NOUN
65 Which comes first, theoretical hypothesizing or empirical research In practice, theorizing and experimentation feed on each other, and questions of this type cannot be answered. For this reason, we will approach the topic of hypothesis testing from both directions. On the one hand, we may suppose that the theory has come first and that the purpose of the experiment is to evaluate its acceptability. This will lead to the execution of significance tests. Alternatively, we may perform the experiment first and then consider what theoretical hypotheses would be consistent with the results. This will lead to the construction of confidence intervals. Students would already have encountered the logic underlying significance tests and confidence intervals in an introductory statistics course. Students will thus be familiar with most of the concepts in the following applications to regression analysis. There is, however, one topic that maybe new the use of one-tailed tests. Such tests are used very frequently in regression analysis. Indeed, they are, or they ought to be, more common than the traditional textbook two-tailed tests. It is, therefore, important that you understand the rationale for their use, and this involves a sequence of small analytical steps. None of this should present any difficulty, but be warned that, if students attempt to use a shortcut or, worse, try to reduce the whole business to the mechanical use of a few formulae, you will be asking for trouble.
2.2.3.6.1 Formulation of a Null Hypothesis We will start by assuming that the theory precedes the experiment and that you have some thehypothetical relationship in your mind. For example, you may believe that the percentage rate of price inflation in an economy, p, depends on the percentage rate of wage inflation,
w, according to the linear equation
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