Manul Otocolobus
kiwifarms.net
- Joined
- Nov 2, 2021
An attempt to infer Pat's IQ score from his GPA.
- GPA scores are correlated with IQ scores;
- The literature reports a range of correlation coefficients (r), and the median of the reports is around 0.5;
- A correlation coefficient of 0.5 is described as "moderately positive";
- We know Patrick's GPA score, namely, 1.7;
- The mean GPA in the USA, from recent reports, is 3.0, with a standard deviation (SD) of 0.4;
- The non-Hispanic white mean IQ is 100, with an SD of 15. Also, the mean IQ of those whose highest level of schooling is high school is 100;
- A GPA of 1.7 is 3.25 SDs below the average;
- r x SD_y = SD_x (SD_y is the number of SDs of GPA above/below the mean, SD_x is the number of SDs of IQ above/below the mean);
- 0.5 x (-3.25) = -1.625, i.e., Pat's IQ score would be 1.625 SDs below the mean;
- Pat's IQ = 100 + (-1.625 x 15) = 100 - 24.375 = 75.625 ≈ 76
- An IQ of 76 is categorized as "borderline (retarded)".
This isn't an exact figure; it is approximately 76 because:
- r is 0.5; and
- for any given GPA, there will be a cluster of IQ scores around 76, i.e., the standard error.
That notwithstanding, an IQ score in this low range does explain much about Pat's behavior documented in the current thread.
PS:- It would be useful if someone reviewed my logic and arithmetic. I think it's good because the result is not outlandish; it's in the range of the expected.
If you adjust is to the proper 1.66, is he enough standard deviations below average to classify as likely to have an IQ somewhere below the cutoff for retarded?
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