up:: [[Independent Measures ANOVA Tests]] Tags:: # Factorial ANOVA Tests Factorial [[Independent Measures ANOVA Tests]] tests are a type of ANOVA test done on [[Factorial Design]]. ###### What are the questions of a factorial ANOVA test? 1. Do the factors affect our independent variable? 2. Do the factors affect each other? ###### What is the main effect? The mean differences among all the levels of one factor. For example, in this case the main effect for Factor A (males versus females) would be 8 - 4 or 4 and the main effect for factor B would be 7 - 5. ![[Pasted image 20221102072023.png]] ### Calculating f-ratios for factorial ANOVA Three separate hypothesis tests are calculated, each with it's own f-ratio. - One on the main effect of factor F1 - One on the main effect of factor F2 - One on the interactions between F1 and F2 ![[Pasted image 20221021154229.png|700]] If there is an interaction between F1 and F2 there is debate among statistics researchers about whether the main effects are really significant or just tangentially significant based on strong interaction. This is because significant interaction effects mean that the probability of a significant difference in means being shown in between one factor changes depending on the level of the other factor. ### What are the null and alternative hypothesis for factorial tests? There are three different couplets of H0: and H1: for factorial designs. The first two H0: is that the levels of the factor have the same means. The first two H1: is that there is a difference in means between the factors. The third H0: is that the there is no interaction between the two factors where as the H1: is that there is some interaction between the factors. ### The 19 calculations of the Factorial ANOVA tests ![[Pasted image 20221024145520.png]] ### Factorial ANOVA table: ![[Pasted image 20221024151632.png|1000]] ### How many f-crit values do you need for a factorial ANOVA? You need to calculate a separate f ratio for each of the different tests mentioned up above. This means if you have two factors, you will have three f-ratios because you need one for Factor A, one for Factor B, and one for the interaction between Factor A and B. ### Calculating effect size for factorial ANOVA: ![[Pasted image 20221024154719.png]] To do [[Post hoc pairwise comparisons]] see this note and go to the factorial ANOVA section. However, if there are more than two levels to the factor we are analyzing, we will have to do [[Post hoc non pairwise tests]]. Related: ___ # Resources