What is an analysis of Variance (ANOVA) and when would a researcher use ANOVA for data analysis? Provide an example. What are post hoc comparisons and why are they conducted?

     An analysis of Variance (ANOVA) is a statistical procedure, which is for testing variation among the means of more than two groups, and is used for the study of two groups (Aron, Aron, & Coups, 2009). To determine if there is a difference on some variable between two or more groups a researcher uses ANOVA. ANOVA is a technique, which can be used to test the hypothesis that the means among two or more groups are equal, under an assumption that the sampled populations are normally distributed (Aron, Aron, & Coups, 2009). ANOVA is equivalent to more than one t-tests, therefore compare the means of three groups is easily accomplished with conducting a 1-way ANOVA with the three groups instead of conducting three different t-test. An example of using ANOVA is when conducting a one-way ANOVA to determine if there are significant differences between the reading levels of a set of triplets in fifth grade in three different english classes of the same school. These three environments (three different classes) form the three levels of the factor. Post hoc comparisons are several comparisons, which are not specified in advance (Aron, Aron, & Coups, 2009). After an analysis of variance post hoc comparisons are conducted as part of an exploratory analysis (Aron, Aron, & Coups, 2009).  

 Reference

 Aron, A., Aron, E. N., & Coups, E. (2009). Statistics for psychology (5th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.