Question

When should we use a non-parametric test (or a distribution-free test)?

Answer 1

• Nonparametric tests are also called distribution-free tests because they don't assume that your data follow a specific distribution. Here we have to not know exactly which distribution follow our data.non parametric test  does not assume anything about the underlying distribution .

•The hypothesis does not involve a parametric of the probability function of the population.

the observation are not as accurate as required for a parametric inference.Also when the measurements are on the nominal or ordinal scale.

•The assumption necessary necessary for a validity of a parametric method are suspected to hold good for example- the assumption of normal population is doubtful.

• one wants to avoid complicated analysis of data.

• most of the nonparametric methods are applicable for ordered statistics.

• Any inference based on the parametric analysis which does not uphold the underlying assumptions necessitated for it will be erroneous. In such a situation nonparametric method can safely be used.

• You use nonparametric tests when your data don't meet the assumptions of the parametric test i.e the assumption about normally distributed data.

• Nonparametric tests do not rely on any distribution.

• Nonparametric tests are less powerful because they use less information in their calculation.

For example, a parametric correlation uses information about the mean and deviation from the mean while a nonparametric correlation will use only the ordinal position of pairs of scores. i.e nonparametric test less powerful comparatively parametric test it is the one drawback of nonparametric test.

• More statistical power when assumptions for the parametric tests have been violated. When assumptions haven't been violated, they can be almost as powerful.

•The only non parametric test you are likely to come across in elementary stats is the chi-square test. However, there are several others. For example: the Kruskal Willis test is the non parametric alternative to the One way ANOVA and the Mann Whitney is the non parametric alternative to the two sample t test.