Scenario: Researchers provided both content of class and gender of instructor within vignettes for 2 classes of students that were manipulated by the experimenter. For example, the content manipulated in the two different classes was either counseling or research methods. The gender of the instructor manipulated in the vignettes was either male or female. In the research results, the main effects indicated instructor gender and course content were not statistically significant.

Answer each question in a maximum of 250 words excluding citations: Which of the following research designs is the above experimenter using? Why do you say that? What is the strength of the design that you selected from the list below?

a) Inverted U

b) 2 x 2

c) IV x PV

d) None of the above (What alternative design then?)

Instruction: Provide a definition of your concept design from our text then, discuss support for your selection including an example from research that illustrates your point. Do so with a maximum of 250 words excluding citations.

**Complex Experimental Designs**

· Define *factorial design* and discuss reasons a researcher would use this design.

· Describe the information provided by main effects and interaction effects in a factorial design.

· Describe an IV × PV design.

· Discuss the role of simple main effects in interpreting interactions.

· Compare the assignment of participants in an independent groups design, a repeated measures design, and a mixed factorial design.

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THUS FAR WE HAVE FOCUSED PRIMARILY ON THE SIMPLEST EXPERIMENTAL DESIGN, IN WHICH ONE INDEPENDENT VARIABLE IS MANIPULATED AND ONE DEPENDENT VARIABLE IS MEASURED. However, researchers often investigate problems that demand more complicated designs. These complex experimental designs are the subject of this chapter.

We begin by discussing the idea of increasing the number of levels of an independent variable in an experiment. Then, we describe experiments that expand the number and types of independent variables. These changes impact the complexity of an experiment.

**INCREASING THE NUMBER OF LEVELS OF AN INDEPENDENT VARIABLE**

In the simplest experimental design, there are only two levels of the independent variable. However, a researcher might want to design an experiment with three or more levels for several reasons. First, a design with only two levels of one independent variable cannot provide very much information about the exact form of the relationship between the independent and dependent variables. For example, Figure 10.1 is based on the outcome of an experiment on the relationship between amount of “mental practice” and performance on a motor task: dart throwing score (Kremer, Spittle, McNeil, & Shinners, 2009). Mental practice consisted of imagining practice throws prior to an actual dart throwing task. Does mental practice improve dart performance? The solid line describes the results when only two levels were used—no mental practice throws and 100 mental practice throws. Because there are only two levels, the relationship can be described only with a straight line. We do not know what the relationship would be if other practice amounts were included as separate levels of the independent variable. The broken line in Figure 10.1 shows the results when 25, 50, and 75 mental practice throws are also included. This result is a more accurate description of the relationship between amount of mental practice and performance. The amount of practice is very effective in increasing performance up to a point, after which further practice is not helpful. This type of relationship is termed a *positive monotonic relationship;* there is a positive relationship between the variables, but it is not a strictly positive linear relationship. An experiment with only two levels cannot yield such exact information.

**FIGURE 10.1**

Linear versus positive monotonic functions

*Note:* Data based on an experiment conducted by Kremer, Spittle, McNeil, and Shinners (2009); that experiment did not include a 75-practice-throws condition.

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**FIGURE 10.2**

Curvilinear relationship

*Note:* At least three levels of the independent variable are required to show curvilinear relationships.

Recall from Chapter 4 that variables are sometimes related in a curvilinear or nonmonotonic fashion; that is, the direction of relationship changes. Figure 10.2 shows an example of a curvilinear relationship; this particular form is called an *inverted-U* because the wide range of levels of the independent variable produces an inverted U shape (recall our discussion of inverted-U relationships in Chapter 4). An experimental design with only two levels of the independent variable cannot detect curvilinear relationships between variables. If a curvilinear relationship is predicted, at least three levels must be used. As Figure 10.2 shows, if only levels 1 and 3 of the independent variable had been used, no relationship between the variables would have been detected. Many such curvilinear relationships exist in psychology. The relationship between fear arousal and attitude change is one example—we can be scared into changing an attitude, but if we think that a message is “over the top,” attitude change does not occur. In other words, increasing the amount of fear aroused by a persuasive message increases attitude change up to a moderate level of fear; further increases in fear arousal actually reduce attitude change.

