# 8.2: Non-Equivalent Groups Designs

- Page ID
- 16127

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Learning Objectives

- Describe the different types of nonequivalent groups quasi-experimental designs.
- Identify some of the threats to internal validity associated with each of these designs.

Recall that when participants in a between-subjects experiment are randomly assigned to conditions, the resulting groups are likely to be quite similar. In fact, researchers consider them to be equivalent. When participants are not randomly assigned to conditions, however, the resulting groups are likely to be dissimilar in some ways. For this reason, researchers consider them to be nonequivalent. A ** nonequivalent groups design**, then, is a between-subjects design in which participants have not been randomly assigned to conditions. There are several types of nonequivalent groups designs we will consider.

## Posttest Only Nonequivalent Groups Design

The first nonequivalent groups design we will consider is the **posttest only nonequivalent groups design. **In this design, participants in one group are exposed to a treatment, a nonequivalent group is not exposed to the treatment, and then the two groups are compared. Imagine, for example, a researcher who wants to evaluate a new method of teaching fractions to third graders. One way would be to conduct a study with a treatment group consisting of one class of third-grade students and a control group consisting of another class of third-grade students. This design would be a nonequivalent groups design because the students are not randomly assigned to classes by the researcher, which means there could be important differences between them. For example, the parents of higher achieving or more motivated students might have been more likely to request that their children be assigned to Ms. Williams’s class. Or the principal might have assigned the “troublemakers” to Mr. Jones’s class because he is a stronger disciplinarian. Of course, the teachers’ styles, and even the classroom environments might be very different and might cause different levels of achievement or motivation among the students. If at the end of the study there was a difference in the two classes’ knowledge of fractions, it might have been caused by the difference between the teaching methods—but it might have been caused by any of these confounding variables.

Of course, researchers using a posttest only nonequivalent groups design can take steps to ensure that their groups are as similar as possible. In the present example, the researcher could try to select two classes at the same school, where the students in the two classes have similar scores on a standardized math test and the teachers are the same sex, are close in age, and have similar teaching styles. Taking such steps would increase the internal validity of the study because it would eliminate some of the most important confounding variables. But without true random assignment of the students to conditions, there remains the possibility of other important confounding variables that the researcher was not able to control.

## Pretest-Posttest Nonequivalent Groups Design

Another way to improve upon the posttest only nonequivalent groups design is to add a pretest. In the **pretest-posttest nonequivalent groups design **there is a treatment group that is given a pretest, receives a treatment, and then is given a posttest. But at the same time there is a nonequivalent control group that is given a pretest, does not receive the treatment, and then is given a posttest. The question, then, is not simply whether participants who receive the treatment improve, but whether they improve *more* than participants who do not receive the treatment.

Imagine, for example, that students in one school are given a pretest on their attitudes toward drugs, then are exposed to an anti-drug program, and finally, are given a posttest. Students in a similar school are given the pretest, not exposed to an anti-drug program, and finally, are given a posttest. Again, if students in the treatment condition become more negative toward drugs, this change in attitude could be an effect of the treatment, but it could also be a matter of history or maturation. If it really is an effect of the treatment, then students in the treatment condition should become more negative than students in the control condition. But if it is a matter of history (e.g., news of a celebrity drug overdose) or maturation (e.g., improved reasoning), then students in the two conditions would be likely to show similar amounts of change. This type of design does not completely eliminate the possibility of confounding variables, however. Something could occur at one of the schools but not the other (e.g., a student drug overdose), so students at the first school would be affected by it while students at the other school would not.

Returning to the example of evaluating a new measure of teaching third graders, this study could be improved by adding a pretest of students’ knowledge of fractions. The changes in scores from pretest to posttest would then be evaluated and compared across conditions to determine whether one group demonstrated a bigger improvement in knowledge of fractions than another. Of course, the teachers’ styles, and even the classroom environments might still be very different and might cause different levels of achievement or motivation among the students that are independent of the teaching intervention. Once again, differential history also represents a potential threat to internal validity. If asbestos is found in one of the schools causing it to be shut down for a month then this interruption in teaching could produce a difference across groups on posttest scores.

If participants in this kind of design are randomly assigned to conditions, it becomes a true between-groups experiment rather than a quasi-experiment. In fact, it is the kind of experiment that Eysenck called for—and that has now been conducted many times—to demonstrate the effectiveness of psychotherapy.

## Interrupted Time-Series Design with Nonequivalent Groups

One way to improve upon the interrupted time-series design is to add a control group. The ** interrupted time-series design with nonequivalent groups ** involves taking a set of measurements at intervals over a period of time both before and after an intervention of interest in two or more nonequivalent groups. Once again consider the manufacturing company that measures its workers’ productivity each week for a year before and after reducing work shifts from 10 hours to 8 hours. This design could be improved by locating another manufacturing company who does not plan to change their shift length and using them as a nonequivalent control group. If productivity increased rather quickly after the shortening of the work shifts in the treatment group but productivity remained consistent in the control group, then this provides better evidence for the effectiveness of the treatment.

