Does Order of Procedure Affect Statistical Significance?
Order refers to which comes first: the test data or the specification of the hypotheses to be tested. When the hypotheses come first the test is "prospective" and when the data come first the test is "retrospective". Traditionally, prospective tests have been required. However, there is a well-known generally accepted hypothesis test in which the data preceded the hypotheses. In that study the statistical significance was calculated the same as it would have been had the hypotheses preceded the data. A related question in use of statistics in the physical sciences is whether probability theory applies to the known past in the same way that it applies to the unknown future. Although these questions have been discussed, there are few references in this area of statistics. It hardly seems reasonable to accord the same status to a hypothesis that explains the results of an experiment after the results are known as to a hypothesis that predicts the results of an experiment before they are known. This is because it is well known that predicting an event before it occurs is more difficult than explaining it after it occurs.
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