Finally, researchers frequently are interested in comparing more than two groups. Suppose you want to know whether playing with an animal has beneficial effects on nursing home residents. You could have two conditions, such Page 204as a no-animal control group and a group in which a dog is brought in for play each day. However, you might also be interested in knowing the effect of a cat and a bird, and so you could add these two groups to your study. Or you might be interested in comparing the effect of a large versus a small dog in addition to a no-animal control condition. In an actual study with four groups, Strassberg and Holty (2003) compared responses to women’s Internet personal ads. The researchers first devised a control ad portraying a woman with generally positive attributes, such as liking painting and hiking. The other ads each added a more specific characteristic: (1) slim and attractive, (2) sensual and passionate, or (3) financially independent and ambitious. Contrary to the researchers’ initial expectations, the independent/ambitious woman received many more responses than the other three.

**INCREASING THE NUMBER OF INDEPENDENT VARIABLES: FACTORIAL DESIGNS**

Researchers often manipulate more than one independent variable in a single experiment. Typically, two or three independent variables are operating simultaneously. This type of experimental design is a closer approximation of real-world conditions, in which independent variables do not exist by themselves. Researchers recognize that in any given situation a number of variables are operating to affect behavior. In Chapter 8, we described a hypothetical experiment in which exercise was the independent variable and mood was the dependent variable. An actual experiment on the relationship between exercise and depression was conducted by Dunn, Trivedi, Kampert, Clark, and Chambliss (2005). The participants were randomly assigned to one of two exercise conditions—a low or high amount, with energy expenditure of either 7.0 or 17.5 kcal per kilogram per week. The dependent variable was the score on a standard depression measure after 12 weeks of exercise. You might be wondering how often the participants exercised each week. Indeed, the researchers did wonder if frequency of exercising would be important, so they scheduled some subjects to exercise 3 days per week and others to exercise 5 days per week. Thus, the researchers designed an experiment with two independent variables—in this case, (1) amount of exercise and (2) frequency of exercise.

**Factorial designs** are designs with more than one independent variable (or *factor*). In a factorial design, all levels of each independent variable are combined with all levels of the other independent variables. The simplest factorial design—known as a 2 × 2 (two by two) factorial design—has two independent variables, each having two levels.

An experiment by Hermans, Engels, Larsen, and Herman (2009) illustrates a 2 × 2 factorial design. Herman et al. studied modeling of food intake when someone is with another person who is eating. What influences whether you will model the other person’s eating? In the experiment, a subject was paired with a same-sex confederate to view and rate movie trailers—they were seated in a comfortable living room environment with a bowl of M&Ms within easy reach on a coffee table. After 10 minutes of viewing, there was a break period. Two independent variables were manipulated: (1) confederate sociability and (2) confederate food intake. The sociable confederate initiated a conversation; the unsociable confederate did not initiate a conversation, responded with only brief answers if the subject said something, and avoided eye contact. The confederate also was first to reach for the M&Ms. One piece was taken in the low food intake condition; a total of six pieces were taken during the break. In the high food intake condition, four pieces were taken immediately; a total of 24 pieces were eaten by the confederate in this condition. During the break period (lasting 15 minutes), the subject could ignore the bowl of M&Ms or eat as many as desired.

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**FIGURE 10.3**

2 × 2 factorial design: Setup of food intake modeling experiment

This 2 × 2 design results in four experimental conditions: (1) sociable confederate—low food intake, (2) unsociable confederate—low food intake, (3) sociable confederate—high food intake, (4) unsociable confederate—high food intake. A 2 × 2 design always has four groups. Figure 10.3 shows how these experimental conditions are created.

The general format for describing factorial designs is

and so on. A design with two independent variables, one having two levels and the other having three levels, is a 2 × 3 factorial design; there are six conditions in the experiment. A 3 × 3 design has nine conditions.

*Interpretation of Factorial Designs*

Factorial designs yield two kinds of information. The first is information about the effect of each independent variable taken by itself: the **main effect** of an independent variable. In a design with two independent variables, there are two main effects—one for each independent variable. The second type of information is called an **interaction.** If there is an interaction between two independent variables, the effect of one independent variable depends on the particular level of the other variable. In other words, the effect that an independent variable has on the dependent variable depends on the level of the other independent variable. Interactions are a new source of information that cannot be obtained in a simple experimental design in which only one independent variable is manipulated.

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**TABLE 10.1** 2 × 2 factorial design: Results of the food intake modeling

To illustrate main effects and interactions, we can look at the results of the Hermans et al. (2009) study on food intake modeling. Table 10.1 illustrates a common method of presenting outcomes for the various groups in a factorial design. The number in each cell represents the mean number of M&Ms consumed by the subjects in the four conditions.