Similarly, in the example of examining the effects of taking attendance on student absences in a research methods course, the design could be improved by using students in another section of the research methods course as a control group. If a consistently higher number of absences was found in the treatment group before the intervention, followed by a sustained drop in absences after the treatment, while the nonequivalent control group showed consistently high absences across the semester then this would provide superior evidence for the effectiveness of the treatment in reducing absences.

## Pretest-Posttest Design With Switching Replication

Some of these nonequivalent control group designs can be further improved by adding a switching replication. Using a **pretest-posttest design with switching replication design, **nonequivalent groups are administered a pretest of the dependent variable, then one group receives a treatment while a nonequivalent control group does not receive a treatment, the dependent variable is assessed again, and then the treatment is added to the control group, and finally the dependent variable is assessed one last time.

As a concrete example, let’s say we wanted to introduce an exercise intervention for the treatment of depression. We recruit one group of patients experiencing depression and a nonequivalent control group of students experiencing depression. We first measure depression levels in both groups, and then we introduce the exercise intervention to the patients experiencing depression, but we hold off on introducing the treatment to the students. We then measure depression levels in both groups. If the treatment is effective we should see a reduction in the depression levels of the patients (who received the treatment) but not in the students (who have not yet received the treatment). Finally, while the group of patients continues to engage in the treatment, we would introduce the treatment to the students with depression. Now and only now should we see the students’ levels of depression decrease.

One of the strengths of this design is that it includes a built in replication. In the example given, we would get evidence for the efficacy of the treatment in two different samples (patients and students). Another strength of this design is that it provides more control over history effects. It becomes rather unlikely that some outside event would perfectly coincide with the introduction of the treatment in the first group and with the delayed introduction of the treatment in the second group. For instance, if a change in the weather occurred when we first introduced the treatment to the patients, and this explained their reductions in depression the second time that depression was measured, then we would see depression levels decrease in both the groups. Similarly, the switching replication helps to control for maturation and instrumentation. Both groups would be expected to show the same rates of spontaneous remission of depression and if the instrument for assessing depression happened to change at some point in the study the change would be consistent across both of the groups. Of course, demand characteristics, placebo effects, and experimenter expectancy effects can still be problems. But they can be controlled for using some of the methods described in Chapter 5.

## Switching Replication with Treatment Removal Design

In a basic pretest-posttest design with switching replication, the first group receives a treatment and the second group receives the same treatment a little bit later on (while the initial group continues to receive the treatment). In contrast, in a **switching replication with treatment removal design**, the treatment is removed from the first group when it is added to the second group. Once again, let’s assume we first measure the depression levels of patients with depression and students with depression. Then we introduce the exercise intervention to only the patients. After they have been exposed to the exercise intervention for a week we assess depression levels again in both groups. If the intervention is effective then we should see depression levels decrease in the patient group but not the student group (because the students haven’t received the treatment yet). Next, we would remove the treatment from the group of patients with depression. So we would tell them to stop exercising. At the same time, we would tell the student group to start exercising. After a week of the students exercising and the patients not exercising, we would reassess depression levels. Now if the intervention is effective we should see that the depression levels have decreased in the student group but that they have increased in the patient group (because they are no longer exercising).

Demonstrating a treatment effect in two groups staggered over time and demonstrating the reversal of the treatment effect after the treatment has been removed can provide strong evidence for the efficacy of the treatment. In addition to providing evidence for the replicability of the findings, this design can also provide evidence for whether the treatment continues to show effects after it has been withdrawn.

## Key Takeaways

- Quasi-experimental research involves the manipulation of an independent variable without the random assignment of participants to conditions or counterbalancing of orders of conditions.
- There are three types of quasi-experimental designs that are within-subjects in nature. These are the one-group posttest only design, the one-group pretest-posttest design, and the interrupted time-series design.
- There are five types of quasi-experimental designs that are between-subjects in nature. These are the posttest only design with nonequivalent groups, the pretest-posttest design with nonequivalent groups, the interrupted time-series design with nonequivalent groups, the pretest-posttest design with switching replication, and the switching replication with treatment removal design.
- Quasi-experimental research eliminates the directionality problem because it involves the manipulation of the independent variable. However, it does not eliminate the problem of confounding variables, because it does not involve random assignment to conditions or counterbalancing. For these reasons, quasi-experimental research is generally higher in internal validity than non-experimental studies but lower than true experiments.
- Of all of the quasi-experimental designs, those that include a switching replication are highest in internal validity.

## Exercises

- Practice: Imagine that two professors decide to test the effect of giving daily quizzes on student performance in a statistics course. They decide that Professor A will give quizzes but Professor B will not. They will then compare the performance of students in their two sections on a common final exam. List five other variables that might differ between the two sections that could affect the results.
- Discussion: Imagine that a group of obese children is recruited for a study in which their weight is measured, then they participate for 3 months in a program that encourages them to be more active, and finally their weight is measured again. Explain how each of the following might affect the results:
- regression to the mean
- spontaneous remission
- history
- maturation