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Parametric or nonparametric statistical tests: when is which test appropriate? Siegel (1956) purports that there are four considerations that are involved in choosing an appropriate statistical test: (lì the power of the test; (2) the way the sample of scores is drawn; (3) the nature of the population the sample is drawn from, and (4) the type of measurement of the variables. In order for a parametric statistical test to be used, certain assumptions or conditions must be met. The observations must be independent and must be drawn from normally distributed populations. In addition, the variables must be measured on either the interval or ratio scale. If these conditions cannot be met, a nonparametric test should be used. A nonparametric statistical test does not require an assumption concerning the parameters of the population from which the sample is drawn. Nonparametric statistics require data to be measured only on an ordinal or nominal scale.
A continuing controversy among statisticians exists, however, over whether or not it is valid to use parametric statistics with data measured on an ordinal scale. One side of the argument asserts that if parametric statistics are used with ordinal data, the research findings will be distorted (Siegel, 1956). Proponents belonging to the other side of the argument believe that the use of parametric statistics with ordinal data is appropriate since the type of statistical test, nonparametric or parametric, and the scale of measurement used are two separate considerations (Armstrong, 1981). Even if one does believe in the latter argument, the researcher must still make certain his or her ordinal data meet all the assumptions for a particular parametric test before using it.
The crux of why this controversy holds significance for researchers is that nonparametric statistics are less powerful than parametric statistics. The probability of failing to reject the null hypothesis when it is indeed false is higher if a researcher uses nonparametric statistics. In this case, the investigator obtains significant results but the nonparametric statistic is not strong enough to detect the significance,...