Main effects A main effect is the effect each variable has by itself. The main effect of independent variable A, confederate sociability, is the overall effect of the variable on the dependent measure. Similarly, the main effect of independent variable B, confederate food intake, is the effect of number of M&Ms that the confederate ate on the number of M&Ms consumed by the subject.

The main effect of each independent variable is the overall relationship between that independent variable and the dependent variable. For independent variable A, is there a relationship between sociability and food intake? We can find out by looking at the overall means in the sociable and unsociable confederate conditions. These overall main effect means are obtained by averaging across all participants in each group, irrespective of confederate food intake (low or high). The main effect means are shown in the rightmost column and bottom row (called the margins of the table) of Table 10.1. The average number of M&Ms consumed by participants in the sociable confederate condition is 6.13, and the number eaten in the unsociable condition is 6.39. Note that the overall mean of 6.13 in the sociable confederate condition is the average of 6.58 in the sociable—low food intake group and 5.68 in the sociable—high food intake group (this calculation assumes equal numbers of participants in each group). You can see that overall, somewhat more M&Ms are eaten when the confederate is unsociable. Statistical tests would enable us to determine whether this is a significant main effect.

Page 207The main effect for independent variable B (confederate food intake) is the overall relationship between that independent variable, by itself, and the dependent variable. You can see in Table 10.1 that the average number of candies consumed by subjects in the low food intake condition is 4.36, and the overall number eaten in the high food intake condition is 8.16. Thus, in general, more M&Ms are eaten by subjects when they were with a confederate who had consumed a high number of M&Ms (this is a modeling effect).

Interactions These main effect means tell us that, overall, subjects eat (1) slightly more M&Ms when the confederate is unsociable and (2) considerably more when the confederate eats a large amount of candy. There is also the possibility that an interaction exists; if so, the main effects of the independent variables must be qualified. This is because an interaction between independent variables indicates that the effect of one independent variable is different at different levels of the other independent variable. That is, an interaction tells us that the effect of one independent variable depends on the particular level of the other.

We can see an interaction in the results of the Herman et al. (2009) study. The effect of confederate food intake is different depending on whether the confederate is sociable or unsociable. When the confederate is unsociable, subjects consume many more M&Ms when the confederate food intake is high (10.68 in the unsociable condition versus 2.14 in the sociable condition). However, when the confederate is sociable, confederate food intake has little effect and in fact is the opposite of what would be expected based on modeling (6.58 in the low food intake condition and 5.68 in the high food intake condition). Thus, the relationship between confederate food intake and subject food intake is best understood by considering both independent variables: We must consider the food intake of the confederate *and* whether the confederate is sociable or unsociable.

Interactions can be seen easily when the means for all conditions are presented in a graph. Figure 10.4 shows a bar graph of the results of Herman et al. food intake modeling experiment. Note that all four means have been graphed. Two bars compare low versus high confederate food intake in the sociable confederate condition; the same comparison is shown for the unsociable confederate. You can see that confederate food intake has a small effect on the participants’ modeling of M&Ms consumed when the confederate is sociable; however, when the confederate is unsociable, the participants do model the food intake of the confederate. Herman et al. (2009) noted that they expected to observe the modeling effect primarily when the confederate is sociable; why do you think someone might actually model the food intake of the unsociable confederate instead?

**FIGURE 10.4**

Interaction between confederate sociability and food intake

Page 208The concept of interaction is a relatively simple one that you probably use all the time. When we say “it depends,” we are usually indicating that some sort of interaction is operating—it depends on some other variable. Suppose, for example, that a friend has asked you if you want to go to a movie. Whether you want to go may reflect an interaction between two variables: (1) Is an exam coming up? and (2) Who stars in the movie? If there is an exam coming up, you will not go under any circumstance. If you do not have an exam to worry about, your decision will depend on whether you like the actors in the movie; that is, you will be much more likely to go if a favorite star is in the movie.

You might try graphing the movie example in the same way we graphed the food intake example in Figure 10.4. The dependent variable (likelihood of going to the movie) is always placed on the vertical axis. One independent variable is placed on the horizontal axis. Bars are then drawn to represent each of the levels of the other independent variable. Graphing the results in this manner is a useful method of visualizing interactions in a factorial design.

