Test information in item response theory (IRT) is defined as:
The denominator is basically the squared value of the standard error of measurement (SEM). The SEM is defined in classical test theory (CTT) as:
In IRT, we assume T to have a variance of 1 in the population, so let's say Sxx = 1. (Although the variance of theta is not necessarily the same as the variance of the observed test scores. I just do not know what the observed version of theta would be in IRT.). Then:
It follows that:
and
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