The psych package contains a function ?alpha which calculates test reliability and some item statistics. When fed raw data (a data.frame with binary values for correct/incorrect answers), it returns, among other things, mean and st. dev. for each item. However, sometimes it doesn't, and only provides item-whole correlation.
Why is that?
The docu states that mean and sd are only calculated "For data matrices [...]", and that x is "A data.frame or matrix of data, or a covariance or correlation matrix". But how does it know whether I'm giving it raw data or a correlation matrix?
The alpha command of psych detects if the input x is a correlation matrix using the isCorrelation command.
Let consider the dataset given in this tutorial:
datafilename <- "http://personality-project.org/R/datasets/extraversion.items.txt"
items <- read.table(datafilename,header=TRUE)
df <- with(items, data.frame(q_262 ,q_1480 ,q_819 ,q_1180 ,q_1742 ))
The object df is a data.frame whose columns represent the responses to five items. The command isCorrelation (used inside alpha) correctly detect that this is not a correlation matrix:
library(psych)
isCorrelation(df)
[1] FALSE
If we calculate the correlation matrix of df and pass to isCorrelation, we get again a correct answer:
mtx <- cor(df)
isCorrelation(mtx)
[1] TRUE
Looking inside isCorrelation one can see that a correlation matrix is defined as an object which is not a data.frame (hence, is a matrix) and which is symmetric:
isCorrelation <- function (x)
{
return(!is.data.frame(x) && isSymmetric(unname(x)))
}