Chapter 8 Factorial Designs Power Point presentation to

Chapter 8 Factorial Designs Power. Point presentation to accompany Research Design Explained 4 th edition; © 2000 Mark Mitchell & Janina Jolley

The 2 X 2 Factorial Design l l l The two by two yields four (two pairs of) simple main effects Averaging a treatment’s main effects lets you find the overall main effect: The average effect of varying a factor Comparing a factor’s simple main effects lets you find the interaction between two factors *Power. Point presentation to accompany Research Design Explained © 2000 Mark Mitchell & Janina Jolley 4 th edition;

Interactions Are Important: l l l Interesting questions in modern psychology are often questions about interactions External validity questions are questions involving interactions Questions in applied psychology are often questions involving interactions *Power. Point presentation to accompany Research Design Explained © 2000 Mark Mitchell & Janina Jolley 4 th edition;

Potential Results of a 2 X 2 Factorial Experiment l l l A main effect and no interaction Two main effects and An interaction Interaction without main effects One main effect and An interaction No main effects and no interaction *Power. Point presentation to accompany Research Design Explained © 2000 Mark Mitchell & Janina Jolley 4 th edition;

The Mathematics behind an ANOVA table l l l SS effect/df effect= MS for effect Df for main effect = Levels of main effect -1 Df for interaction between two variables = df for 1 st main effect X df for 2 nd main effect Df for error term = Number of participants - total number of groups MS effect / MS error = F The larger F, the more likely the result is to be significant. *Power. Point presentation to accompany Research Design Explained © 2000 Mark Mitchell & Janina Jolley 4 th edition;

Interpreting the Results of a 2 X 2 Experiment l l Main effects without interactions: It all adds Up Interactions: When combining factors leads to effects that appear to differ from the sum of the individual effects *Power. Point presentation to accompany Research Design Explained © 2000 Mark Mitchell & Janina Jolley 4 th edition;

Ordinal Interactions: “True” Interaction or Measurement. Induced Mirage? l l Ordinal interactions may mean that combining treatments multiplies their individual effects Ordinal interactions may be measurement induced mirages *Power. Point presentation to accompany Research Design Explained © 2000 Mark Mitchell & Janina Jolley 4 th edition;

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 *Power. Point presentation to accompany Research Design Explained © 2000 Mark Mitchell & Janina Jolley 4 th edition;

Cross-Over (Disordinal) Interactions: When Interactions Really Are Interactions l Cross-over interactions can’t be the result of having ordinal data *Power. Point presentation to accompany Research Design Explained © 2000 Mark Mitchell & Janina Jolley 4 th edition;

Putting the 2 X 2 to Work l l Adding a replication factor to increase generalizability Using an interaction to find an exception to the rule: Looking at a potential moderating factor *Power. Point presentation to accompany Research Design Explained © 2000 Mark Mitchell & Janina Jolley 4 th edition;

The Hybrid Design: A Factorial Design that Allows You to Study Non-Experimental Variables l l Limitation: Can’t make causal statements about the nonexperimental factor Advantages – Increasing generalizability – Studying effects of similarity – Finding an exception to the rule *Power. Point presentation to accompany Research Design Explained © 2000 Mark Mitchell & Janina Jolley 4 th edition;

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 l l Find moderating variables Look at the effects of similarity Answer more interesting questions *Power. Point presentation to accompany Research Design Explained © 2000 Mark Mitchell & Janina Jolley 4 th edition;