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Tests of significance
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Fisher's tests of statistical significance
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Tests of significance are a statistical technology used for ascertaining the likelihood of empirical data, and, from there, for inferring a real effect, such as a correlation between variables or the effectiveness of a new treatment. Fisher, starting around 19252, standardized the interpretation of statistical significance and was the main driving force behind the popularity of tests of significance in empirical research, especially in the social and behavioral sciences.
Fisher's tests of statistical significance Reading tests of significance Probability of the data Statistical significance Running tests of significance
The following sections address the interpretation of tests of significance as well as a basic procedure for performing tests of significance. They are based on a procedure that improves Fisher's original ideas in order to prevent current misuses, such as the null hypothesis testing procedure leading to pseudoscientific interpretations, which were partly initiated by Fisher himself.
Reading tests of significance A typical test of significance comprises two related elements: the calculation of the probability of the data and an assessment of the statistical significance of that probability.
Probability of the data The probability of the data is normally reported using two related statistics: a test statistic (z, t, F…) and an associated probability (p, *10). The information provided by the test statistic is of little immediate usability and can be ignored in most cases. The associated probability, on the other hand, tells how probable the test results are, and forms the basis for assessing statistical significance. z=1.96, p=0.025