Psych 311 1nd Edition Lecture 23 Outline of Last Lecture I Review of ANOVA II One Way ANOVA Example Outline of Current Lecture I II III IV V One Way ANOVA Example Repeated Measures ANOVA Comparing F s Post Hoc Tests Factorial ANOVA Current Lecture I One Way ANOVA Example M1 10 SS1 90 M2 15 SS2 70 What happens if we change M2 from 15 to 20 F between group variance within group variance MSbt MSwi wi average of the 2 variances bt difference between means In order to reject Ho F needs to be large Changing M2 from 15 20 will change the bt group variance because it will make the numerator larger therefore increasing SSbt and F What happens if we change SS M1 10 SS1 50 M2 15 SS2 70 SSwi will decrease denominator therefore F will increase II Repeated Measures ANOVA Use repeated measures ANOVA when you measure the same group 2 or more times 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 basic logic behind a repeated measures ANOVA is the same as the logic behind the one way ANOVA Although it differs in that there s a second parsing of variance and the design not test eliminates individual differences ID from the between group variance while the test not design mathematically removes the ID variance from the within group variance ID are the characteristics the individuals bring to the group design eliminates this by using same group multiple times The benefits of eliminating and removing ID s is that they might otherwise obscure treatment effect effect of IV we are minimizing noise in data this makes effect apparent Repeated Measures ANOVA parsing s TV total variance BTG between groups variance IV without ID s Second parsing appears only for the repeated measures ANOVA WIG within groups variance SE BTS between subject variance ID s We remove this using the test III Comparing F s First parsing occurs in both the oneway ANOVA and the repeated measures ANOVA One Way ANOVA Error Variance remaining SE This becomes the denominator after we remove BTS varianceANOVA Repeated Measures F MSbt MSwi F MSbt MSerror Msbt obtained or observed difference between groups or conditions effect of IV MSbt obtained or observed difference between groups or conditions without influence of ID s effect of IV MSwi sampling error MSerror sampling error but with ID s removed If F 1 00 then Ho is true FTR If F 1 00 then Ho is true FTR IV Post Hoc Tests Step 6 for Repeated Measures ANOVA The logic behind the post hoc test for a repeated measures ANOVA is the same for oneway ANOVA NOTE applies to both one way and repeated measures ANOVA You ONLY need to conduct a post hoc test if two conditions are met 1 If you re comparing 3 or more groups K 2 2 If you reject Ho The post hoc test tells you where your significance occurs between which groups V 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 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