Describe the assumptions, advantages and disadvantages of non-parametric statistics.
Assumptions of Non-Parametric Tests:
A non-parametric statistical test is based on a model that specifies only very general conditions and none regarding the specific form of the distribution from which the sample was drawn.
Certain assumptions are associated with most non- parametric statistical tests, namely:
1. That the observations are independent;
2. The variable under study has underlying continuity;
3. Non-parametric procedures lest different hypothesis about population than do parametric procedures;
4. Unlike parametric tests, there are non-parametric tests that may be applied appropriately to data measured in an ordinal scale, and others to data in a nominal or categorical scale.
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Advantages of Non-Parametric Tests:
1. If the sample size is very small, there may be no alternative to using a non-parametric statistical test unless the nature of the population distribution is known exactly.
2. Non-parametric tests typically make fewer assumptions about the data and may be more relevant to a particular situation. In addition, the hypothesis tested by the non-parametric test may be more appropriate for the research investigation.
3. Non-parametric statistical tests are available to analyze data which are inherently in ranks as well as data whose seemingly numerical scores have the strength of ranks. That is, the researcher may only be able to say of his or her subjects that one has more or less of the characteristic than another, without being able to say how much more or less.
For example, in studying such a variable such as anxiety, we may be able to state that subject A is more anxious than subject B without knowing at all exactly how much more anxious A is.
If data are inherently in ranks, or even if they can be categorized only as plus or minus (more or less, better or worse), they can be treated by non-parametric methods, whereas they cannot be treated by parametric methods unless precarious and, perhaps, unrealistic assumptions are made about the underlying distributions.
4. Non-parametric methods are available to treat data which are simply classificatory or categorical, i.e., are measured in a nominal scale. No parametric technique applies to such data.
5. There are suitable non-parametric statistical tests for treating samples made up of observations from several different populations. Parametric tests often cannot handle such data without requiring us to make seemingly unrealistic assumptions or requiring cumbersome computations.
6. Non-parametric statistical tests typically are much easier to learn and to apply than are parametric tests. In addition, their interpretation often is more direct than the interpretation of parametric tests.
Disadvantages of Non-Parametric Tests:
1. If all of the assumptions of a parametric statistical method are, in fact, met in the data and the research hypothesis could be tested with a parametric test, then non-parametric statistical tests are wasteful.
2. The degree of wastefulness is expressed by the power-efficiency of the non-parametric test.
3. Another objection to non-parametric statistical tests is that they are not systematic, whereas parametric statistical tests have been systematized, and different tests are simply variations on a central theme.
4. Another objection to non-parametric statistical tests has to do with convenience. Tables necessary to implement non-parametric tests are scattered widely and appear in different formats.