Iv x pv factorial design example

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

LEARNING OBJECTIVES

· 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.