce unique challenges when attempting to determine the effects of any one intervention and have been less commonly utilized in rehabilitation. An ATD was used to monitor disruptive behaviors in the school setting throughout a baseline followed by an alternating treatment phase with randomized presentation of a control condition or an exercise condition. 23 Results showed that 30 minutes of moderate to intense physical activity decreased behavioral disruptions through 90 minutes after the intervention. 23 An ATD was also used to compare the effects of commercially available and custom-made video prompts on the performance of multi-step cooking tasks in four participants with autism. 22 Results showed that participants independently performed more steps with the custom-made video prompts ( Figure 5 ). 22

An example of results from a single case alternating treatment study conducted on four participants with autism (data on two participants were used for this example). After the observation phase (baseline), effects of commercially available and custom-made video prompts on the performance of multi-step cooking tasks were identified (treatment phase), after which only the best treatment was used (best treatment phase). Custom-made video prompts were most effective for improving participants’ performance of multi-step cooking tasks. Data were extracted from Mechling at al. (2013) 22 utilizing Rohatgi’s WebPlotDigitizer software. 78

Regardless of the SC study design, replication and randomization should be incorporated when possible to improve internal and external validity. 11 The reversal design is an example of replication across study phases. The minimum number of phase replications needed to meet quality standards is three (A 1 B 1 A 2 B 2 ), but having four or more replications is highly recommended (A 1 B 1 A 2 B 2 A 3 …). 11 , 14 In cases when interventions aim to produce lasting changes in participants’ abilities, replication of findings may be demonstrated by replicating intervention effects across multiple participants (as in multiple-participant AB designs), or across multiple settings, tasks, or service providers. When the results of an intervention are replicated across multiple reversals, participants, and/or contexts, there is an increased likelihood a causal relationship exists between the intervention and the outcome. 2 , 12

Randomization should be incorporated in SC studies to improve internal validity and the ability to assess for causal relationships among interventions and outcomes. 11 In contrast to traditional group designs, SC studies often do not have multiple participants or units that can be randomly assigned to different intervention conditions. Instead, in randomized phase-order designs , the sequence of phases is randomized. Simple or block randomization is possible. For example, with simple randomization for an A 1 B 1 A 2 B 2 design, the A and B conditions are treated as separate units and are randomly assigned to be administered for each of the pre-defined data collection points. As a result, any combination of A-B sequences is possible without restrictions on the number of times each condition is administered or regard for repetitions of conditions (e.g., A 1 B 1 B 2 A 2 B 3 B 4 B 5 A 3 B 6 A 4 A 5 A 6 ). With block randomization for an A 1 B 1 A 2 B 2 design, two conditions (e.g., A and B) would be blocked into a single unit (AB or BA), randomization of which to different time periods would ensure that each condition appears in the resulting sequence more than two times (e.g., A 1 B 1 B 2 A 2 A 3 B 3 A 4 B 4 ). Note that AB and reversal designs require that the baseline (A) always precedes the first intervention (B), which should be accounted for in the randomization scheme. 2 , 11

In randomized phase start-point designs , the lengths of the A and B phases can be randomized. 2 , 11 , 24 – 26 For example, for an AB design, researchers could specify the number of time points at which outcome data will be collected, (e.g., 20), define the minimum number of data points desired in each phase (e.g., 4 for A, 3 for B), and then randomize the initiation of the intervention so that it occurs anywhere between the remaining time points (points 5 and 17 in the current example). 27 , 28 For multiple-baseline designs, a dual-randomization, or “regulated randomization” procedure has been recommended. 29 If multiple-baseline randomization depends solely on chance, it could be the case that all units are assigned to begin intervention at points not really separated in time. 30 Such randomly selected initiation of the intervention would result in the drastic reduction of the discriminant and internal validity of the study. 29 To eliminate this issue, investigators should first specify appropriate intervals between the start points for different units, then randomly select from those intervals, and finally randomly assign each unit to a start point. 29

Single Case Analysis Techniques for Intervention Research

The What Works Clearinghouse (WWC) single-case design technical documentation provides an excellent overview of appropriate SC study analysis techniques to evaluate the effectiveness of intervention effects. 1 , 18 First, visual analyses are recommended to determine whether there is a functional relation between the intervention and the outcome. Second, if evidence for a functional effect is present, the visual analysis is supplemented with quantitative analysis methods evaluating the magnitude of the intervention effect. Third, effect sizes are combined across cases to estimate overall average intervention effects which contributes to evidence-based practice, theory, and future applications. 2 , 18

