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Openpsychometrics FSIQ test underestimates IQ scores by about 5 points
I have seen scores from this test circulate on twitter and gcs:
Looking closely, there seems to be a bit of a problem here. If you average out the scores in picture 1, you get a score of 127.7, and if you average out the scores in picture 2, you get 131. However, the Full Scale IQ score is below both of these averages. This is impossible, as the full scale score should always be above the average of the subtests.
Let me illustrate this with a simulation. Lets say I have 3 vectors b, c, and d.
c and d correlate at 0.63
b and c correlate at 0.43
b and d correlate at 0.62
In every single case, the FSIQ score was more extreme than the average score of each subtest. This is obvious if you look at the first 19 rows:
Empirically speaking, it looks like this is also true outside of simulations. Some researchers assigned the openpsychometrics FSIQ test to 88 college students, 72 of which also took the WASI-II. On average, the students scored about 5 points less on the FSIQ test than the WASI-II.
Emil also sent me this document, proving that the average of the subtests should always be less extreme than the full scale score.
edit: apparently if you refresh it… the score increases
In the example scores, I was the 123 score. The person who told me said their score increased to above 130. Still, my point still stands about it not being possible for the average of the subtests to be larger than the full scale score.