The non-parametric test is a test that does not depend on the particular form of the basic frequency function from which the samples are drawn. In other words, a non-parametric test does not make any assumption regarding the form of the population. We now give some of the assumptions behind non-parametric tests in statistics and their advantages and disadvantages.
Assumptions behind Non Parametric Tests:
- Sample observations are independent.
- The variable under study is continuous.
- The probability distribution function is continuous.
- Lower order moments exist.
Advantages of Non Parametric Tests:
- Non-parametric methods are readily comprehensible, very simple and easy to apply, and do not require complicated sample theory.
- No assumption is made about the form of the frequency function of the
parent population from which sampling is done.
- No parametric technique will apply to the data which are measured in nominal scale while non-parametric methods exist to deal with such data.
- Since most socio-economic data is not in general normally distributed, non-parametric tests have found applications in Psychometry, Sociology, and Education.
- Non-parametric tests are available to deal with the data which are given in ranks or
whose seemingly numerical scores have the strength of ranks. For instance, no parametric test can be applied if the scores are given in grades.
- The assumptions behind these are fewer and much weaker than those associated with parametric tests.
Disadvantages of Non Parametric Tests:
- Non-parametric tests can be used only if the measurements are nominal or ordinal.
Even in that case, if a parametric test exists it is more powerful than the non-parametric test. In other words, if all assumptions of a statistical model are satisfied by
the data and if the measurements are of required strength, then the non-parametric tests are wasteful of time and data.
- So far, no non-parametric tests exist for testing interactions in the ANOVA model unless special assumptions about the additivity of the model are made.
- Non-parametric tests are designed to test statistical hypothesis only and not for
estimating the parameters.
Fundamentals of Mathematical Statistics – SC Gupta