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Nonparametric Statistical Techniques
by John Martino

In the development of modern statistical methods, the first techniques of inference which appeared were those which made a good many assumptions about the nature of the population from which the scores were drawn. Since population values are parameters, these statistical techniques are called parametric.

More recently we have seen the development of a large number of techniques of inference which do not make numerous or stringent assumptions about parameters. These newer distribution-free or nonparametric techniques result in conclusions which require fewer qualifications. Having used one of them, we may say that Regardless of the shape of the population(s), we may conclude that It is with these techniques that the following relates to:

A parametric statistical test is a test whose model specifies certain conditions about the parameters of the population from which the research sample was drawn. Since these conditions are not ordinarily tested, they are assumed to hold. The meaningfulness of the results of a parametric test depends on the validity of these assumptions. Parametric tests also require that the scores under analysis result from measurement in the strength of at least an interval scale.

A nonparametric statistical test is a test whose model does not specify conditions about the parameters of the population from which the sample was drawn. Certain assumptions are associated with most nonparametric statistical tests, i.e., that the observations are independent and that the variable under study has underlying continuity, but these assumptions are fewer and much weaker than those associated with parametric tests. Moreover, nonparametric tests do not require measurement so strong as that required for the parametric tests; most nonparametric tests apply to data in an ordinal scale, and some apply also to data in a nominal scale.

Advantages of Nonparametric Statistical Tests

• Probability statements obtained from most nonparametric statistical tests are exact probabilities (except in the case of large samples, where excellent approximations are available), regardless of the shape of the population distribution from which the random sample was drawn.
  
• If sample sizes are small as N=6 are used, there is no alternative to using a nonparametric statistical test unless the nature of population distribution is known exactly.
  
• There are suitable nonparametric statistical tests for treating samples made up of observations from several different populations. None of the parametric tests can handle such data without requiring us to make seemingly unrealistic assumptions.
  
• Nonparametric statistical tests are available to treat data which are inherently in ranks as well as data whose seemingly numerical scores have the strength of ranks.
  
• Nonparametric methods are available to treat data which are simply classifactory, i.e., are measured in a nominal scale.
  
• Nonparametric statistical tests are typically much easier to learn and to apply than are parametric tests.

Disadvantages of Nonparametric Statistical Tests

• If all the assumptions of the parametric statistical model are in fact met in the data, and if the measurement is of the required strength, then nonparametric statistical tests are wasteful of data. The degree of wastefulness is expressed by the power-efficiency of the nonparametric test.
  
• There are no nonparametric methods for testing interactions in the analysis of variance model, unless special assumptions are made about additivity.