The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Chapter Twelve: Designing, Conducting, Analyzing, and Interpreting Experiments with Multiple Independent Variables – Part 2 Chapter Twelve: Designing, Conducting, Analyzing, and Interpreting Experiments with Multiple Independent Variables – Part 2

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Statistical Analysis: What Do Your Data Show? Naming Factorial Designs Labels you may hear that reflect the size of the design include: Factorial ANOVA Two-way ANOVA Three-way ANOVA X by Y

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Naming Factorial Designs For designs that use random assignment for all IVs, labels that describe how participants are assigned to groups might include:

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Naming Factorial Designs For designs that use random assignment for all IVs, labels that describe how participants are assigned to groups might include: Independent groups; Independent samples Completely randomized Completely between-subjects Completely between-groups Totally between-subjects Totally between-groups

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Naming Factorial Designs Designs that use matching or repeated measures may be called: Randomized block Completely within-subjects Completely within-groups Totally within-subjects Totally within-groups Repeated Measure

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Naming Factorial Designs Designs that use a mixture of “between” and “within” assignment procedures may be referred to as:

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Naming Factorial Designs Designs that use a mixture of “between” and “within” assignment procedures may be referred to as: Mixed factorial

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Planning the Statistical Analysis Suppose you are examining the data from the previous (Chapter 11) experiment and you think you detected an oddity in the data: It appears that salesclerks may have responded differently to female and male customers in addition to the different styles of dress.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Rationale of Factorial ANOVA The rationale behind ANOVA for factorial designs is basically the same as we saw in Chapter 11, with one major modification. We still use ANOVA to partition (divide) the variability into two sources – treatment variability and error variability.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Rationale of Factorial ANOVA For a two-IV factorial design we use the following equations: Factor A = IV A variability error variability

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Rationale of Factorial ANOVA For a two-IV factorial design we use the following equations: Factor B = IV B variability error variability

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Rationale of Factorial ANOVA For a two-IV factorial design we use the following equations: Factor A by B = interaction variability error variability

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Understanding Interactions When two variables interact, their joint effect may not be obvious or predictable from examining their separate effects. For example, drinking a glass or two of wine may be a pleasurable and relaxing experience and driving may be a pleasurable and relaxing experience but is drinking wine and driving an extremely pleasurable and relaxing experience?

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Understanding Interactions When two variables interact, their joint effect may not be obvious or predictable from examining their separate effects. Combinations of drugs, in particular, are likely to have synergistic effects so that a joint effect occurs that is not predictable from either drug alone.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Understanding Interactions Synergistic Effects Dramatic consequences that occur when you combine two or more substances, conditions, or organisms. The effects are greater than what is individually possible.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Interpreting Computer Statistical Output We will deal with 2 X 2 analyses in these three different categories to fit our clothing-by-customer-sex experiment: Two-way ANOVA for independent samples Two-way ANOVA for correlated samples Two-way ANOVA for mixed samples

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples The two-way ANOVA for independent samples requires that we have two IVs (clothing style and customer sex) with independent groups.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples The two-way ANOVA for independent samples requires that we have two IVs (clothing style and customer sex) with independent groups. To create this design we would use four different randomly assigned groups of salesclerks.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples The two-way ANOVA for independent samples requires that we have two IVs (clothing style and customer sex) with independent groups. To create this design we would use four different randomly assigned groups of salesclerks. The DV scores represent clerks’ response times in waiting on customers.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Source Table In the body of the source table, we want to examine only the effects of the two IVs (clothing and customer sex) and their interaction. The remaining source (w. cell or Within) is the error term and is used to test the IV effects. Different statistical programs will use a variety of different names for the error term.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Source Table The effect of sex shows an F ratio of 3.70, with a probability of.07. This IV shows marginal significance.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Marginal Significance Marginal significance refers to statistical results with a probability of chance between 5% and 10% (almost significant but not quite). Researchers often talk about such results as if they reached the p =.05 level. Dealing with marginally significant results means you run an increased risk of making a Type I error (accepting the experimental hypothesis when the null hypothesis is true).

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Source Table The effect of sex shows an F ratio of 3.70, with a probability of.07. This IV shows marginal significance. The probability of “clothes” falls below.01 in the table. The interaction between clothing and customer sex produced an F ratio of 6.65 and has p =.02, therefore denoting significance.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Two-Way ANOVA for Independent Samples Source Table A significant interaction renders the main effects moot because those main effects are qualified by the interaction and are not straightforward.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Hypothetical Experiment 1 In the following study, male and female participants were instructed to press a button on a computer keyboard as soon as they detected a tone through their headphones. Participants were randomly assigned to hear either a loud tone or a soft tone. The researchers measured the amount of time it took participants to press the computer button (in milliseconds). Smaller numbers indicate better performance on the task.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Source Table – Hypothetical 1

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Hypothetical Experiment 2 In the following study, male and female participants were instructed to press a button on a computer keyboard as soon as they detected a tone through their headphones. The researchers were interested in determining if a disturbing visual image would distract from the tone and thus reduce the reaction time of participants. Half of the time, participants saw a graphic image (bloody body) on the computer screen at the exact moment the tone sounded, and the other half of the time the participants saw a non- graphic image (non-bloody body). The researchers measured the amount of time it took participants to press the computer button (in milliseconds). Smaller numbers indicate better performance on the task.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Souce Table – Experiment 2

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Hypothetical Experiment 3 In the following study, participants were instructed to press a button on a computer keyboard as soon as they detected a tone through their headphones. Half of the time the computer screen flashed a light at the exact moment the tone was presented, and the other half of the time there was no flash of light. In addition, half of the time a sensor on the participant’s arm pulsed (causing a slight tickle) at the exact moment of the tone, and half of the time the sensor did not pulse. The researchers were interested in determining the extent to which these distractions would cause participants to have delayed reaction times to the tone. The researchers measured the amount of time it took participants to press the computer button (in milliseconds). Smaller numbers indicate better performance on the task.

The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education Source Table –Experiment 3