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