Nonparametric testing is an essential skill that any business manager or marketer doing statistical analysis should have. The statistics course normally teaches only parametric statistics, but there are many real-life data analysis situations in business that require non-parametric analysis. This article will examine the 5 most common situations that require nonparametric tests instead of parametric analysis.
Statistical procedures are parametric or non-parametric. Parametric statistical tests require assumptions about the population from which the samples are drawn. For example, many data analysis tools, such as the t-test, chi-square tests, z-tests, and F-tests, and many types of hypothesis tests, require that the underlying population be normally distributed. Some of these also require equal variations from both populations.
Sometimes these requirements cannot be assumed. Examples of this would be if the population is highly skewed or if the underlying distribution or variations are completely unknown.
The nonparametric tools have no assumptions regarding the distribution of the underlying populations or the variance. Most of these are very easy to perform, but are not usually as accurate as parametric methods, and the null hypothesis is often difficult to reject when using a non-parametric method.
When to use nonparametric methods
1) The most important use of nonparametric tools occurs when sampling from populations that are not known to be normally distributed. Parametric methods require that all underlying populations be normally distributed. Parametric tests will produce incorrect answers when sampling from nonnormally distributed populations. Nonparametric tests are an answer to this situation.
2) Nonparametric approaches are often used as substitutes for shortcuts for more complicated parametric analyzes. Quite often, you can get a quick response that requires little computation by running a nonparametric test.
3) Nonparametric tools are often used when data is classified but cannot be quantified. For example, how would you quantify consumer ratings as very satisfied, moderately satisfied, simply satisfied, less than satisfied, dissatisfied?
4) Nonparametric statistics can be applied when there are many outliers that can skew the results. Nonparametric statistics often evaluate medians rather than means, and therefore if the data has one or two outliers, the result of the analysis is not affected.
5) They are especially useful when it comes to non-numerical data, such as having customers rank products or attributes based on their preferences.
The most used nonparametric tests are:
– The signal test
– Rank signed by Wilcoxon
– Wilcoxon qualifying sum
– Mann-Whitney
– Kruskal-Wallis
– Spearman’s correlation coefficient
My blog contains articles with specific instructions on how and when to perform each of these nonparametric tests in Excel. Nonparametric methods are perhaps more useful than classical parametric tools that require samples to be drawn from normally distributed populations. Nonparametric tests are rarely taught in statistics courses. That’s a shame because nonparametric tests can often be a real life saver for anyone who has to analyze data on a regular basis.
