A matrix version of cor.test()

corr.test in the psych package is designed to do this:

library("psych")
data(sat.act)
corr.test(sat.act)

As noted in the comments, to replicate the p-values from the base cor.test() function over the entire matrix, then you need to turn off adjustment of the p-values for multiple comparisons (the default is to use Holm’s method of adjustment):

 corr.test(sat.act, adjust = "none")

[But be careful when interpreting those results!]

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