*Factorial Designs with Manipulated and Nonmanipulated Variables*

One common type of factorial design includes both experimental (manipulated) and nonexperimental (measured or nonmanipulated) variables. These designs—sometimes called **IV** × **PV designs** (i.e., independent variable by participant variable)—allow researchers to investigate how different types of individuals (i.e., participants) respond to the same manipulated variable. These “participant variables” are personal attributes such as gender, age, ethnic group, personality characteristics, and clinical diagnostic category. You will sometimes see participant variables described as *subject variables* or *attribute variables*. This is only a difference of terminology.

The simplest IV × PV design includes one manipulated independent variable that has at least two levels and one participant variable with at least two levels. The two levels of the subject variable might be two different age groups, groups of low and high scorers on a personality measure, or groups of males and females. An example of this design is a study by Furnham, Gunter, and Peterson (1994). Do you ever try to study in the presence of a distraction such as a television program? Furnham et al. showed that the ability to study with such a distraction depends on whether you are more extraverted or introverted. The manipulated variable was distraction. College students read material in silence and within hearing range of a TV drama. Thus, a repeated measures design was used and the order of the conditions was counterbalanced. After they read the material, the students completed a reading comprehension measure. The participant variable was extraversion: Participants completed a measure of extraversion and then were classified as extraverts or introverts. The results are shown in Figure 10.5. There was a main effect of distraction and an interaction.

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**FIGURE 10.5**

Interaction in IV × PV design

Overall, students had higher comprehension scores when they studied in silence. In addition, there was an interaction between extraversion and distraction. Without a distraction, the performance of extraverts and introverts was almost the same. However, extraverts performed better than introverts when the TV was on. You can speculate whether similar results would be obtained today when text messages are a potential distraction.

Factorial designs with both manipulated independent variables and participant variables offer a very appealing method for investigating many interesting research questions. Such experiments recognize that full understanding of behavior requires knowledge of both situational variables and the personal attributes of individuals.

*Outcomes of a 2 × 2 Factorial Design*

A 2 × 2 factorial design has two independent variables, each with two levels. When analyzing the results, researchers deal with several possibilities: (1) There may or may not be a significant main effect for independent variable A, (2) there may or may not be a significant main effect for independent variable B, and (3) there may or may not be a significant interaction between the independent variables.

Figure 10.6 illustrates the eight possible outcomes in a 2 × 2 factorial design. For each outcome, the means are given and then graphed using line graphs. In addition, for each graph in Figure 10.6, the main effect for each variable (A and B) is indicated by a Yes (indicating the presence of a main effect) or No (no main effect). Similarly, the A × B interaction is either present (“Yes” on the figure) or not present (“No” on the figure). The means that are given in the figure are idealized examples; such perfect outcomes rarely occur in actual research. Nevertheless, you should study the graphs to determine for yourself why, in each case, there is or is not a main effect for A, a main effect for B, and an A × B interaction.

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**FIGURE 10.6**

Outcomes of a factorial design with two independent variables

Page 211Before you begin studying the graphs, it will help think of concrete variables to represent the two independent variables and the dependent variable. You might want to think about the example of the effect of amount and frequency of exercise on depression. Suppose that independent variable A is amount of exercise per week (A1 is low exercise—fewer calories per week; A2 is higher amount of exercise—more calories per week) and independent variable B is frequency of exercise (B1 is 3 times per week and B2 is 5 times per week). The dependent variable (DV) is the score on a depression measure, with higher numbers indicating greater depression.

The top four graphs illustrate outcomes in which there is no A × B interaction, and the bottom four graphs depict outcomes in which there is an interaction. When there is a statistically significant interaction, you need to carefully examine the means to understand why the interaction occurred. In some cases, there is a strong relationship between the first independent variable and the dependent variable at one level of the second independent variable; however, there is no relationship or a weak relationship at the other level of the second independent variable. In other outcomes, the interaction may indicate that one independent variable has opposite effects on the dependent variable, depending on the level of the second independent variable.

The independent and dependent variables in Figure 10.6 do not have concrete variable labels. As an exercise, interpret each of the graphs using actual variables from three different hypothetical experiments, using the scenarios suggested below. This works best if you draw the graphs, including labels for the variables, on a separate sheet of paper for each experiment. You can try depicting the data as either line graphs or bar graphs. The data points in both types of graphs are the same and both have been used in this chapter. In general, line graphs are used when the levels of the independent variable on the horizontal axis (independent variable A) are quantitative—low and high amounts. Bar graphs are more likely to be used when the levels of the independent variable represent different categories, such as one type of therapy compared with another type.

