Simultaneous statistical inference

Previously we explained how contrasts are used to better support the research hypothesis.

Performing statistical analysis on 1 contrast is straightforward. It leads to either a Student t-test or an F-test.

Currently we will focus on testing several contrasts simultaneously.

It should be emphasized that two kinds of tests can be performed.

• Planned. All contrasts are determined in advance of the experiment. More stringent assumptions about the lack of unintended bias on part of the researcher can be assumed. For instance, a complete set of orthogonal contrasts is used, we may assume that the contrasts are independent.
• Unplanned. Typically, this is a result of augmenting the research hypothesis after the experiment is performed and preliminary data analysis has been carried out. Thus, we would like to pick an additional contrast, which will typically not be independent of the planned contrasts (either explicitly or implicitly chosen). This determines the kind of statistic that must be used, and the distribution that must be used to test the null hypothesis.

Various approaches are examined in subsequent articles.