These are tests or procedures that do not require comparisons of other procedures or tests so as to give out appropriate results. The non-parametric alternative counterpart to these procedures’ tests are the McNamara chi-square test, Mann – Whitney U tests and the Wilcoxon rank-sum tests, this is because these tests are normally used when comparing two independent samples.

The Wilcoxon signed-rank test is usually used when a researcher wants to carry out a test on whether the median of a symmetric population is zero.

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The Wilcoxon sum rank test / The Mann-Whitney U test is normally used to test whether a pair of samples are drawn from the same population. When the two populations are shifted concerning each other, this test becomes a preferred non-parametric counterpart of the independent sample compared to the McNamara chi-square test.

On the other hand, the McNamara chi-square test is very useful when comparing the observed frequency of a given variable contained in one group with what is expected. This test exploits the use of Chi-square that is a family of probability distributions. These probability distributions tend to vary greatly with their degree of freedom. In the case of a two-way chi-square, the observed frequencies are compared with the derived expected frequencies. These frequencies are only for a particular group. on the other hand, these observed frequencies are normally compared with the expected frequencies that are derived from the marginal summations of the cross-tabulation table but only in a two-way chi-square. The following formula is always used when calculating the chi-square:

X ^ 2 = ∑ [(f (o) – f (e)) ^ 2 / f (e)]

The following are the examples of the Mann-Whitney U test: The two-tailed negative hypothesis where the difference between two variables is not present for example where there is no difference between the clothing of male and female students in a particular institution or class whereby:

H(o) represents the number of male and female students that have the same mode of clothing and that H(A) represent male and female students that do not have the same modes of clothing.