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Post-Analysis after an Analysis of Variance

A significant result in an analysis of variance (ANOVA) in Excel tells you that an effect is lurking somewhere in the data. Post-analysis tests tell you where. Two types of tests are possible — either planned or unplanned.

Assume that the Between Groups variable has only two levels. For this reason, had a significant effect resulted, no further test would be necessary. The Within Groups variable, however, is significant. Ordinarily, the test would proceed. In this case, however, the interaction between the variables necessitates a different path.

With the interaction, post-analysis tests can proceed in either (or both) of two ways. You can examine the effects of each level of the A variable on the levels of the B variable, or you can examine the effects of each level of the B variable on the levels of the A variable. Statisticians refer to these as simple main effects.

For example, the first way examines the means for the three fonts in a book and the means for the three fonts in the e-reader. The second way examines the means for the book versus the mean for the e-reader with Haettenschweiler font, with Arial, and with Callibri.

Statistics texts provide complicated formulas for calculating these analyses. Excel makes them easy. To analyze the three fonts in the book, do a repeated measures ANOVA for Subjects 1 through 4. To analyze the three fonts in the e-reader, do a repeated measures ANOVA for Subjects 5 through 8.

For the analysis of the book versus the e-reader in the Haettenschweiler font, that’s a single-factor ANOVA for the Haettenschweiler data. To do this, you’d have to rearrange the numbers into two columns. Of course, you’d go through a similar procedure for each of the other fonts.

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