Analysis of Variance (ANOVA)

What is an analysis of variance (ANOVA)? Describe the theory underlying it. In ANOVA, what does F = 1 mean? What are the differences between a two sample t test and ANOVA hypothesis testing?

Analysis of Variance, ANOVA, is the hypothesis testing procedure used when a study has three or more sample groups (Aron, Aron, & Coups, 2009). When using ANOVA, the researcher analyzes the variances. By analyzing these variances, they are able to conclude what the different means mean. F represents the F ratio. This is the ratio of the between – groups population variance estimate to the within-groups population variance estimate (Aron, Aron, & Coups, 2009). In ANOVA testing, F=1 is what the null hypothesis equals. If the F ratio is larger than 1, then the null hypothesis is rejected. One of the major differences between a two sample t test and ANOVA testing is the number of samples study. T test has 2 whereas ANOVA has 3 or more.

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

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