Non parametric test

Non parametric test
Tests of hypotheses which deal with population parameters are called parametric, tests.

There are situations, particularly in psychological or in market research studies, where in the basic assumptions underlying the parametric tests are not valid or one does not have the knowledge of the distribution of the population parameter being tested. The tests which handle problems of these types are known as nonparametric tests or distribution free tests.
In the recent past, the nonparametric test have gained importance basically for three reasons:
(i) These tests require no or less restricting assumptions than the corresponding parametric tests,
(ii) These tests are more suitable for analyzing ranked, scaled or rated data, and
(iii) These tests involve very few arithmetic computations.
However, it must be understood that when basic assumptions about the parametric tests are valid, the nonparametric tests are less powerful than the parametric tests. Thus, there is a greater risk of accepting of false hypothesis and thus committing tests yield less defined thereby, when the null hypothesis is rejected, the nonparametric tests yield less precise conclusions compared to the parametric tests. For example, in parametric tests we have a test for quality of two population means compared to the two population distributions are identical of two population means compared to the two population distributions are identical in nonparametric tests. In this case, a rejection of null hypothesis in a parametric test would mean that the two population means are not equal while the rejection of the null hypothesis in the nonparametric test leads to the conclusion that the two population distributions are different, the specific form of the difference between the two distributions is not clearly specified.
The following are some of the typical situations for using nonparametric tests:
i) In a consumer behaviour survey for new package design, the response are not likely to be normally distributed but clustering around two extreme positions, with a very few respondents giving a neutral response to the package design.
ii) Sometimes, the responses to a question are given in terms of names (nominal data), which cannot be treated as numbers. For example, if we ask young graduates “in which part of the country would you like to take up a job and live”, the replies could be north, north-west, west or south, etc. Nominal data can be analysed only by nonparametric methods.
iii) In mailed questionnaire method of survey, more often partially filled missions data and make necessary adjustments to extract maximum information form the available data.
iv) Nonparametric tests can be used to provide reasonably good results even for very small samples.