A note on measurement scales and statistical testing

In elementary books on applied statistics (e.g., Siegel, 1988; Agresti, 1990) and books on research methodology in psychology and personality assessment (e.g., Aiken, 1999), it is often suggested that the choice of a statistical test and the choice of statistical operations should be determined by the level of measurement of the data. Although schemes based on this idea will in many situations lead to reasonable choices, a more liberal attitude towards the choice of tests is advocated. Depending on the deviations from the null hypotheses that the researcher expects, it can be quite reasonable, for example, to use Wilcoxon's rank sum test when comparing two groups on the basis of nominal data. Examples are given to illustrate our propositions.