Non-Parametric Tests

Most of the statistical tests need an important assumption to be met if they are to be correctly applied. This assumption is that the population of data from which a sample or samples are drawn is generally distributed. These statistical tests permit considerable latitude and deviation from normality. The central limit theorem, for instance allow the normality assumption to be by passed from the sufficiently large samples. If the distribution from which the sample is drawn is badly skewed or is otherwise grossly not-normal however for the smaller samples these statistical tests will not yield the meaningful result.

A second assumption that most of the test rest is that of meaningful sample statistics. Such as the mean and standard deviation, can be derived from the samples and used to estimate the corresponding population.

The Statisticians have devised alternate procedures that can be used to test hypotheses about the data which are not-normal or for which meaningful sample statistics cannot be calculated. As these tests do not depend on the shape of the distribution. They are termed as distribution-free rests. These tests do not depend upon the population parameters. Such as the mean and the variance; they are also known as non-parametric tests. The chi-square test is formulated by Karl Pearson in 1900.

Most experimental situations yield a data which can be tested in the usual way. If the data from a distribution is bounded on one end however, the income distributions are bounded at their lower end at zero, while they are practically unlimited at their upper end.

The merits of non-parametric tests are as follows:

1. The Non-parametric tests are distribution free. They do not need any assumption to be made about population following the normal or any other distribution.

2. Normally they are simple to understand and easy to apply when the sample sizes are small.

3. Most non-parametric test does not need lengthy & laborious computations and hence are less time-consuming. If significant results are obtained then no further work is necessary.

4. The Non-parametric tests are applicable to all types of data-qualitative like nominal scaling of data in rank form as well as data that have been measured more accurately.

5. Many non-parametric techniques make it possible to work with very small samples. This is particularly helpful to the researcher collecting pilot study data or to the medical researcher working with a rare disease.

6. Non-parametric techniques make fewer and less stringent assumptions than so the classical procedures.