Fig 1: The graph that summarizes the first flaw (assuming thin tailed situations), showing that “correlation” is meaningless in the absence of symmetry. We construct (in red) an intelligence test (horizontal), that is 100% correlated with negative performance (when IQ is, say, below 100) and 0% with upside, positive performance. We progressively add noise (with a 0 mean) and see correlation (on top) drop but shift to both sides. Performance is on the vertical axis. The problem gets worse with the “g” intelligence based on principal components. By comparison we show (graph below) the distribution of
IQ and SAT scores . Most “correlations” entailing IQ suffer the same pathology. Note: this is in spite of the fact that IQ tests overlap with the SAT! (To echo Haldane, one ounce of rigorous algebra is worth more than a century of verbalistic statisticopsycholophastering).
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