Tetrachoric correlation coefficients are computed when two conditions are met: (1) the tetrachorics option is set as "Yes" in the System worksheet, and (2), Lertap finds that the item scores are just zeros and ones.


These conditions are in fact easy to satisfy.  The tetrachoric option's default setting in the System worksheet is No when Lertap is first installed, but this may quickly be changed to Yes.  And cognitive test items are very often scored on just a right/wrong basis, with one point for a correct answer, zero points otherwise.


What are tetrachoric correlation coeffcients?  They're estimates of what the correlation between two items would be if responses to the items had an underlying normal distribution, instead of the simple right/wrong dichotomy used to score the items.  Some researchers and test developers are at times willing to assume underlying normal distributions, especially when they are interested in aspects of IRT modelling.


For more reading, use Lertap's references page, looking at Crocker and Algina, Lord, and/or Glass and Stanley.  Or, search the Internet for definitions and discussions.


To compute the tetrachorics, Lertap uses an algorithm created by Brown (1977) (see References).  Brown's algorithm calls for the use of two normal-curve functions: "AlNorm", and "PPND".  Lertap uses two in-built Excel functions instead: NORMINV and NORMSDIST.