Non-parametric tests cover techniques that do not rely on data belonging to any distribution. These include distribution free methods, which do not rely on assumptions that the data are drawn from a given probability distribution. As such it is the opposite of parametric statistics. It includes non-parametric statistical models, inference and statistical tests. Following are the nonparametric tests

## The Sign test:

The sign test is one of the simplest nonparametric tests. It is for use with 2 repeated (or correlated) measures and measurement is assumed to be at least ordinal. For each subject, subtract the 2nd score from the 1st, and write down the sign of the difference. (That is write “-” if the difference score is negative, and “+” if it is positive.) The usual null hypothesis for this test is that there is no difference between the two treatments. If this is so, then the number of + signs (or - signs, for that matter) should have a binomial distribution1 with p = .5, and N = the number of subjects. In other words, the sign test is just a binomial test with + and - in place of Head and Tail (or Success and Failure).

## Mann-Whitney U Test:

The null hypothesis assumes that the two sets of scores are samples from the same population; and therefore, because sampling was random, the two sets of scores do not differ systematically from each other.

The alternative hypothesis, on the other hand, states that the two sets of scores do differ systematically.

## Runs Test:

The runs test (also called Wald–Wolfowitz test after Abraham Wald and Jacob Wolfowitz) is a non-parametric statistical test that checks a randomness hypothesis for a two-valued data sequence. More precisely, it can be used to test the hypothesis that the elements of the sequence are mutually independent.

## Rank Sum Test:

The t-test is the standard test for testing that the difference between population means for two non-paired samples are equal. If the populations are non-normal, particularly for small samples, then the t-test may not be valid. The rank sum test is an alternative that can be applied when distributional assumptions are suspect.

March 09, 2018