Hypothetical experiment 1: Effect of age of defendant and type of substance use during an offense on months of sentence. A male, age 20 or 50, was found guilty of causing a traffic accident while under the influence of either alcohol or marijuana.

Independent variable A: Type of Offense—Alcohol versus Marijuana

Independent variable B: Age of Defendant—20 versus 50 years of age

Dependent variable: Months of sentence (range from 0 to 10 months)

Page 212Hypothetical experiment 2: Effect of gender and violence on recall of advertising. Participants (males and females) viewed a video on a computer screen that was either violent or not violent. They were then asked to read print ads for eight different products over the next 3 minutes. The dependent variable was the number of ads correctly recalled.

Independent variable A: Exposure to Violence—Nonviolent versus Violent Video

Independent variable B: Participant Gender—Male versus Female

Dependent variable: Number of ads recalled (range from 0 to 8)

Hypothetical experiment 3: Devise your own experiment with two independent variables and one dependent variable.

*Interactions and Simple Main Effects*

A statistical procedure called *analysis of variance* is used to assess the statistical significance of the main effects and the interaction in a factorial design. When a significant interaction occurs, the researcher must statistically evaluate the individual means. If you take a look at Table 10.1 and Figure 10.4 once again, you see a clear interaction. When there is a significant interaction, the next step is to look at the **simple main effects.** A simple main effect analysis examines mean differences at *each level* of the independent variable. Recall that the main effect of an independent variable averages across the levels of the other independent variable; with simple main effects, the results are analyzed as if we had separate experiments at each level of the other independent variable.

Simple main effect of confederate food intake In Figure 10.4, we can look at the simple main effect of confederate food intake. This will tell us whether the difference between the low and high confederate food intake is significant when the confederate is (1) sociable and (2) unsociable. In this case, the simple main effect of confederate food intake is significant when the confederate is unsociable (means of 2.14 versus 10.63), but the simple main effect of confederate food intake is not significant when the confederate is sociable (means of 6.58 and 5.68).

Simple main effect of sociability We could also examine the simple main effect of confederate sociability; here we would compare the sociable versus unsociable conditions when the food intake is low and then when food intake is high. The simple main effect that you will be most interested in will depend on the predictions that you made when you designed the study. The exact statistical procedures do not concern us; the point here is that the pattern of results with all the means must be examined when there is a significant interaction in a factorial design.

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*Assignment Procedures and Factorial Designs*

The considerations of assigning participants to conditions that were discussed in Chapter 8 can be generalized to factorial designs. There are two basic ways of assigning participants to conditions: (1) In an independent groups design, different participants are assigned to each of the conditions in the study and (2) in a repeated measures design, the *same* individuals participate in all conditions in the study. These two types of assignment procedures have implications for the number of participants necessary to complete the experiment. We can illustrate this fact by looking at a 2 × 2 factorial design. The design can be completely independent groups, completely repeated measures, or a **mixed factorial design**—that is, a combination of the two.

Independent groups (between-subjects) design In a 2 × 2 factorial design, there are four conditions. If we want a completely **independent groups (between-subjects) design,** a different group of participants will be assigned to each of the four conditions. The food intake modeling study illustrates a factorial design with different individuals in each of the conditions. Suppose that you have planned a 2 × 2 design and want to have 10 participants in each condition; you will need a total of 40 *different* participants, as shown in the first table in Figure 10.7.

Repeated measures (within-subjects) design In a completely **repeated measures (within-subjects) design,** the same individuals will participate in *all* conditions. Suppose you have planned a study on the effects of marijuana: One factor is marijuana (marijuana treatment versus placebo control) and the other factor is task difficulty (easy versus difficult). In a 2 × 2 completely repeated measures design, each individual would participate in all of the conditions by completing both easy and difficult tasks under both marijuana treatment conditions. If you wanted 10 participants in each condition, a total of 10 subjects would be needed, as illustrated in the second table in Figure 10.7. This design offers considerable savings in the number of participants required. In deciding whether to use a completely repeated measures assignment procedure, however, the researcher would have to consider the disadvantages of repeated measures designs.