Visual Analysis

Traditionally, SC study data are presented graphically. When more than one participant engages in a study, a spaghetti plot showing all of their data in the same figure can be helpful for visualization. Visual analysis of graphed data has been the traditional method for evaluating treatment effects in SC research. 1 , 12 , 31 , 32 The visual analysis involves evaluating level, trend, and stability of the data within each phase (i.e., within-phase data examination) followed by examination of the immediacy of effect, consistency of data patterns, and overlap of data between baseline and intervention phases (i.e., between-phase comparisons). When the changes (and/or variability) in level are in the desired direction, are immediate, readily discernible, and maintained over time, it is concluded that the changes in behavior across phases result from the implemented treatment and are indicative of improvement. 33 Three demonstrations of an intervention effect are necessary for establishing a functional relation. 1

Within-phase examination

Level, trend, and stability of the data within each phase are evaluated. Mean and/or median can be used to report the level, and trend can be evaluated by determining whether the data points are monotonically increasing or decreasing. Within-phase stability can be evaluated by calculating the percentage of data points within 15% of the phase median (or mean). The stability criterion is satisfied if about 85% (80% – 90%) of the data in a phase fall within a 15% range of the median (or average) of all data points for that phase. 34

Between-phase examination

Immediacy of effect, consistency of data patterns, and overlap of data between baseline and intervention phases are evaluated next. For this, several nonoverlap indices have been proposed that all quantify the proportion of measurements in the intervention phase not overlapping with the baseline measurements. 35 Nonoverlap statistics are typically scaled as percent from 0 to 100, or as a proportion from 0 to 1. Here, we briefly discuss the Nonoverlap of All Pairs ( NAP ), 36 the Extended Celeration Line ( ECL ), the Improvement Rate Difference ( IRD) , 37 and the TauU and the TauU-adjusted, TauU adj , 35 as these are the most recent and complete techniques. We also examine the Percentage of Nonoverlapping Data ( PND ) 38 and the Two Standard Deviations Band Method, as these are frequently used techniques. In addition, we include the Percentage of Nonoverlapping Corrected Data ( PNCD ) – an index applying to the PND after controlling for baseline trend. 39

Nonoverlap of all pairs (NAP)

Each baseline observation can be paired with each intervention phase observation to make n pairs (i.e., N = n A * n B ). Count the number of overlapping pairs, n o , counting all ties as 0.5. Then define the percent of the pairs that show no overlap. Alternatively, one can count the number of positive (P), negative (N), and tied (T) pairs 2 , 36 :

Extended Celeration Line (ECL)

ECL or split middle line allows control for a positive Phase A trend. Nonoverlap is defined as the proportion of Phase B ( n b ) data that are above the median trend plotted from Phase A data ( n B< sub > Above Median trend A </ sub > ), but then extended into Phase B: ECL = n B Above Median trend A n b ∗ 100

As a consequence, this method depends on a straight line and makes an assumption of linearity in the baseline. 2 , 12

Improvement rate difference (IRD)

This analysis is conceptualized as the difference in improvement rates (IR) between baseline ( IR B ) and intervention phases ( IR T ). 38 The IR for each phase is defined as the number of “improved data points” divided by the total data points in that phase. IRD, commonly employed in medical group research under the name of “risk reduction” or “risk difference” attempts to provide an intuitive interpretation for nonoverlap and to make use of an established, respected effect size, IR B - IR B , or the difference between two proportions. 37

TauU and TauU adj

Each baseline observation can be paired with each intervention phase observation to make n pairs (i.e., n = n A * n B ). Count the number of positive (P), negative (N), and tied (T) pairs, and use the following formula: TauU = P - N P + N + τ

The TauU adj is an adjustment of TauU for monotonic trend in baseline. Each baseline observation can be paired with each intervention phase observation to make n pairs (i.e., n = n A * n B ). Each baseline observation can be paired with all later baseline observations (n A *(n A -1)/2). 2 , 35 Then the baseline trend can be computed: TauU adf = P - N - S trend P + N + τ ; S trend = P A – NA

Online calculators might assist researchers in obtaining the TauU and TauU adjusted coefficients ( http://www.singlecaseresearch.org/calculators/tau-u ).

Percentage of nonoverlapping data (PND)

If anticipating an increase in the outcome, locate the highest data point in the baseline phase and then calculate the percent of the intervention phase data points that exceed it. If anticipating a decrease in the outcome, find the lowest data point in the baseline phase and then calculate the percent of the treatment phase data points that are below it: PND = n B Overlap A n b ∗ 100 . A PND < 50 would mark no observed effect, PND = 50–70 signifies a questionable effect, and PND > 70 suggests the intervention was effective. 40 The percentage of nonoverlapping (PNDC) corrected was proposed in 2009 as an extension of the PND. 39 Prior to applying the PND, a data correction procedure is applied eliminating pre-existing baseline trend. 38

