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That is because Spearman's ρ limits the outlier to the value of its rank. In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman [1] and often denoted by the Greek letter (rho) or as , is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables).
White test is a statistical test that establishes whether the variance of the errors in a regression model is constant: that is for homoskedasticity. This test, and an estimator for heteroscedasticity-consistent standard errors , were proposed by Halbert White in 1980. [ 1 ]
The null hypothesis of this chi-squared test is homoscedasticity, and the alternative hypothesis would indicate heteroscedasticity. Since the Breusch–Pagan test is sensitive to departures from normality or small sample sizes, the Koenker–Bassett or 'generalized Breusch–Pagan' test is commonly used instead.
Dave Kerby (2014) recommended the rank-biserial as the measure to introduce students to rank correlation, because the general logic can be explained at an introductory level. The rank-biserial is the correlation used with the Mann–Whitney U test, a method commonly covered in introductory college courses on statistics. The data for this test ...
This ensures that the hypothesis test maintains its specified false positive rate (provided that statistical assumptions are met). [35] The p-value is the probability that a test statistic which is at least as extreme as the one obtained would occur under the null hypothesis. At a significance level of 0.05, a fair coin would be expected to ...
If the test statistic has a p-value below an appropriate threshold (e.g. p < 0.05) then the null hypothesis of homoskedasticity is rejected and heteroskedasticity assumed. If the Breusch–Pagan test shows that there is conditional heteroskedasticity, one could either use weighted least squares (if the source of heteroskedasticity is known) or ...
In statistics, the Page test for multiple comparisons between ordered correlated variables is the counterpart of Spearman's rank correlation coefficient which summarizes the association of continuous variables. It is also known as Page's trend test or Page's L test. It is a repeated measure trend test. The Page test is useful where:
The motivation to test differences between samples is that ranks are in some sense maximally invariant to monotone transformations. This may be important when there is outliers or when dealing with ordinal data .