Measurement scales and statistics

A debate has continued for more than forty years about the kinds of significance test that can legitimately be performed. One tradition declares that when the data are measured on an ordinal scale, parametric statistics should not be used. The other maintains that only mathematical characteristics of the numbers have to be satisfied in order to justify parametric methods. Two errors in particular have made consensus difficult to reach.Firstly, some writers fail to distinguish between statistical treatment of the data, considered merely as numbers, and the use of numerical results to justify statements about the world. Secondly, statistical significance is sometimes treated as a property of the world or of the data whereas in fact it is a numerical answer to one question out of many alternative questions that might be asked about the data. Each such question has a different, correct answer. These errors often lead to misinterpretation of what classical significance tests actually tell us about the world.If each null hypothesis is framed so as to include any necessary presuppositions of the statistical technique used, the inferences that follow from its rejection, or from a failure to reject it, become much clearer. Doing so also clarifies the interpretation to be made when different tests yield different results

Econometrics · Epistemology · Geography · Interpretation (philosophy) · Null hypothesis · Parametric statistics · Presupposition · Property (philosophy) · Scale (ratio) · Statistical hypothesis testing · Statistical inference · Statistics · Test (biology) · Advanced Statistical Methods and Models · Computer Science · Forecasting Techniques and Applications · Mathematics · Philosophy · Psychology

• Variables and Quantity

  Open Access•Santo Di Nuovo•Integrative Psychological and…•2009

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