ANOVA 101

Since this blog targets different audience spectrum, I thought it will be useful to introduce basic information about ANOVA (analysis of variance) in a question format.

What is ANOVA?

A statistical method used to determine if there is a significant difference exist when comparing the mean of 3 or more independent groups, the ANOVA test is called the F test. It tests the null hypothesis

– H0: MeanA= MeanB = MeanC

Why variance not mean?

When trying to find significant difference between 3 or more groups, it will be difficult to represent such difference by a single mean value. If the means of the analyzed groups are close then we tend to have low variance, but if they are far apart they will have high variance. A multiple T-test can be performed but that will complicate calculations and increase type 1 error.

What assumptions should be made when running ANOVA?

Two basic assumptions should be made, the first is the samples should be normally distributed, and the second, the populations should have equal (homogeneity) of variance. Levene’s test or Bartlett test assesses this assumption.

What is two way ANOVA?

Is an extension of one way ANOVA? It examines the effect of two independent variables (IV) on one continuous dependent variable. Each of the independent variable may have any number of levels. It goes beyond finding the effect of each independent variable but also it finds if there is an interaction exist between them. When running a two way ANOVA, three F values will be obtained. One will tell us if the first IV have an effect on the DV, the second value will tell us if there is an effect from the second IV on the DV, and the third value will tell us if the interaction between the two IVs have an effect on the DV.

What is MANOVA?

Multivariate analysis of variance test if one or more independent variables have effect on a two or more dependent variables. Individual ANOVAs may show no significant effect, but taken together they might, due to the interactions between the IVs.

Is ANOVA enough to answer our research question?

Often the statistical test performed will test the if there is a significant effect exist, but will not answer questions, so further analysis is required beyond ANOVA such as post hoc tests (Tukey test,..etc) to further brake down effects and understand data.