covs_test {quest}

Covariances Test of Significance

Description

covs_test computes sample covariances and tests for their significance with the Pearson method assuming multivariate normality of the data. Note, the normal-theory significance test for the covariance is much more sensitive to departures from normality than the significant test for the mean. This function is the covariance analogue to the psych::corr.test() function for correlations.

Usage

covs_test(data, vrb.nm, use = "pairwise", ci.level = 0.95, rtn.dfm = FALSE)

Arguments

data

data.frame of data.

vrb.nm

character vector of colnames specifying the variables in data to conduct the significant test of the covariances.

use

character vector of length 1 specifying how missing values are handled. Currently, there are only two options: 1) "pairwise" for pairwise deletion (i.e., cov(use = "pairwise.complete.obs")), or 2) "complete" for listwise deletion (i.e., cov(use = "complete.obs")).

ci.level

numeric vector of length 1 specifying the confidence level. It must be between 0 and 1 - or it can be NULL in which case confidence intervals are not computed and the return object does not have "lwr" or "upr" columns.

rtn.dfm

logical vector of length 1 specifying whether the return object should be an array (FALSE) or data.frame (TRUE). If an array, then the first two dimensions are the matrix dimensions from the covariance matrix and the 3rd dimension (aka layers) contains the statistical information (e.g., est, se, t). If data.frame, then the first two columns are the matrix dimensions from the covariance matrix expanded and the rest of the columns contain the statistical information (e.g., est, se, t).

Value

If rtn.dfm = FALSE, an array where its first two dimensions are the matrix dimensions from the covariance matrix and the 3rd dimension (aka layers) contains the statistical information detailed below. If rtn.dfm = TRUE, a data.frame where its first two columns are the expanded matrix dimensions from the covariance matrix and the rest of the columns contain the statistical information detailed below:

cov

sample covariances

se

standard errors of the covariances

t

t-values

df

degrees of freedom (n - 2)

p

two-sided p-values

lwr

lower bound of the confidence intervals (excluded if ci.level = NULL)

upr

upper bound of the confidence intervals (excluded if ci.level = NULL)

See Also

cov for covariance matrix estimates, corr.test for correlation matrix significant testing,

Examples

# traditional use
covs_test(data = attitude, vrb.nm = names(attitude))
covs_test(data = attitude, vrb.nm = names(attitude),
   ci.level = NULL) # no confidence intervals
covs_test(data = attitude, vrb.nm = names(attitude),
   rtn.dfm = TRUE) # return object as data.frame

# NOT same as simple linear regression slope
covTest <- covs_test(data = attitude, vrb.nm = names(attitude),
   ci.level = NULL, rtn.dfm = TRUE)
x <- covTest[with(covTest, rownames == "rating" & colnames == "complaints"), ]
lm_obj <- lm(rating ~ complaints, data = attitude)
y <- coef(summary(lm_obj))["complaints", , drop = FALSE]
print(x); print(y)
z <- x[, "cov"] / var(attitude$"complaints")
print(z) # dividing by variance of the predictor gives you the regression slope
# but the t-values and p-values are still different

# NOT same as correlation coefficient
covTest <- covs_test(data = attitude, vrb.nm = names(attitude),
   ci.level = NULL, rtn.dfm = TRUE)
x <- covTest[with(covTest, rownames == "rating" & colnames == "complaints"), ]
cor_test <- cor.test(x = attitude[[1]], y = attitude[[2]])
print(x); print(cor_test)
z <- x[, "cov"] / sqrt(var(attitude$"rating") * var(attitude$"complaints"))
print(z) # dividing by sqrt of the variances gives you the correlation
# but the t-values and p-values are still different