Sunday, July 19, 2009

Dichotomous data and rates

At last I have in my possession the Rasch book. Amazon offers it second hand from $235 (as at today). By going through the Institute for Objective Measurement, I got it for $30.

Reading the foreword there are two important things, which Rasch made clear to other people. The first is that if a test is constructed to produce dichotomous data, it must be properly graduated. In the guts of the book Rasch produces a model for data generated by a properly spaced test, and then defines parameters which have to be met by real data, for that data to be said to fit the model. The second is almost a sleight of hand, by which he states that the probability of a result is a function of the ability of the person and the difficulty of the test, and the probability of another result is a similar function of the ability of the person and the difficulty of the test; and then he combines the two using the a couple of rules for the probability of a specified combination of events, and makes one of the parameters (either ability or difficulty, depending on his mood) disappear, thus creating an objective measure of the remaining parameter.

The most interesting thing from my perspective of the example given in the forward is that it does not concern dichotomous data but rather reading rates. Yet the first four chapters of the main book deal entirely with dichotomous data, and almost all the subsequent theory and research deals with dichotomous data. I think for the sake of completeness, I will revisit these chapters, and then I hope to develop some code based on the chapters which deal with reading rates.

No comments: