    Chapter 6: Analysing the Data Part III: Common Statistical Tests # Nonparametric tests

Occasionally, the assumptions of the t-tests are seriously violated. In particular, if the type of data you have is ordinal in nature and not at least interval. On such occasions an alternative approach is to use nonparametric tests. We are not going to place much emphasis on them in this unit as they are only occasionally used. But you should be aware of them and have some familiarity with them.

Nonparametric tests are also referred to as distribution-free tests. These tests have the obvious advantage of not requiring the assumption of normality or the assumption of homogeneity of variance. They compare medians rather than means and, as a result, if the data have one or two outliers, their influence is negated.

Parametric tests are preferred because, in general, for the same number of observations, they are more likely to lead to the rejection of a false hull hypothesis. That is, they have more power. This greater power stems from the fact that if the data have been collected at an interval or ratio level, information is lost in the conversion to ranked data (i.e., merely ordering the data from the lowest to the highest value).

The following table gives the non-parametric analogue for the paired sample t-test and the independent samples t-test. There is no obvious comparison for the one sample t-test. Chi-square is a one-sample test and there are alternatives to chi-square but we will not consider them further. Chi-square is already a non-parametric test. Pearson's correlation also has non-parametric alternative (Spearman's correlation) but we will not deal with it further either.

There are a wide range of alternatives for the two group t-tests, the ones listed are the most commonly use ones and are the defaults in SPSS. Generally, running nonparametric procedures is very similar to running parametric procedures, because the same design principle is being assessed in each case. So, the process of identifying variables, selecting options, and running the procedure are very similar. The final p-value is what determines significance or not in the same way as the parametric tests. SPSS gives the option of two or three analogues for each type of parametric test, but you need to know only the ones cited in the table. Same practice with these tests is given in Assignment II.

 Parametric test Non-parametric analogue One-sample t-test Nothing quite comparable Paired sample t-test Wilcoxon T Test Independent samples t-test Mann-Whitney U Test Pearson's correlation Spearman's correlation

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