General procedures

In the preceding chapter, some basic procedures that can be used to compare and to combine levels of significance and effect size estimates were presented. In addition to the basic procedures presented, there are various alternative methods available for combining probability levels that are especially useful under particular circumstances.

In this section on general procedures we summarize the major methods for combining the probabilities obtained from two or more studies testing essentially the same directional hypothesis. Although it is possible to do so, no consideration is given here to questions of combining results from studies in which the direction of the results cannot be made immediately apparent, as would be the case for F tests (employed in analysis of variance) with df > 1 for the numerator or for chi-square tests (of independence in contingency tables) with df > 1. Although the present section is intended to be self-contained, it is not intended to serve as a summary of all the useful ideas on the topic at hand that are contained in the literature referenced. The seminal work of Mosteller and Bush (1954) is especially recommended. For a review of the relevant literature see Rosenthal (1978a).

The basic methods

Table 11.1 presents the results of a set of five illustrative studies.