chapter  14
23 Pages

Fisher, Gosset, and Alternative Hypothesis Significance Testing (Ahst): Using the Bootstrap to Test Scientific Hypotheses About the Multiple Correlation

WithJoseph Lee Rodgers, William Howard Beasley

This chapter, originally presented as part of a conference celebrating the career of Michael Browne, has both an historical and a methodological goal. The historical goal is to speculate about how Fisher and Gosset would have developed hypothesis testing if modern computational methods had been available to them. We propose that Fisher’s hypothesis testing system, which has with revision become Null Hypothesis Significance Testing (NHST), might instead have been developed as Alternative Hypothesis SignificanceTesting (AHST). This suggestion ismotivated by the potential

to develop empirical sampling distributions using resampling methods (specifically, the bootstrap) to evaluate settings in which features of the model that a researcher wishes to evaluate are reflected in the bootstrap sampling frame. The methodological goal involves extending past AHST theory by building and evaluating sampling distributions for the multiple correlation coefficient, R, within a multiple regression model in the context of AHST.