**FIGURE 10.7**

Number of participants (P) required to have 10 observations in each condition

Page 214Mixed factorial design using combined assignment The Furnham, Gunter, and Peterson (1994) study on television distraction and extraversion illustrates the use of both independent groups and repeated measures procedures in a mixed factorial design. The participant variable, extraversion, is an independent groups variable. Distraction is a repeated measures variable; all participants studied with both distraction and silence. The third table in Figure 10.7 shows the number of participants needed to have 10 per condition in a 2 × 2 mixed factorial design. In this table, independent variable A is an independent groups variable. Ten participants are assigned to level 1 of this independent variable, and another 10 participants are assigned to level 2. Independent variable B is a repeated measures variable, however. The 10 participants assigned to A1 receive both levels of independent variable B. Similarly, the other 10 participants assigned to A2receive both levels of the B variable. Thus, a total of 20 participants are required.

*Increasing the Number of Levels of an Independent Variable*

The 2 × 2 is the simplest factorial design. With this basic design, the researcher can arrange experiments that are more and more complex. One way to increase complexity is to increase the number of levels of one or more of the independent variables. A 2 × 3 design, for example, contains two independent variables: Independent variable A has two levels, and independent variable B has three levels. Thus, the 2 × 3 design has six conditions.

Table 10.2 shows a 2 × 3 factorial design with the independent variables of task difficulty (easy, hard) and anxiety level (low, moderate, high). The dependent variable is performance on the task. The numbers in each of the six cells of the design indicate the mean performance score of the group. The overall means in the margins (rightmost column and bottom row) show the main effects of each of the independent variables. The results in Table 10.2 indicate a main effect of task difficulty because the *overall* performance score in the easy-task group is higher than the hard-task mean. However, there is no main effect of anxiety because the mean performance score is the same in each of the three anxiety groups. Is there an interaction between task difficulty and anxiety? Note that increasing the amount of anxiety has the effect of increasing performance on the easy task but *decreasing* performance on the hard task. The effect of anxiety is different, depending on whether the task is easy or hard; thus, there is an interaction.

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**TABLE 10.2** 2 × 3 factorial design

This interaction can be easily seen in a graph. Figure 10.8 is a line graph in which one line shows the effect of anxiety for the easy task and a second line represents the effect of anxiety for the difficult task. As noted previously, line graphs are used when the independent variable represented on the horizontal axis is quantitative—that is, the levels of the independent variable are increasing amounts of that variable (not differences in category).

*Increasing the Number of Independent Variables in a Factorial Design*

We can also increase the number of variables in the design. A 2 × 2 × 2 factorial design contains three variables, each with two levels. Thus, there are eight conditions in this design. In a 2 × 2 × 3 design, there are 12 conditions; in a 2 × 2 × 2 × 2 design, there are 16. The rule for constructing factorial designs remains the same throughout.

**FIGURE 10.8**

Line graph of data from 3 (anxiety level) × 2 (task difficulty) factorial design

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**TABLE 10.3** 2 × 2 × 2 factorial design

A 2 × 2 × 2 factorial design is constructed in Table 10.3. The independent variables are (1) instruction method (lecture, discussion), (2) class size (10, 40), and (3) student gender (male, female). Note that gender is a nonmanipulated variable and the other two variables are manipulated variables. The dependent variable is performance on a standard test.

Notice that the 2 × 2 × 2 design can be seen as two 2 × 2 designs, one for the males and another for the females. The design yields main effects for each of the three independent variables. For example, the overall mean for the lecture method is obtained by considering all participants who experience the lecture method, irrespective of class size or gender. Similarly, the discussion method mean is derived from all participants in this condition. The *two* means are then compared to see whether there is a significant main effect: Is one method superior to the other *overall?*

The design also allows us to look at interactions. In the 2 × 2 × 2 design, we can look at the interaction between (1) method and class size, (2) method and gender, and (3) class size and gender. We can also look at a three-way interaction that involves all three independent variables. Here, we want to determine whether the nature of the interaction between two of the variables differs depending on the particular level of the other variable. Three-way interactions are rather complicated; fortunately, you will not encounter too many of these in your explorations of behavioral science research.

Sometimes students are tempted to include in a study as many independent variables as they can think of. A problem with this is that the design may become needlessly complex and require enormous numbers of participants. The design previously discussed had 8 groups; a 2 × 2 × 2 × 2 design has 16 groups; adding yet another independent variable with two levels means that 32 groups would be required. Also, when there are more than three or four independent variables, many of the particular conditions that are produced by the combination of so many variables do not make sense or could not occur under natural circumstances.