Two Standard Deviation Band Method

When the stability criterion described above is met within phases, it is possible to apply the two standard deviation band method. 12 , 41 First, the mean of the data for a specific condition is calculated and represented with a solid line. In the next step, the standard deviation of the same data is computed and two dashed lines are represented: one located two standard deviations above the mean and the other – two standard deviations below. For normally distributed data, few points (less than 5%) are expected to be outside the two standard deviation bands if there is no change in the outcome score due to the intervention. However, this method is not considered a formal statistical procedure, as the data cannot typically be assumed to be normal, continuous, or independent. 41

Statistical Analysis

If the visual analysis indicates a functional relationship (i.e., three demonstrations of the effectiveness of the intervention effect), it is recommended to proceed with the quantitative analyses, reflecting the magnitude of the intervention effect. First, effect sizes are calculated for each participant (individual-level analysis). Moreover, if the research interest lies in the generalizability of the effect size across participants, effect sizes can be combined across cases to achieve an overall average effect size estimate (across-case effect size).

Note that quantitative analysis methods are still being developed in the domain of SC research 1 and statistical challenges of producing an acceptable measure of treatment effect remain. 14 , 42 , 43 Therefore, the WWC standards strongly recommend conducting sensitivity analysis and reporting multiple effect size estimators. If consistency across different effect size estimators is identified, there is stronger evidence for the effectiveness of the treatment. 1 , 18

Individual-level effect size analysis

The most common effect sizes recommended for SC analysis are: 1) standardized mean difference Cohen’s d ; 2) standardized mean difference with correction for small sample sizes Hedges’ g ; and 3) the regression-based approach which has the most potential and is strongly recommended by the WWC standards. 1 , 44 , 45 Cohen’s d can be calculated using following formula: d = X A ¯ - X B ¯ s p , with X A ¯ being the baseline mean, X B ¯ being the treatment mean, and s p indicating the pooled within-case standard deviation. Hedges’ g is an extension of Cohen’s d , recommended in the context of SC studies as it corrects for small sample sizes. The piecewise regression-based approach does not only reflect the immediate intervention effect, but also the intervention effect across time:

i stands for the measurement occasion ( i = 0, 1,… I ). The dependent variable is regressed on a time indicator, T , which is centered around the first observation of the intervention phase, D , a dummy variable for the intervention phase, and an interaction term of these variables. The equation shows that the expected score, Ŷ i , equals β 0 + β 1 T i in the baseline phase, and ( β 0 + β 2 ) + ( β 1 + β 3 ) T i in the intervention phase. β 0 , therefore, indicates the expected baseline level at the start of the intervention phase (when T = 0), whereas β 1 marks the linear time trend in the baseline scores. The coefficient β 2 can then be interpreted as an immediate effect of the intervention on the outcome, whereas β 3 signifies the effect of the intervention across time. The e i ’s are residuals assumed to be normally distributed around a mean of zero with a variance of σ e 2 . The assumption of independence of errors is usually not met in the context of SC studies because repeated measures are obtained within a person. As a consequence, it can be the case that the residuals are autocorrelated, meaning that errors closer in time are more related to each other compared to errors further away in time. 46 – 48 As a consequence, a lag-1 autocorrelation is appropriate (taking into account the correlation between two consecutive errors: e i and e i –1 ; for more details see Verbeke & Molenberghs, (2000). 49 In Equation 1 , ρ indicates the autocorrelation parameter. If ρ is positive, the errors closer in time are more similar; if ρ is negative, the errors closer in time are more different, and if ρ equals zero, there is no correlation between the errors.

Across-case effect sizes

Two-level modeling to estimate the intervention effects across cases can be used to evaluate across-case effect sizes. 44 , 45 , 50 Multilevel modeling is recommended by the WWC standards because it takes the hierarchical nature of SC studies into account: measurements are nested within cases and cases, in turn, are nested within studies. By conducting a multilevel analysis, important research questions can be addressed (which cannot be answered by single-level analysis of SC study data), such as: 1) What is the magnitude of the average treatment effect across cases? 2) What is the magnitude and direction of the case-specific intervention effect? 3) How much does the treatment effect vary within cases and across cases? 4) Does a case and/or study level predictor influence the treatment’s effect? The two-level model has been validated in previous research using extensive simulation studies. 45 , 46 , 51 The two-level model appears to have sufficient power (> .80) to detect large treatment effects in at least six participants with six measurements. 21

Furthermore, to estimate the across-case effect sizes, the HPS (Hedges, Pustejovsky, and Shadish) , or single-case educational design ( SCEdD)-specific mean difference, index can be calculated. 52 This is a standardized mean difference index specifically designed for SCEdD data, with the aim of making it comparable to Cohen’s d of group-comparison designs. The standard deviation takes into account both within-participant and between-participant variability, and is typically used to get an across-case estimator for a standardized change in level. The advantage of using the HPS across-case effect size estimator is that it is directly comparable with Cohen’s d for group comparison research, thus enabling the use of Cohen’s (1988) benchmarks. 53

Valuable recommendations on SC data analyses have recently been provided. 54 , 55 They suggest that a specific SC study data analytic technique can be chosen based on: (1) the study aims and the desired quantification (e.g., overall quantification, between-phase quantifications, randomization, etc.), (2) the data characteristics as assessed by visual inspection and the assumptions one is willing to make about the data, and (3) the knowledge and computational resources. 54 , 55 Table 1 lists recommended readings and some commonly used resources related to the design and analysis of single-case studies.

