Implementation of corrected two sample tests for Pearson, Kendall and Spearman correlation tests, corrected Mann-Whitney (Wilcoxon) rank sum test, corrected Wilcoxon signed rank test. A robust variance test, a median test and a test for independence between two continuous variables based on the Kolmogorov-Smirnov’s distance are also implemented. All the tests are asymptotically calibrated meaning that the probability of rejection under the null hypothesis is asymptotically equal to the level of the test.
The package contains the functions:
cortest that implements the corrected Pearson,
Kendall’s and Spearman’s tests. As compared to the original tests in
cor.test which all assume independence between the variables under the
null hypothesis, the corrected tests assume that the correlation (of the
different types) is equal to 0 under the null.wilcoxtest that implements the corrected version of the
Wilcoxon test for two independent samples (which is equivalent to
Mann-Whitney in that case) and for two paired samples. In the two
independent sample case, as compared to the original test in wilcox.test
which assumes that the variables have the same distribution under the
null hypothesis, the corrected test assumes under the null that the
probability that one variable exceeds the other is equal to 0.5.vartest that implements a variance test based on the
Welch correction for the variables (x_i-mean(x))^2 and (y_i-mean(y))^2.
As compared to the original test in var.test which only works under the
Gaussian scenario, the corrected test works for any distribution of the
two variables as long as the fourth order moments exist for both
variables. The test can be applied to more than two groups. In the two
sample case, the function also returns the confidence interval for the
difference of the two variances.mediantest that tests if the median of the random
variable (one sample case) or of the difference between two random
variables (two sample case) is equal to 0. The test is based on
asymptotic results on the rank statistics for the uniform distribution.
Confidence intervals for the median (one sample case) or for the
difference between two random variables (two sample case) are
returned.indeptestthat tests the independence between two
continuous variables. The test is based on the maximum distance between
the joint empirical cumulative distribution function and the product of
the marginals. The distribution of this test has been numerically
obtained, the test is exact for all n<=150 and approximated for
n>150.tiebreak which randomly breaks ties in vectors, either
inside the vector or between two vectors.The dataset Evans can also be loaded from the
robusTest package, this dataset was originally provided
in the lbreg package.