up:: [[Independent Measures ANOVA Tests]] Tags:: # Post hoc pairwise comparisons A post hoc pairwise comparisons test is how you determine what groups after an [[Independent Measures ANOVA Tests]] test are statistically different from each other. ###### When do you do a post hoc pairwise comparison? 1. When you show a difference between groups using an ANOVA test. 2. There are three or more groups to compare. ## What three methods are there to correct for the cumulative P(Type 1 error)? Before we can do the post hoc pairwise test we must account for the cumulative P(Type 1 error) that comes from the [[Multiple comparisons fallacy]]. ### Bonferroni's correction [[Multiple comparisons fallacy#^74d9f9]] ### Tukey HSD Test Tukey's HSD test works when we can directly compare *two* groups together. In other words, for pairwise groups. HSD represents the critical value for which a difference in means is significant. It requires you have already done a [[Independent Measures ANOVA Tests]] test and then that you compare the means between groups after calculating it. Equation for Tukey HSD: ![[Pasted image 20221019150718.png]] To calculate q we must use the [[Studentized range statistic (q) table]] with the within groups df and k (number of groups). Once you have the value for HSD you analyze whether two groups are statistically different from each other by subtracting means between groups and seeing if they are outside of the range of HSD. ###### What is the error term? It's the same as within groups df. ### Scheffe's post hoc test Test re-calculates the f-ratio done with the [[Independent Measures ANOVA Tests#What is the general 9 calculations needed for an ANOVA test?|9 calculations done in a ANOVA test]] with some minor adjustments. Like the Tukey HSD test, it also requires that you have undergone an [[Independent Measures ANOVA Tests]] test before doing it. You can keep all of the calculations undergone during your ANOVA test except for the SS between and the MS between. You recalculate these by comparing only two groups instead of all the groups as a whole. This gets rid of the [[Multiple comparisons fallacy]]. #### Calculating SSbetween-two Use the SSbetween equation with the two specific groups you are comparing: ![[Pasted image 20221017152900.png|500]] #### MS-between for Scheffe's test: ![[Pasted image 20221019152146.png]] f-ratios calculated in the Scheffe's test are called Fscheffe's. #### f-ratio equation for a Scheffe's test is: ![[Pasted image 20221019152233.png]] Then you compare these f-ratios to the f-crit values. If they are outside of the boundaries those groups are deemed to have significantly different means. Related: [[Post hoc non pairwise tests]] ___ # Resources