Psych 311 1nd Edition Lecture 24 Outline of Last Lecture I One Way ANOVA Example II Repeated Measures ANOVA III Comparing F s IV Post Hoc Tests V Factorial ANOVA Outline of Current Lecture I Factorial ANOVA Is same information as on last set of notes Current Lecture I Factorial ANOVA Factorial Design a strategy for asking a research question in which you combine two or more IV s Factorial ANOVA the HT you use for a factorial design Terminology Factors IV s Levels of groups or conditions per IV remember you must have at lest 2 levels per an IV Two way design 2 IV s Three way design 3 IV s etc Mixed factorial 2 or more IV s that are a combination of independent samples and repeated measures Example We want to know if 1 putting a smiley face on a bill will affect one s tip amount and 2 whether gender of the server affects tip amount IV s smiley face and gender We can answer this as two separate questions but if we combine them we can 1 answer the same 2 questions and 2 get the added benefit of seeing whether These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute the combination of the IV s lead to results above and beyond the two separate studies Nomenclature how we write about factorial ANOVA s ex 2x2 factorial design each number represents an IV the number value indicates the number of level for that IV ex 2x3x3 factorial ANOVA has 3 IV s the first IV has two levels the second and third IV has 3 levels ex 2x2x3 mixed factorial with repeated measures on the latter factor there are 3 IV s first two each with 2 levels the 3rd IV with 3 levels this is a combination of repeated measures and independent samples IV 3 is the repeated measures sample IV 1 and 2 are the independent samples between subject groups the IV s chosen or their of levels does not determine whether it is the repeated measures or independent samples its based on the wording of the description In a factorial ANOVA we can evaluate several things Main effect effect of 1 IV in isolation by itself there is a main effect for each IV Interactions affect of combination of IV s together rather than each individually ex What is the effect of one washing hands with either soap or water or both of X s of germs Soap Water Yes No Yes X XXX No XXX XXXXX Interpretation The combination of soap and water together is better than soap or water alone Follow up of tip example 2X2 factorial design IV1 use of or not IV2 gender of waiter For this factorial ANVOA we conduct 3 separate F tests 1 for main effect of 2 for main effect of gender 3 for interaction between and gender Gender Male Female Main effect for No 21 28 24 5 Yes 18 33 25 5 Main effect for gender 19 5 30 5 DV tip 1 Compare gender groups without consideration of women make more tips 2 Compare effect of without consideration of gender about the same amount in tips 3 Compare interaction of and gender women make more with than without men make less with than without When looking at data on a graph if there are nonparallel lines then there is an interaction If there are parallel lines then there isn t an interaction NOTE main effect and interactions are independent you can have main effects without interactions interactions without main effects both main effects and interactions neither main effects nor interactions Post Hoc Test logic behind post hoc test in a factorial ANOVA is the same as one way ANOVA and repeated measures ANOVA total variance