Computes a correlation matrix and runs hypothesis tests with corrections for multiple comparisons
correlate(
x,
y = NULL,
test = FALSE,
corr.method = "pearson",
p.adjust.method = "holm"
)Matrix or data frame containing variables to be correlated
Optionally, a second set of variables to be correlated with those in x
Should hypothesis tests be displayed? (Default=FALSE)
What kind of correlations should be computed? Default is "pearson", but "spearman" and "kendall" are also supported
What method should be used to correct for multiple comparisons. Default value is "holm", and the allowable values are the same as for p.adjust
The printed output shows the correlation matrix, and if tests are
requested it also reports a matrix of p-values and sample sizes associated
with each correlation (these can vary if there are missing data). The
underlying data structure is an object of class correlate (an S3
class). It is effectively a list containing four elements:
correlation is the correlation matrix, p.value is the matrix
of p-values, sample.size is the matrix of sample sizes, and
args is a vector that stores information about what the user
requested.
The correlate function calculates a correlation matrix
between all pairs of variables. Much like the cor function, if the
user inputs only one set of variables (x) then it computes all
pairwise correlations between the variables in x. If the user
specifies both x and y it correlates the variables in
x with the variables in y.
Unlike the cor function, correlate does not generate an
error if some of the variables are categorical (i.e., factors). Variables
that are not numeric (or integer) class are simply ignored. They appear in
the output, but no correlations are reported for those variables. The
decision to have the correlate function allow the user a little
leniency when the input contains non-numeric variables should be explained.
The motivation is pedagogical rather than statistical. It is sometimes the
case in psychology that students need to work with correlation matrices
before they are comfortable subsetting a data frame, so it is convenient
to allow them to type commands like correlate(data) even when
data contains variables for which Pearson/Spearman correlations
are not appropriate. (It is also useful to use the output of
correlate to illustrate the fact that Pearson correlations should
not be used for categorical variables).
A second difference between cor and correlate is that
correlate runs hypothesis tests for all correlations in the
correlation matrix (using the cor.test function to do the work).
The results of the tests are only displayed to the user if
test=TRUE. This is a pragmatic choice, given the (perhaps
unfortunate) fact that psychologists often want to see the results
of these tests: it is probably not coincidental that the corr.test
function in the psych package already provides this functionality
(though the output is difficult for novices to read).
The concern with running hypothesis tests for all elements of a correlation
matrix is inflated Type I error rates. To minimise this risk, reported
p-values are adjusted using the Holm method. The user can change this
setting by specifying p.adjust.method. See p.adjust
for details.
Missing data are handled using pairwise complete cases.
# data frame with factors and missing values
data <- data.frame(
anxiety = c(1.31,2.72,3.18,4.21,5.55,NA),
stress = c(2.01,3.45,1.99,3.25,4.27,6.80),
depression = c(2.51,1.77,3.34,5.83,9.01,7.74),
happiness = c(4.02,3.66,5.23,6.37,7.83,1.18),
gender = factor( c("male","female","female","male","female","female") ),
ssri = factor( c("no","no","no",NA,"yes","yes") )
)
# default output is just the (Pearson) correlation matrix
correlate( data )
#>
#> CORRELATIONS
#> ============
#> - correlation type: pearson
#> - correlations shown only when both variables are numeric
#>
#> anxiety stress depression happiness gender ssri
#> anxiety . 0.784 0.906 0.924 . .
#> stress 0.784 . 0.693 -0.453 . .
#> depression 0.906 0.693 . 0.247 . .
#> happiness 0.924 -0.453 0.247 . . .
#> gender . . . . . .
#> ssri . . . . . .
# other types of correlation:
correlate( data, corr.method="spearman" )
#>
#> CORRELATIONS
#> ============
#> - correlation type: spearman
#> - correlations shown only when both variables are numeric
#>
#> anxiety stress depression happiness gender ssri
#> anxiety . 0.500 0.900 0.900 . .
#> stress 0.500 . 0.543 -0.257 . .
#> depression 0.900 0.543 . 0.429 . .
#> happiness 0.900 -0.257 0.429 . . .
#> gender . . . . . .
#> ssri . . . . . .
# two meaningful subsets to be correlated:
nervous <- data[,c("anxiety","stress")]
happy <- data[,c("happiness","depression","ssri")]
# default output for two matrix input
correlate( nervous, happy )
#>
#> CORRELATIONS
#> ============
#> - correlation type: pearson
#> - correlations shown only when both variables are numeric
#>
#> happiness depression ssri
#> anxiety 0.924 0.906 .
#> stress -0.453 0.693 .
# the same examples, with Holm-corrected p-values
correlate( data, test=TRUE )
#>
#> CORRELATIONS
#> ============
#> - correlation type: pearson
#> - correlations shown only when both variables are numeric
#>
#> anxiety stress depression happiness gender ssri
#> anxiety . 0.784 0.906 0.924 . .
#> stress 0.784 . 0.693 -0.453 . .
#> depression 0.906 0.693 . 0.247 . .
#> happiness 0.924 -0.453 0.247 . . .
#> gender . . . . . .
#> ssri . . . . . .
#>
#> ---
#> Signif. codes: . = p < .1, * = p<.05, ** = p<.01, *** = p<.001
#>
#>
#> p-VALUES
#> ========
#> - total number of tests run: 6
#> - correction for multiple testing: holm
#>
#> anxiety stress depression happiness gender ssri
#> anxiety . 0.467 0.171 0.150 . .
#> stress 0.467 . 0.467 0.733 . .
#> depression 0.171 0.467 . 0.733 . .
#> happiness 0.150 0.733 0.733 . . .
#> gender . . . . . .
#> ssri . . . . . .
#>
#>
#> SAMPLE SIZES
#> ============
#>
#> anxiety stress depression happiness gender ssri
#> anxiety 5 5 5 5 5 4
#> stress 5 6 6 6 6 5
#> depression 5 6 6 6 6 5
#> happiness 5 6 6 6 6 5
#> gender 5 6 6 6 6 5
#> ssri 4 5 5 5 5 5
correlate( nervous, happy, test=TRUE )
#>
#> CORRELATIONS
#> ============
#> - correlation type: pearson
#> - correlations shown only when both variables are numeric
#>
#> happiness depression ssri
#> anxiety 0.924. 0.906 .
#> stress -0.453 0.693 .
#>
#> ---
#> Signif. codes: . = p < .1, * = p<.05, ** = p<.01, *** = p<.001
#>
#>
#> p-VALUES
#> ========
#> - total number of tests run: 4
#> - correction for multiple testing: holm
#>
#> happiness depression ssri
#> anxiety 0.100 0.103 .
#> stress 0.367 0.255 .
#>
#>
#> SAMPLE SIZES
#> ============
#>
#> happiness depression ssri
#> anxiety 5 5 .
#> stress 6 6 .