Nonparametric Statistics

Advantages of Nonparametric Procedures

When one is presented with the choice between a nonparametric procedure and its parametric counterpart, the former has several advantages. When a distribution-free nonparametric method exists, exact p values for tests and exact coverage probabilities for confidence intervals can be calculated under fairly general assumptions about the population. Conversely, the p values reported for parametric tests under the assumption of normality are exact only when the population distribution is normal; for other distributions, typically the p values are approximate, with the approximation being better for larger sample sizes. Many nonparametric statistics are relatively simple functions of the ranks of the observations. This implies that one can make inferences about the population without having to know the magnitudes of the sample observations. In addition, when a nonparametric procedure is only a function of the ranks of the observations, the procedure will be insensitive to outliers.

One can compare the performance of a nonparametric method to its parametric counterpart (if one exists) by examining the asymptotic relative efficiency of the two techniques. A given estimator of a parameter (say, the sample average for the center of a symmetric population) is more efficient than a competing estimator if the variance of the former is less than the variance of the latter when the sample size is extremely large. When the underlying population distribution is normal, nonparametric analogues of many of the classical procedures based on the assumption of normality are only slightly less efficient. That is, as the sample size gets large, the variance of the nonparametric estimator is not much larger than the variance of the parametric estimator. When the population distribution is not normal, the nonparametric method can be significantly more efficient than the competing parametric method.

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