correlate: Correlation matrices

In lsr: Companion to "Learning Statistics with R"

Description

Computes a correlation matrix and runs hypothesis tests with corrections for multiple comparisons

Usage

correlate(
  x,
  y = NULL,
  test = FALSE,
  corr.method = "pearson",
  p.adjust.method = "holm"
)

Arguments

x	Matrix or data frame containing variables to be correlated
y	Optionally, a second set of variables to be correlated with those in x
test	Should hypothesis tests be displayed? (Default=FALSE)
corr.method	What kind of correlations should be computed? Default is "pearson", but "spearman" and "kendall" are also supported
p.adjust.method	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

Details

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.

Value

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.

Examples

# 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 )

# other types of correlation:
correlate( data, corr.method="spearman" )

# 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 )

# the same examples, with Holm-corrected p-values
correlate( data, test=TRUE )
correlate( nervous, happy, test=TRUE )

lsr documentation built on Dec. 11, 2021, 9:10 a.m.