Complex Experimental Designs Chp 10 Experimental Designs with only two levels of the independent provides limited information about the relationship between the independent and (review High (medium) Low anxiety and test performance and curvilinear relationships ) dependent variables If a curvilinear relationship is predicted then at least three levels of a variable must be used as many curvilinear relationships exist in psychology (example of fear and attitude change-increasing the amount of fear aroused by a persuasive message increases attitude change only up to a moderate level after which further increases in fear arousal actually reduce attitude change) pg 198 Factorial Designs Designs with multiple levels of the independent variable are more representative of actual events

Factorial designs are designs with more than one independent variable (factor) All levels of each independent variable are combined with all levels of the other independent variable(s) pg199 A researcher might be interested in the effect of whether or not a stimulus person (shown in a photograph) is smiling or not on ratings of the friendliness of that person. The researcher might also be interested in whether or not the stimulus person is looking directly at the camera makes a difference. In a factorial design, the two levels of the first independent variable (smiling and not smiling) would be combined with the two levels of the second (looking directly or not) to produce four distinct conditions: smiling and looking at the camera, smiling and not looking at the camera, not smiling and looking at the camera,

and not smiling and not looking at the camera Interpretation of Factorial Designs Two types of effects are studied in a factorial design Main effect and Interaction effect If there are two independent variables there is a main effect for each of them pg200 Main effect-is the overall effect of one independent variable and the dependent variable,-the overall effect of each independent variable. In the example of Therapy type and Therapy Duration there is a main effect for Therapy type and a main effect for duration of therapy Interaction

effects occur when the is an interaction between the two independent variables such that the effect of one independent variable depend on the level of the other independent variable Factorial Designs Type of Therapy (B) Duration of Therapy (B) Factorial design 2x2 with four experimenta l conditions Behavioral Cognitive Short n = 50

n = 50 Long n = 50 n = 50 A design with two independent variables with one variable at two levels and the other at three is a 2 x 3 factorial design with six conditions. A 3 x 3 design will have nine conditions Factorial Designs Type of Therapy (B) Behavioral Cognitive Short Duration of Therapy (B) n = 50 n = 50

Long n = 50 n = 50 In the above experiment the type of psychotherapy (cognitive vs. behavioral) is one main effect for the first independent variable (Therapy type) and the duration of psychotherapy (short vs. long)a second main effect of Therapy duration Interpretation of Factorial Designs In the experiment, the main effect of type (cognitive vs. behavioral) is the difference between the average score for the cognitive group and the average score for the behavioral group ignoring duration. That is, short-duration subjects and long-duration subjects are combined together in computing these averages. The main effect of duration is the difference between the average score for the short-duration group and the average score for the long-duration group this time ignoring type.

Interpretation of Factorial Designs We see that the subjects in the cognitive conditions scored higher on average than the subjects in the behavioral conditions indicating a main effect for Therapy type This 2x 2 factorial design has four experimental conditions-short duration behavioral therapy, long duration behavioral therapy, short duration cognitive therapy and long duration cognitive therapy Interpretation of Factorial Designs Interaction effect- whenever the effect of one independent variable depends on the level of the other -If cognitive psychotherapy is pg201

better than behavioral psychotherapy when the therapy is short but not when the therapy is long, then there is an interaction between type and duration of therapy When we say it depends we are indicating that some type of interaction is at work. You would like to go to Vegas if you have enough money and you have completed Interpretation of Factorial Designs Effects are all independent of each other. A 2x2 factorial experiment might result in no main effects and no interaction, one main effect and no interaction, two main effects and no interaction, no main effects and an interaction, one main effect and an interaction, or two main effects and an interaction. In looking at results presented in a design table or (more

importantly) a graph, you can interpret what happened in terms of main effects and interactions. Factorial Designs with Manipulated and Nonmanipulated variables One common type of factorial design includes both experimental (manipulated) and nonexperimental (nonmanipulated) variables These designs investigate how different people respond to certain situations. They investigate how the manipulated (independent) variable affects certain personal characteristics or attributes (age, gender,personality types etc.) Interactions and Moderator Variables Moderator variables influence the relationship between two other variables A moderator is a variable (z) whereby x and y have a different relationship between each other at the various levels of z. Note that

this is essentially what is entailed in an interaction. a moderator variable is one that influences the strength of a relationship between two other variables, and a mediator variable is one that explains the relationship between the two other variables Whereas moderator variables specify when certain effects will hold, mediators speak to how or why such effects occur (Baron & Kenny, 2986, p. 1176). Mediate vs. Moderate Mediating variable-Synonym for intervening variable. Example: Parents transmit their social status to their children directly, but they also do so

indirectly, through education: Parents status childs education childs status- education is a mediating variable (mediators explain) Moderating variable A variable that influences, or moderates, the relation between two other variables and thus produces an interaction effect. a moderator is a third variable that affects the correlation of two variables if we were to replicate the Asch Experiment experiment with a female subject and found that her answers (Y variable) were not affected by confederates answers (X variable), then we could say that gender is a Moderator (M) in this case https://www.youtube.com/watch? v=3ymkfDBwel0

Moderators vs. Confounders Moderator: A moderator is a variable (z) whereby x and y have a different relationship between each other at the various levels of z. Note that this is essentially what is entailed in an interaction. A variable that influences, or moderates, the relation between two other variables and thus produces an interaction effect. Confounder: A third variable that is related to x in a non-causal manner and is related to y either causally or correlationally. The third variable (z) is related to y even when x is not present. A confounding variable is an extraneous variable (i.e., a variable that is not a focus of the study) that is statistically related to (or correlated with) the independent variable. A variable that obscures the effects of another variable. Confound vs

