correlation_test
statistics: h = correlation_test (x, y)
statistics: [h, p] = correlation_test (y, x)
statistics: [h, p, stats] = correlation_test (y, x)
statistics: […] = correlation_test (y, x, Name, Value)
Perform a correlation coefficient test to determine whether two samples x and y come from uncorrelated populations.
h = correlation_test (y, x) tests the null
hypothesis that the two samples x and y come from uncorrelated
populations. The result is h = 0 if the null hypothesis cannot be
rejected at the significance level alpha, or h = 1 if it can.
y and x must be vectors of equal length with finite real
numbers.
The p-value of the test is returned in p. stats is a structure with the following fields:
| Field | Value |
|---|---|
method | the type of correlation coefficient used for the test |
tstat | the t statistic, for Pearson’s and Spearman’s coefficients |
df | its degrees of freedom, n - 2 |
zval | the z statistic, for Kendall’s coefficient |
dist | the respective distribution for the test |
alt | the alternative hypothesis for the test |
CorrCoef | the correlation coefficient, the effect size |
CorrCoefCI | its 100 (1 - alpha)% confidence interval, one-sided for a one-sided test |
Pearson’s and Spearman’s coefficients are tested with
t = r sqrt ((n - 2) / (1 - r^2)) on n - 2 degrees of freedom,
as R’s cor.test does without an exact test; Kendall’s with its
normal approximation, whose variance allows for ties. The confidence
interval is Fisher’s z transform of the coefficient, with standard
error 1 / sqrt (n - 3) for Pearson’s,
sqrt ((1 + r^2 / 2) / (n - 3)) for Spearman’s and
sqrt (0.437 / (n - 4)) for Kendall’s, after Bonett and Wright (2000).
[…] = correlation_test (…, name, value)
specifies one or more of the following name/value pairs:
| Name | Value |
|---|---|
'alpha' | the significance level of h and the level of the confidence interval. Default is 0.05. |
'tail' | a string specifying the alternative hypothesis |
'both' | corrcoef is not 0 (two-tailed, default) |
'left' | corrcoef is less than 0 (left-tailed) |
'right' | corrcoef is greater than 0 (right-tailed) |
'method' | a string specifying the correlation coefficient used for the test |
'pearson' | Pearson’s product moment correlation (Default) |
'kendall' | Kendall’s rank correlation tau |
'spearman' | Spearman’s rank correlation rho |
See also: regression_ftest, regression_ttest
Source Code: correlation_test