Full Exploration of 2x2 Between-Subjects Designs Two IVs = 2c2 factorial design e.g. how boys and girls react to exposure to family aggression and violence 60 T 50 Exposed to Violence 60 I Not Exposed to Violence 40 50 Mean Aggression Score 40 30 20 Aggression Score 30 10 0 Exposed to Violence Not Exposed to Violence 20 10 0 Boys I Girls Main effects: · Boys are more aggressive than girls · Exposure to family aggression leads to more aggression Interaction: · The effect of family aggression exposure is only present in boys not girls · Post hoc ("after this" in Latin) tests are used to uncover specific differences between three or more group means when an analysis of variance (ANOVA) F test is significant. · ANOVA tells you if you have an overall differences between groups but post hoc tells you which specific groups differed. Post hoc tests should only be run when you have a significant difference. Post hoc tests attempt to control the familywise error Conducting multiple comparisons: · Conducting multiple tests leads us to inflate the type 1 error rate (say its positive but it's not) . Every time we run a new testft we increase the alpha . Thereforeft with enough testsft we will always find a significant results . Thereforeft we must correct our alpha level - Bonferroni correction or post hoc tests Problems with multiple comparisons: · Leads to false positions. E.g. if you conducts 1fifi statistical tests with a p value of .fi5ft you'd expect at least 5 of the tests to be significant due to chance · The most common way to control type 1/familywise error is through Bonferroni correction - divide the alpha by how many additional tests there are Bonferroni Correction: · Useful when these are a fairly small number of multiple comparisons . If you have a large number of multiple comparisons and you've looking for many that might be significantft the Bonferroni comparison may lead to a very high rate of false
negatives - it is unlikely that lots of comparisons will have an extremely low significance Restricted contrasts . These adjustments are to the alpha level: · Bonferroni correction: · a = aFwC · Šidák-Bonferroni Procedure: · a = 1 - (1 - arw)1/c Post hoc tests (pairwise comparisons): · Tukey HSD (honest significant difference) - to determine if the relationship between two sets of data is significant - 3 or more (ANOVA). His test compares the difference between means of values rather than pairs of valuesft divide the absolute value of difference of means by standard error · Games-Howellft Hochberg GT2ft Gabriel's (adjusts for unequal variances) - non- parametric test (did not meet homogeneity of variance assumptions) to compare combinations of groups. It is different to Tukey's test as it does not assume equal variances and sample sizes. · Fisher-Hayter (step procedure) · Neuman-Keulsft Ryan-Einot-Gabriel-Welsch . Scheffe's Procedure (corrects the alpha level) - allows the investigator to do all possible testsft and still maintain