Page 217The designs described thus far all use the same logic for determining whether the independent variable did in fact cause a change on the dependent variable measure. In the next chapter, we will consider alternative designs that use somewhat different procedures for examining the relationship between independent and dependent variables.

**ILLUSTRATIVE ARTICLE: COMPLEX EXPERIMENTAL DESIGNS**

As the saying goes, “money can’t buy happiness.” Mogilner (2010) put this idea to an empirical test in a series of three experiments that examined the impact of our thinking on how we spend our time.

Participants in the first experiment were given a scrambled-word task that included words that either primed them to think about money (“sheets the change price”), time (“sheets the change clock”), or nothing in particular (“sheets the change socks”). Then participants were given a list of activities and were asked to indicate their own plans for the day as well as the plans of a typical American. The author concluded that participants primed to think about money (based on the scrambled-word task) focused more on plans to work; in contrast, the participants primed to think about time indicated that they were motivated to engage in social connections.

First, acquire and read the article:

Mogilner, C. (2010). The pursuit of happiness: Time, money, and social connection. *Psychological Science, 21*, 1348–1354. doi:10.1177/0956797610380696

Then, after reading the article, consider the following:

1. Identify each independent variable in Experiment 1a.

2. Identify each dependent variable in Experiment 1a.

3. What type of assignment procedure was used for Experiment 1a?

4. The author attempted to improve the external validity of the study in Experiment 1b and Experiment 2. Do you think that she was successful? Why or why not?

5. Create a graph for the dependent variable of *socializing,* with the independent variable *prime* on the *x*-axis and separate lines for one’s own plans and plans of others. Describe what you see: Do you see a main effect for either of the independent variables? Do you see the interaction?

6. Create a graph for the dependent variable of *work,* with the independent variable *prime* with prime on *x*-axis. Describe what you see: Do you see a main effect for either of the independent variables? Do you see the interaction?

Page 218** Study Terms**

Factorial design (p. 204)

Independent groups design (Between-subjects design) (p. 213)

Interaction (p. 206)

IV × PV design (p. 208)

Main effect (p. 205)

Mixed factorial design (p. 213)

Repeated measures design (Within-subjects design) (p. 213)

Simple main effect (p. 212)

*Review Questions*

1. Why would a researcher have more than two levels of the independent variable in an experiment?

2. What is a factorial design? Why would a researcher use a factorial design?

3. What are main effects in a factorial design? What is an interaction?

4. Describe an IV × PV factorial design.

5. Identify the number of conditions in a factorial design on the basis of knowing the number of independent variables and the number of levels of each independent variable.

*Activities*

1. Research participants read an “eating diary” of either a male or female stimulus person. The information in the diary indicated that the person ate either large meals or small meals. After reading this information, participants rated the person’s femininity and masculinity. (Based on a study by Chaiken and Pliner, 1987.)

a. Identify the design of this experiment.

b. How many conditions are in the experiment?

c. Identify the independent variable(s) and dependent variable(s).

d. Is there a participant variable in this experiment? If so, identify it. If not, can you suggest a participant variable that might be included?

2. The mean femininity ratings were (higher numbers indicate greater femininity): male—small meals (2.02), male—large meals (2.05), female—small meals (3.90), and female—large meals (2.82). Assume there are equal numbers of participants in each condition.

a. Are there any main effects?

b. Is there an interaction?

c. Graph the means.

d. Describe the results in a brief paragraph.

3. Assume that you want 15 participants in each condition of your experiment, which uses a 3 × 3 factorial design. How many *different* participants do you need for (a) a completely independent groups assignment, (b) a completely repeated measures assignment, and (c) a mixed factorial design with both independent groups assignment and repeated measures variables?Page 219

4. Practice graphing the results of the experiment on the effect of amount and frequency of exercise on depression. In the actual experiment, there was a main effect of amount of exercise: Participants in the high exercise (17.5 kcal) condition had lower depression scores after 12 weeks than the participants in the low exercise (7.0 kcal) condition. There was no main effect of amount of exercise: It did not matter whether exercise was scheduled for 3 or 5 times per week. There was no interaction effect. For this activity, higher scores on the depression measure indicate greater depression. Scores on this measure can range from 0 to 16.

5. Read each of the following research scenarios and then fill in the correct answer in each column of the ta