Recommend readings and resources related to the design and analysis of single-case studies.

Quality Appraisal Tools for Single-Case Design Research

Quality appraisal tools are important to guide researchers in designing strong experiments and conducting high-quality systematic reviews of the literature. Unfortunately, quality assessment tools for SC studies are relatively novel, ratings across tools demonstrate variability, and there is currently no “gold standard” tool. 56 Table 2 lists important SC study quality appraisal criteria compiled from the most common scales; when planning studies or reviewing the literature, we recommend readers consider these criteria. Table 3 lists some commonly used SC quality assessment and reporting tools and references to resources where the tools can be located.

Summary of important single-case study quality appraisal criteria.

Quality assessment and reporting tools related to single-case studies.

When an established tool is required for systematic review, we recommend use of the What Works Clearinghouse (WWC) Tool because it has well-defined criteria and is developed and supported by leading experts in the SC research field in association with the Institute of Education Sciences. 18 The WWC documentation provides clear standards and procedures to evaluate the quality of SC research; it assesses the internal validity of SC studies, classifying them as “Meeting Standards”, “Meeting Standards with Reservations”, or “Not Meeting Standards”. 1 , 18 Only studies classified in the first two categories are recommended for further visual analysis. Also, WWC evaluates the evidence of effect, classifying studies into “Strong Evidence of a Causal Relation”, “Moderate Evidence of a Causal Relation”, or “No Evidence of a Causal Relation”. Effect size should only be calculated for studies providing strong or moderate evidence of a causal relation.

The Single-Case Reporting Guideline In BEhavioural Interventions (SCRIBE) 2016 is another useful SC research tool developed recently to improve the quality of single-case designs. 57 SCRIBE consists of a 26-item checklist that researchers need to address while reporting the results of SC studies. This practical checklist allows for critical evaluation of SC studies during study planning, manuscript preparation, and review.

Single-case studies can be designed and analyzed in a rigorous manner that allows researchers strength in assessing causal relationships among interventions and outcomes, and in generalizing their results. 2 , 12 These studies can be strengthened via incorporating replication of findings across multiple study phases, participants, settings, or contexts, and by using randomization of conditions or phase lengths. 11 There are a variety of tools that can allow researchers to objectively analyze findings from SC studies. 56 While a variety of quality assessment tools exist for SC studies, they can be difficult to locate and utilize without experience, and different tools can provide variable results. The WWC quality assessment tool is recommended for those aiming to systematically review SC studies. 1 , 18

SC studies, like all types of study designs, have a variety of limitations. First, it can be challenging to collect at least five data points in a given study phase. This may be especially true when traveling for data collection is difficult for participants, or during the baseline phase when delaying intervention may not be safe or ethical. Power in SC studies is related to the number of data points gathered for each participant so it is important to avoid having a limited number of data points. 12 , 58 Second, SC studies are not always designed in a rigorous manner and, thus, may have poor internal validity. This limitation can be overcome by addressing key characteristics that strengthen SC designs ( Table 2 ). 1 , 14 , 18 Third, SC studies may have poor generalizability. This limitation can be overcome by including a greater number of participants, or units. Fourth, SC studies may require consultation from expert methodologists and statisticians to ensure proper study design and data analysis, especially to manage issues like autocorrelation and variability of data. 2 Fifth, while it is recommended to achieve a stable level and rate of performance throughout the baseline, human performance is quite variable and can make this requirement challenging. Finally, the most important validity threat to SC studies is maturation. This challenge must be considered during the design process in order to strengthen SC studies. 1 , 2 , 12 , 58

SC studies can be particularly useful for rehabilitation research. They allow researchers to closely track and report change at the level of the individual. They may require fewer resources and, thus, can allow for high-quality experimental research, even in clinical settings. Furthermore, they provide a tool for assessing causal relationships in populations and settings where large numbers of participants are not accessible. For all of these reasons, SC studies can serve as an effective method for assessing the impact of interventions.

Acknowledgments

This research was supported by the National Institute of Health, Eunice Kennedy Shriver National Institute of Child Health & Human Development (1R21HD076092-01A1, Lobo PI) and the Delaware Economic Development Office (Grant #109).

Some of the information in this manuscript was presented at the IV Step Meeting in Columbus, OH, June 2016.