1. PowerPoint presentation to accompany Research Design Explained 5th edition ; ©2004 Mark Mitchell & Janina Jolley Chapter 11 Factorial Designs

2. PowerPoint presentation to accompany Research Design Explained 5th edition ; ©2004 Mark Mitchell & Janina Jolley The 2X2 Factorial Design l The two by two yields four (two pairs of) simple main effects l Averaging a treatment’s main effects lets you find the overall main effect: The average effect of varying a factor l Comparing a factor’s simple main effects lets you find the interaction between two factors

3. PowerPoint presentation to accompany Research Design Explained 5th edition ; ©2004 Mark Mitchell & Janina Jolley Interactions Are Important: l Interesting questions in modern psychology are often questions about interactions l External validity questions are questions involving interactions l Questions in applied psychology are often questions involving interactions

4. PowerPoint presentation to accompany Research Design Explained 5th edition ; ©2004 Mark Mitchell & Janina Jolley Potential Results of a 2X2 Factorial Experiment l A main effect and no interaction l Two main effects and no interaction l Two main effects and An interaction l Interaction without main effects l One main effect and An interaction l No main effects and no interaction

5. PowerPoint presentation to accompany Research Design Explained 5th edition ; ©2004 Mark Mitchell & Janina Jolley The Mathematics behind an ANOVA table l SS effect / df effect = MS for effect l df for main effect = Levels of main effect -1 l df for interaction between two variables = df for 1st main effect X df for 2nd main effect l df for error term = Number of participants - total number of groups l MS effect / MS error = F l The larger F, the more likely the result is to be significant.

6. PowerPoint presentation to accompany Research Design Explained 5th edition ; ©2004 Mark Mitchell & Janina Jolley Interpreting the Results of a 2 X 2 Experiment l Main effects without interactions: It all adds Up l Interactions: When combining factors leads to effects that appear to differ from the sum of the individual effects

7. PowerPoint presentation to accompany Research Design Explained 5th edition ; ©2004 Mark Mitchell & Janina Jolley Ordinal Interactions: “True” Interaction or Measurement- Induced Mirage? l Ordinal interactions may mean that combining treatments multiplies their individual effects l Ordinal interactions may be measurement induced mirages

8. PowerPoint presentation to accompany Research Design Explained 5th edition ; ©2004 Mark Mitchell & Janina Jolley When to Suspect that an Ordinal Interaction May Be a Mirage l When your data may be ordinal. Suspect that your interaction is a mirage if: –Your measure is ordinal, as would be the case if you had ranked data –Ceiling effects appear likely –Floor effects appear likely

9. PowerPoint presentation to accompany Research Design Explained 5th edition ; ©2004 Mark Mitchell & Janina Jolley Cross-Over (Disordinal) Interactions: When Interactions Really Are Interactions l Cross-over interactions can’t be the result of having ordinal data

10. PowerPoint presentation to accompany Research Design Explained 5th edition ; ©2004 Mark Mitchell & Janina Jolley Putting the 2X2 to Work l Adding a replication factor to increase generalizability l Using an interaction to find an exception to the rule: Looking at a potential moderating factor

11. PowerPoint presentation to accompany Research Design Explained 5th edition ; ©2004 Mark Mitchell & Janina Jolley The Hybrid Design: A Factorial Design that Allows You to Study Non-Experimental Variables l Limitation: Can’t make causal statements about the nonexperimental factor l Advantages –Increasing generalizability –Studying effects of similarity –Finding an exception to the rule

12. PowerPoint presentation to accompany Research Design Explained 5th edition ; ©2004 Mark Mitchell & Janina Jolley Concluding Remarks l Factorial experiments allow you to –Look at the effects of more than one factor at a time –Look for interactions, so that you can l Find moderating variables l Look at the effects of similarity l Answer more interesting questions