Analysis of variance

ANOVA stands for Analysis of Variance. ANOVA is a family of multivariate statistical technique for helping to infer whether there are real differences between the means of three or more groups or variables in a population, based on sample data. Before tackling this topic, you should be familiar with normal distribution and testing differences.

Interactions
When two or more IVs combine to have synergistic effects on the DV, an interaction is said to occur. This means that the effect of one IV on the DV is moderated by another IV.
 * Notes on understanding interaction

Effect size
Effect sizes should be reported in addition to significance test results for ANOVA. Of note are eta-squared, partial eta-squared and Cohen's d:
 * 1) Partial eta-squared for each of the main effects and interaction(s) (e.g., via SS formula or SPSS - ANOVA - Options)
 * 2) (Total) eta-squared (e.g., via SS formula (SS between groups / Total SS); equivalent to R2 (total variance explained), i.e., provides % of variance in the dependent variable explained by the independent variables.
 * 3) Cohen's d can be calculated, this is for the differences between two means; i.e., pairwise contrasts. So, you might just want to focus on some contrasts e.g., if there's a significant main effect for gender, then compute the Cohen's d for overall motivation for males and females. You can use the spreadsheet from Tutorial 5 or calculate yourself, using http://en.wikipedia.org/wiki/Effect_size#Cohen.27s_d

Recommended further reading: Measures of Effect Size (Strength of Association) for Analysis of Variance (Becker, 1999).


 * FAQ
 * Should I report effect sizes even when the F tests are not significant?


 * ✅ Effect size and statistical significance are two different, important pieces of information about an ANOVA. In a high power study, the results may be statistically significant but the size of the effect may be trivial. On the other hand, in a low power study, the results may not statistically significant, but the size of the effects may be small, medium, or even large. Thus, both are important.

Power
Power for ANOVAs can usually be calculated as part of the analysis using statistical software (e.g., SPSS).

Data analysis exercises

 * ANOVA data analysis tutorial (3rd year tutorial)