12: Tests of Means — Read — Invisible Network

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Many, if not most experiments are designed to compare means. The experiment may involve only one sample mean that is to be compared to a specific value. Or the experiment could be testing differences among many different experimental conditions, and the experimenter could be interested in comparing each mean with each of the other means. This chapter covers methods of comparing means in many different experimental situations. The topics covered here in sections E, F, I, and J are typically covered in other texts in a chapter on Analysis of Variance. We prefer to cover them here since they bear no necessary relationship to analysis of variance. As discussed by Wilkinson (1999), it is not logical to consider the procedures in this chapter as tests to be performed subsequent to an analysis of variance. Nor is it logical to call them post-hoc tests as some computer programs do.

12.1: Testing a Single Mean
12.2: t Distribution Demo
This demonstration allows you to compare the t distribution to the standard normal distribution.
12.3: Difference between Two Means
It is much more common for a researcher to be interested in the difference between means than in the specific values of the means themselves. This section covers how to test for differences between means from two separate groups of subjects.
12.4: Robustness Simulation
This demonstration allows you to explore the effects of violating the assumptions of normality and homogeneity of variance.
12.5: Pairwise Comparisons
12.6: Specific Comparisons
This section shows how to test these more complex comparisons. The methods in this section assume that the comparison among means was decided on before looking at the data. Therefore these comparisons are called planned comparisons. A different procedure is necessary for unplanned comparisons.
12.7: Correlated Pairs
12.8: Correlated t Simulation
12.9: Specific Comparisons (Correlated Observations)
12.10: Pairwise (Correlated)
12.11: Statistical Literacy
12.E: Tests of Means (Exercises)

Thumbnail: Student's t-distribution with 2 degrees of freedom. (CC BY-SA 3.0; IkamusumeFan).

This page titled 12: Tests of Means was last modified on Sat, 23 Apr 2022 18:23:20 GMT and is shared under a Public Domain license and was authored, remixed, and/or curated by David Lane via source content that was edited to the style and standards of the LibreTexts platform.

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