Confessions of a one-time statistician

In the course of perusing reference 1, I came across talk of something called Rosenthal's pi, sometimes Rosenthal's π.

This was a device to help comparing the results of tests involving multiple choices questions when the number of choices was not the same in the two tests, a device that you need because getting half the answers right when there are just two choices is not the same as getting half the answers right when there are twenty choices. So what do you do when the task is to assess whether the answers in the one test were better than the answers in the other?

But there was not enough at reference 1 for me to be comfortable with pi. So off to Bing to see if he could turn up reference 2, listed at the back of reference 1. And for once Bing was not particularly helpful. He came up with various other papers which talked about this very pi, but not in a way which helped me. While the original paper remained elusive.

I let it all settle for a day or so and then I decide to bite the bullet and ask the American Psychological Association direct. They route me through to something called APA PsycNET (reference 3), where search turns up the paper in question and suggests that I pay US$11.99 or so for it. It being fairly unusual these days for me to want a paper which the likes of Bing and ResearchGate (reference 4) cannot turn up for free, I stumped up the necessary for the pdf. Now partly read.

I don't claim that I understand the detail underlying Rosenthal's pi, but at least I am now comfortable reading about the use that others have made of it. And I do now know how to compute the thing. Perhaps the words logit and log linear struck a distant chord.

I was also reminded that real statisticians would know all about this sort of thing, which has been attracting learned attention for many a year. The name Pearson, for example, was mentioned in connection with something called r, striking another distant chord. Some of my colleagues in the Government Statistical Service really did know about this sort of thing - whereas the sort of statistics that I did was much more akin to accounting. Collecting things up and putting them into boxes - bins in the jargon of scientists in the US - and with the things in question usually being people of one sort or another. On the rare occasions that real statistics were needed, I had to dig out my student textbooks and remind myself what a standard deviation was - never mind a Pearson's r. Wikipedia had not at that time been invented, at least, not for me.

Reference 1: Communication of emotions in vocal expression and music performance: Different channels, same code? -  Juslin, P. N., & Laukka, P. - 2003.

Reference 2: Effect size estimation for one-sample multiple-choice-type data: Design, analysis, and meta-analysis - Rosenthal and Rubin – 1989.

Reference 3: https://www.apa.org/pubs/databases/psycnet/index.aspx.

Reference 4: https://www.researchgate.net/.