Mediator confound vs. mediator An internal validity confound and mediator have the same mathematical relationships to the independent and dependent variables. Both are third variables that explain the relationship between the independent and dependent variables, that is, the shared variance between the independent variable and the confound/mediator is associated with the dependent variable. We choose the label confound or mediator based on our conceptualization of the causal process that relates the independent to the dependent variable. We label this third variable a confound if it is extrinsic to the causal process, and we label it a mediator if it is intrinsic to the causal process. Lets review How to control for confounding variables Confounding variable (continued)This is bad because the point of an experiment is to create a situation in which the only difference between conditions is a difference in the independent variable. This is what allows us to conclude that the manipulation is the cause of differences in the

dependent variable. But if there is some other variable that is changes along with the independent variable, then this confounding variable could be the cause of any difference Controlling confounding variables-Essentially all person variables can be controlled by random assignment. If you randomly assign subjects to conditions, then on average they will be equally intelligent, equally outgoing, equally motivated, and so on variablehttps://www.youtube.com/watch?v=B7QdNYLp_E0 confounding variables Moderator variables A moderator variable changes the strength of an effect or relationship between two variables. Moderators

indicate when or under what conditions a particular effect can be expected. A moderator may increase the strength of a relationship, decrease the strength of a relationship, or change the direction of a relationship. In the classic case, a relationship between two variables is significant (i.e, non-zero) under one level of the moderator and zero under the other level of the moderator. For example, work stress increases drinking problems for people with a highly avoidant (e.g., denial) coping style, but work stress is not related to drinking problems for people who score low on avoidant coping (Cooper, Russell, & Frone, 1990). Example of Moderation Stress Depression Social Support One of the clearest examples of moderation was presented

by Cohen and Wills (1985). They argued that the social support literature (to that point in 1985) had neglected to consider the role of social support as a moderator of the stress to adjustment relationship. This moderation relationship is often depicted as shown above This schematic suggests that the relationship between stress and depression may differ in strength at different levels of social support. In other words, stress may be more strongly associated with depression under conditions of low social support compared to conditions of high social support. Outcomes of a 2 X 2 Factorial Design Two levels to each of two independent variables We must determine if there is a significant main effect for variables A, B and an interaction effect

between the variables In the example to the right there is a Main Effect for Both Room Temperature and Test Difficulty but no interaction effect. Main effects and interaction effects We see that the six subjects in the cognitive conditions scored three points higher on average than the six subjects in the behavioral conditions. This is the main effect of the type of psychotherapy.To see the main effect of the duration of

psychotherapy, we compare the average score in the short condition with the average score in the long condition, now computing these averages across subjects in the cognitive and behavioral conditions. We see that the six subjects in the long conditions scored three points higher on average than the six subjects in the short conditions. This is the main effect of the duration of psychotherapy Main Effects Therapy Type X Duration Below are the same results plotted in the form of a bar graph. The main effect of type is indicated by the fact that the two cognitive bars are higher on average than the two behavioral bars. The main effect of duration is indicated by the fact that the two long-duration (dark) bars are higher on average than the two short-duration (light) bars Main Effects and Interaction Effects Parallel lines in these types of graphs indicate that there are main effects in the results, but no interactions. If the lines are not parallel this is indicative of an interaction.

"Do students do better on hard tests or easy tests?" "It depends, in a fifty degree room there is no difference, but in a ninety degree room they do much better on easy tests. Interaction effect Students do best when the test is easy and the temperature is 90 degrees. Interaction effect Independent Groups, Repeated Measures and Mixed Factorial designs In a 2 x 2 Factorial design with four conditions for an Independent Group (between-subjects) design, a different group of subjects will be assigned to each of the four conditions. Following the example on pg208 if you have a 2 x 2 design with 10 subjects in each condition you will need 40 subjects total

S11,S12,S13, S1,S2,S3, Level 1 Var B Level 2S14, S4,S5,S6,S7,S S15,S16,S17, 2 x 2 8, S9,S10 Independent Level 1 S18, S19,S20 Groups ( Between S31,S32,S34,S S21,S22,S23, Subjects Design 35, S24, S36,S37,S38, Level 2 S25,S26,S27, S39,S40 S28, S29,S30

Var A Independent Groups, Repeated Measures and Mixed Factorial designs In a repeated measures (within-subjects) design the same subjects will participate in ALL conditions Level 1 Var B Level 2 A Level 1 Level 2 S1,S2,S3,

S1,S2,S3, S4,S5,S6,S7,S S4,S5,S6,S7,S 2 x 2 8, S9,S10 8, S9,S10 Repeated measures (withingroups) design S1,S2,S3, S4,S5,S6,S7,S 8, S9,S10 S1,S2,S3, S4,S5,S6,S7,S 8, S9,S10 Var Independent Groups, Repeated Measures and Mixed Factorial designs In a 2 x 2 mixed Factorial design ten different

subjects are assigned to Levels 1 and 2 of Variable A but Variable B is a repeated measures with subjects assigned to each of the two levels of Variable A receiving both Levels of Variable B Level 1 Var A Level 1 Level 2 Variable B Level 2

S1,S2,S3, S1,S2,S3, S4,S5,S6,S7,S S4,S5,S6,S7,S 8, S9,S102 x2 Mixed8, S9,S10 Factorial S11,S12,S13,S S11,S12,S13,Design S14,S15,S16, S17,S18, S19,S20 14,S15,S16,S1 7,S18, S19,S20 Increasing the Number of Levels of an Independent Variable You can increase the complexity of the basic 2 x 2 Factorial design by increasing the number of levels of one or more of the independent

variables pg209