Although the cor function finds the correlations for a matrix, it does not report probability values. cor.test does, but for only one pair of variables at a time. corr.test uses cor to find the correlations for either complete or pairwise data and reports the sample sizes and probability values as well. For symmetric matrices, raw probabilites are reported below the diagonal and correlations adjusted for multiple comparisons above the diagonal. In the case of different x and ys, the default is to adjust the probabilities for multiple tests. Both corr.test and corr.p return raw and adjusted confidence intervals for each correlation.
corr.test(x, y = NULL, use = "pairwise",method="pearson",adjust="holm",
alpha=.05,ci=TRUE,minlength=5)
corr.p(r,n,adjust="holm",alpha=.05,minlength=5,ci=TRUE)A matrix or dataframe
A second matrix or dataframe with the same number of rows as x
use="pairwise" is the default value and will do pairwise deletion of cases. use="complete" will select just complete cases.
method="pearson" is the default value. The alternatives to be passed to cor are "spearman" and "kendall"
What adjustment for multiple tests should be used? ("holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", "none"). See p.adjust for details about why to use "holm" rather than "bonferroni").
alpha level of confidence intervals
A correlation matrix
Number of observations if using corr.p. May be either a matrix (as returned from corr.test, or a scaler. Set to n - np if finding the significance of partial correlations. (See below).
By default, confidence intervals are found. However, this leads to a noticable slowdown of speed, particularly for large problems. So, for just the rs, ts and ps, set ci=FALSE
What is the minimum length for abbreviations. Defaults to 5.
The matrix of correlations
Number of cases per correlation
value of t-test for each correlation
two tailed probability of t for each correlation. For symmetric matrices, p values adjusted for multiple tests are reported above the diagonal.
standard error of the correlation
the alpha/2 lower and upper values, as well as the (Holm or Bonferroni) adjusted confidence intervals.
corr.test uses the cor function to find the correlations, and then applies a t-test to the individual correlations using the formula
$$t = \frac{r * \sqrt(n-2)}{\sqrt(1-r^2)}
$$
$$se = \sqrt(\frac{1-r^2}{n-2}) $$
The t and Standard Errors are returned as objects in the result, but are not normally displayed. Confidence intervals are found and printed if using the print(short=FALSE) option. These are found by using the fisher z transform of the correlation and then taking the range r +/- qnorm(alpha/2) * se and the standard error of the z transforms is $$se = \sqrt(\frac {1}{n-3}) $$. These values are then back transformed to be in correlation units. They are returned in the ci object.
The probability values may be adjusted using the Holm (or other) correction. If the matrix is symmetric (no y data), then the original p values are reported below the diagonal and the adjusted above the diagonal. Otherwise, all probabilities are adjusted (unless adjust="none"). This is made explicit in the output. Confidence intervals are shown for raw and adjusted probabilities in the ci object.
corr.p may be applied to the results of partial.r if n is set to n - s (where s is the number of variables partialed out) Fisher, 1924.
cor.test for tests of a single correlation, Hmisc::rcorr for an equivalant function, r.test to test the difference between correlations, and cortest.mat to test for equality of two correlation matrices.
Also see cor.ci for bootstrapped confidence intervals of Pearson, Spearman, Kendall, tetrachoric or polychoric correlations. In addition cor.ci will find bootstrapped estimates of composite scales based upon a set of correlations (ala cluster.cor).
In particular, see p.adjust for a discussion of p values associated with multiple tests.
Other useful functions related to finding and displaying correlations include lowerCor for finding the correlations and then displaying the lower off diagonal using the lowerMat function. lowerUpper to compare two correlation matrices.
# NOT RUN {
ct <- corr.test(attitude) #find the correlations and give the probabilities
ct #show the results
cts <- corr.test(attitude[1:3],attitude[4:6]) #reports all values corrected for multiple tests
#corr.test(sat.act[1:3],sat.act[4:6],adjust="none") #don't adjust the probabilities
#take correlations and show the probabilities as well as the confidence intervals
print(corr.p(cts$r,n=30),short=FALSE)
#don't adjust the probabilities
print(corr.test(sat.act[1:3],sat.act[4:6],adjust="none"),short=FALSE)
# }
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