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Nonparametric Tests

Nonparametric tests are useful for testing whether group means or medians are distributed the same across groups. In these types of tests, we rank (or place in order) each observation from our data set. Nonparametric tests are widely used when you do not know whether your data follows normal distribution, or you have confirmed that your data do not follow normal distribution. Meanwhile, hypothesis tests are parametric tests based on the assumption that the population follows a normal distribution with a set of parameters.

OriginPro offers the following nonparametric hypothesis tests:

Origin provides a very powerful, comprehensive and useful range of statistics capabilities which go beyond what is offered in many statistical packages. Origin’s ANOVA techniques include all important multiple comparisons tests for means, and a very useful output feature which is rarely found in other statistical packages: automatic creation of means comparison plots which will illustrate significant differences at a glance. A broad range of non-parametric tests is available which include the option of calculating exact p-values based on the exact distribution instead of the asymptotic one, which is very important for small sample size. Also sample size and power calculations are supported.

Reinhard Bergmann, PhD, Novartis Institutes for Biomedical Research

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One-Sample Wilcoxon Signed Rank Test

The One-Sample Wilcoxon Signed Rank Test is a nonparametric alternative to a one-sample t-test. The test determines whether the median of the sample is equal to some specified value. Data should be distributed symmetrically about the median.

Paired-Sample Wilcoxon Signed Rank Test

The Paired-Sample Wilcoxon Signed Rank Test is a nonparametric alternative method to the paired sample t-test. Paired samples are presumed to be drawn, at random, from a single population. Differences between paired samples are assumed to be distributed symmetrically about the median.

Paired Sample Sign Test

The Paired-Sample Sign Test is a simple, nonparametric alternative to the paired sample t-test. It tests tallies (+) and (-) differences between paired samples and tests whether the two are present in equal numbers. While not considered a statistically powerful test, the only requirement that need to be met is that the differences between paired samples are independent such that differences exist within the same continuous population and measurements exist along some scale by which they can be judged to be greater, equal to, or less than each other.

Mann-Whitney Test

The Mann-Whitney Test (M-W) is a useful nonparametric alternative to the two-sample t-test. Because the M-W test is nearly as powerful as a two-sample t-test yet nonparametric, it is considered as a more useful test in certain scenarios.

The M-W test frequently produces a similar result to the two-sample Kolmogorov-Smirnov test but the two tests show differences in sensitivities to changes in location and distribution.

Two-Sample Kolmogorov-Smirnov Test

The Two-Sample Kolmogorov-Smirnov test (K-S) is a nonparametric alternative to the two-sample t-test. In general, the K-S test uses the unsigned differences between two samples to determine whether the two are drawn from the same continuous distribution.

The K-S test and the Mann-Whitney Test (M-W) can be used in similar analyses. Whereas, K-S is less powerful, it is considered more comprehensive because it tests both shape and location of distributions.

Friedman ANOVA

Friedman ANOVA is a nonparametric alternative to the one way repeated measure ANOVA. It is similar to the Kruskal-Wallis ANOVA in its use of ranks to study variance.

Friedman ANOVA can used to compare dependent samples or observations that are repeated on the same subjects. Thus, the test is well-suited to randomized block designs. Variates are ranked within blocks, and ranks are summed by treatment, to compute the test statistics.

Kruskal-Wallis ANOVA

Kruskal-Wallis (K-W) ANOVA is a nonparametric alternative to the one-way analysis of variance (ANOVA) test. The K-W ANOVA uses rank sums to determine whether three or more independent samples are taken from the same distribution (when comparing two samples, the Mann-Whitney test is more often used). When K-W test results are significant, post-hoc tests between pairs of samples can be used to determine which pairs show significant differences.

Mood's Median Test

The Mood's Median Test is a nonparametric alternative to one-way analysis of variance (ANOVA). Mood's Median tests the likelihood that the median values of two samples are equal and, therefore, are drawn from the same population. Mood's Median only accounts for the number of variates that are larger or smaller than the median value and does not take into account their actual differences from the median. Hence, it is regarded as a less powerful alternative to the Kruskal-Wallis ANOVA. Nevertheless, it is more robust in cases where the dataset contains extreme outliers.

Running Simultaneous Nonparametric Tests

You can run multiple nonparametric tests simultaneously. Available options are:

  • (NPH) K Independent Samples: Kruskal-Wallis ANOVA and Mood's Median Test
  • (NPH) Paired Samples: Paired-Sample Wilcoxon Signed Rank Test and Paired-Sample Sign Test
  • (NPH) Two Independent Samples: Mann-Whitney Test and Two-Sample Kolmogorov-Smirnov Test

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