Section 6.5

Fundamentals of Social Statistics by Adam J. McKee

Section 6.5: ANOVA Tests

An obvious limitation of the t-test is that it can only test the differences between two means.  Researchers often find that they need to utilize more than two groups, such as when a medical researcher wishes to have a placebo group and two or more other groups.  The one-way analysis of variance (ANOVA) is designed for just such research situations.  As with the t-tests, the one-way ANOVA results in a probability that can be used to evaluate the null hypothesis.  This probability is based on what is known as an F statistic, and for this reason, ANOVA tests are sometimes known as F tests.

There are several steps along the way to getting to F.  Traditionally, these steps are presented in an ANOVA summary table.  An ANOVA Table presents the source of variation (between groups, within groups, and total), the degrees of freedom for that source, the sum of squares for that source, the mean square for that source, and finally an F statistic.  The level of significance is often presented as an ANOVA table footnote.


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Last Modified:  06/04/2021

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