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SciPy Reference Guide, Release 0.8.dev tiecorrect(rankvals) Tie-corrector for ties in Mann Whitney U and Kruskal Wallis H tests. See Siegel, S. (1956) Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill. Code adapted from |Stat rankind.c code. Returns: T correction factor for U or H ranksums(x, y) Compute the Wilcoxon rank-sum statistic for two samples. The Wilcoxon rank-sum test tests the null hypothesis that two sets of measurements are drawn from the same distribution. The alternative hypothesis is that values in one sample are more likely to be larger than the values in the other sample. This test should be used to compare two samples from continuous distributions. It does not handle ties between measurements in x and y. For tie-handling and an optional continuity correction see ‘stats.mannwhitneyu‘_ Parameters x,y : array_like The data from the two samples Returns z-statistic : float References [R32] The test statistic under the large-sample approximation that the rank sum statistic is normally distributed p-value : float The two-sided p-value of the test wilcoxon(x, y=None) Calculate the Wilcoxon signed-rank test The Wilcoxon signed-rank test tests the null hypothesis that two related samples come from the same distribution. It is a a non-parametric version of the paired T-test. Notes Parameters x : array_like The first set of measurements y : array_like, optional, default None The second set of measurements. If y is not given, then the x array is considered to be the differences between the two sets of measurements. Returns z-statistic : float The test statistic under the large-sample approximation that the signed-rank statistic is normally distributed. p-value : float The two-sided p-value for the test Because the normal approximation is used for the calculations, the samples used should be large. A typical rule is to require that n > 20. 662 Chapter 3. Reference
References [R34] kruskal(*args) Compute the Kruskal-Wallis H-test for independent samples SciPy Reference Guide, Release 0.8.dev The Kruskal-Wallis H-test tests the null hypothesis that the population median of all of the groups are equal. It is a non-parametric version of ANOVA. The test works on 2 or more independent samples, which may have different sizes. Note that rejecting the null hypothesis does not indicate which of the groups differs. Post-hoc comparisons between groups are required to determine which groups are different. Notes Parameters sample1, sample2, ... : array_like Two or more arrays with the sample measurements can be given as arguments. Returns H-statistic : float The Kruskal-Wallis H statistic, corrected for ties p-value : float The p-value for the test using the assumption that H has a chi square distribution Due to the assumption that H has a chi square distribution, the number of samples in each group must not be too small. A typical rule is that each sample must have at least 5 measurements. References [R22] friedmanchisquare(*args) Computes the Friedman test for repeated measurements The Friedman test tests the null hypothesis that repeated measurements of the same individuals have the same distribution. It is often used to test for consistency among measurements obtained in different ways. For example, if two measurement techniques are used on the same set of individuals, the Friedman test can be used to determine if the two measurement techniques are consistent. Notes Parameters measurements1, measurements2, measurements3... : array_like Arrays of measurements. All of the arrays must have the same number of elements. At least 3 sets of measurements must be given. Returns friedman chi-square statistic : float the test statistic, correcting for ties p-value : float the associated p-value assuming that the test statistic has a chi squared distribution Due to the assumption that the test statistic has a chi squared distribution, the p-vale is only reliable for n > 10 and more than 6 repeated measurements. 3.18. Statistical functions (<strong>scipy</strong>.stats) 663
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