![]() In addition, while they may not require normal data, many nonparametric tests have other assumptions that you can’t disregard. For example, t he Kruskal-Wallis test assumes your samples come from populations that have similar shapes and equal variances. And Bonnett's 2-sample standard deviation test performs well for nonnormal data even when sample sizes are as small as 20. For example, the Assistant in Minitab (which uses Welch's t-test) points out that while the 2-sample t-test is based on the assumption that the data are normally distributed, this assumption is not critical when the sample sizes are at least 15. What's your sample size? As long as a certain minimum sample size is met, most parametric tests will be robust to the normality assumption. Keep in mind that nonnormal data does not immediately disqualify your data for a parametric test. If you're waiting for me to tell you which direction you should choose.well, all I can say is, "It depends." But I can give you some established rules of thumb to consider when you're looking at the specifics of your situation. I've briefly outlined differences between parametric and nonparametric hypothesis tests, looked at which tests are equivalent, and considered some of their advantages and disadvantages. Is Parametric or Nonparametric the Right Choice for You? Nonparametric tests are not a one-size-fits-all solution for non-normal data, but they can yield good answers in situations that parametric statistics just won't work. ![]() So if you want to draw conclusions with the same confidence level you'd get using an equivalent parametric test, you will need larger sample sizes. In practical terms, that means nonparametric tests are less likely to detect an effect or association when one really exists. That means you have an increased chance making a Type II error with these tests. Power is the probability that you will correctly reject the null hypothesis when it is false. For starters, they typically have less statistical power than parametric equivalents. Drawbacks of Nonparametric Testsīut nonparametric tests are not completely free from assumptions-they do require data to be an independent random sample, for example.Īnd nonparametric tests aren't a cure-all. Many people also feel that nonparametric analyses are more intuitive. Nonparametric tests also accommodate many conditions that parametric tests do not handle, including small sample sizes, ordered outcomes, and outliers.Ĭonsequently, they can be used in a wider range of situations and with more types of data than traditional parametric tests. In contrast, nonparametric tests are unaffected by the distribution of your data. Advantages of Nonparametric Testsīoth parametric and nonparametric tests draw inferences about populations based on samples, but parametric tests focus on sample parameters like the mean and the standard deviation, and make various assumptions about your data-for example, that it follows a normal distribution, and that samples include a minimum number of data points. Just like the 1960s encompassed both Woodstock and Altamont, so nonparametric tests offer both compelling advantages and serious limitations. So choosing a nonparametric analysis is sort of like removing your data from a stifling, conformist environment, and putting it into a judgment-free, groovy idyll, where your data set can just be what it is, with no hassles about its unique and beautiful shape. Nonparametric analyses free your data from the straitjacket of the normality assumption. The following table lists common parametric tests, their equivalent nonparametric tests, and the main characteristics of each. ![]() In fact, nonparametric statistics don't assume your data follow any distribution at all. ![]() And if the word "nonparametric" looks like five syllables' worth of trouble, don't be intimidated-it's just a big word that usually refers to "tests that don't assume your data follow a normal distribution." If you're stymied by your data's lack of normality, nonparametric statistics might help you find answers. Just let your data be what they are, go to the Stat menu in Minitab Statistical Software, and choose "Nonparametrics." Your data's lack of normality seems to make it poorly suited for analysis. Time to face the truth: despite your best efforts, that data set is never going to measure up to the assumption you may have been trained to fervently look for. So the data you nurtured, that you worked so hard to format and make useful, failed the normality test. ![]()
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