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PaperclipPerfector  3d ago (text post)   11350 thread views

Culture War Roundup for the week of September 28, 2026

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The study explains that the numbers in this table are z-values on a normal distribution, not percentages.

Because the distribution of percentages known was very right-skewed and did not differentiate much between well-known words, it was useful to apply a probit transformation to the percentages. The probit function translates percentages known to z values on the basis of the cumulative normal distribution. That is, a word known by 2.5% of the participants would have a word prevalence of –1.96; a word known by 97.5% of the participants would have a prevalence of +1.96. Because a word known by 0% of participants would return a prevalence score of –∞ and a percentage known of 100% would return a prevalence score of +∞, the range was reduced to percentages known from 0.5% (prevalence = –2.576) to 99.5% (prevalence = +2.576).2

2The specific formula we used in Microsoft Excel was =NORM.INV(0.005+Pknown*0.99;0;1).

A simpler version of this formula is =NORM.S.INV(0.005+Pknown*0.99). The inverse is =(NORM.S.DIST(prevalence,TRUE)-0.005)/0.99. So, for "gauss", prevalences of +0.64 for men vs. +0.31 for women actually mean percentages of 74 percent for men vs. 62 percent for women.

That makes sense. I’ve seen the table reproduced as a graph with percentages, I guess nobody (including me sadly) bothers to read the actual study.

From a quick look, although there’s not a direct easy conversion AFAIK, 0.15 prevalence is about 56% familiarity, 0.5 is about 70%, and 0.8 is 80%, so it’s not the massive gap originally presented.

But I think all the study did was check if the participants knew it was a word or not by having them pick out the real ones from a list of gibberish?

there’s not a direct easy conversion AFAIK

I gave one in an edit.

But I think all the study did was check whether the participants knew it was a word or not by having them pick out the real ones from a list of gibberish.

More or less.

For each vocabulary test, a random sample of 67 words and 33 nonwords was selected. For each letter string, participants had to indicate whether or not they knew the stimulus. At the end of the test, participants received information about their performance, in the form of a vocabulary score based on the percentage of correctly identified words minus the percentage of nonwords identified as words. For instance, a participant who responded “yes” to 55 of the 67 words and to 2 of the 33 nonwords received feedback that they knew 55/67 – 2/33 = 76% of the English vocabulary. Participants could do the test multiple times and always got a different sample of words and nonwords.

But they largely replicated the results by administering three ordinary multiple-choice vocabulary tests, with r = 0.69 vs. the original test.

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