Does IQ predict outcomes only on the "left" side of the IQ distribution (i.e., for people of below average IQ)?

Note: This is a section of a longer article. To go to the start, click here.

No. Following some claims that circulated in the blogosphere (such as this one by Nassim Nicholas Taleb), we have set out to study this research question and, in general, found that whether IQ is more predictive on the left or on the right side of the distribution depends on the outcome. Statistically, we have tested this research question by dividing our sample in three separate groups: low IQ group (IQ < 92), average IQ group (>=92 & <= 108) and high IQ group (IQ > 108) and calculating the correlation between IQ and seven outcomes within each group independently. We chose these cut-off points because roughly a similar proportion of the population should fall into each group (approximately 30% of the population should fall into low and high IQ groups, while around 40% of the population should fall into the average IQ group). Note that a related claim that's been made in the academic literature is that there is a threshold beyond which IQ stops being useful (or becomes less useful) for some outcomes - known as the "threshold hypothesis."

The outcomes that we measured were a) level of education achieved, b) high-school GPA, c) personal income, d) life satisfaction, e) good employee self-report (a measure of how good people report being at their job that combines a number of different job relevant questions such as “I don't do every single thing that my boss asks me to do.”, “I am often told by bosses that I do a great job at work.” or “I always get my work done on time.”), f) self-rated achievement of life goals, g) self-rated accomplishment in life, h) self-rated physical health, and i) the discrepancy between the ideal and the actual time use (participants estimated the ideal time they would like to spend on different activities, as well as the actual time they spend on it, and we summed the absolute differences between the two scores for each activity to make the total time use discrepancy score). In addition we have plotted the smoothed line of best fit to visually represent the relationship between IQ and each outcome throughout IQ distribution.

As can be seen from the tables and figures below, out of the seven outcome that we’ve taken into account for this analysis, there were two for which IQ showed a higher predictiveness on the left side of the distribution (i.e., in the low IQ group, compared to the other two groups): the good employee self-report and the self-rated accomplishment in life, although its correlations with IQ did not differ across the IQ groups as much as did IQ-good-employee correlations. For some of the outcomes, the correlation was even slightly higher on the right side of the IQ distribution (e.g. high-school GPA, educational level, and personal income). An important note here, is that when restricting the range of a variable, as we do here by dividing into three different IQ groups, the magnitude of correlations will tend to drop through an effect known as "range restriction", so please keep that in mind when viewing the table below.

			Correlations of outcomes with IQ for different IQ groups
	For Lower IQ participants (IQs < 92)	For Middle IQ participants (IQs from 92 to 108)	For Higher IQ participants  (IQs > 108)
Educational level	-0.029	0.089	0.114
High-school GPA	-0.018	0.121	0.202
Personal income	-0.040	0.005	0.084
Life satisfaction	-0.093	-0.046	0.01
Self-rated scale about how good an employee they are	0.458	0.052	0.042
Self-rated achievement of life goals	-0.118	-0.017	0.038
Self-rated accomplishment in life	-0.186	-0.067	0.047
Self-rated physical health	-0.037	-0.012	0.002
Time use discrepancy	-0.098	-0.023	0.008

Note that self-rated achievement of life goals is measured on a 5 point likert scale from 0=not at all to 4=very much, using the question: "To what extent have you achieved your biggest goals in life that you've set out to achieve?"

Self-rated accomplishment is measured on a scale of 0 to 100 using this question:

"Suppose that 0 refers to having accomplished nothing at all that people in your country value, and 100 refers to having accomplished as much as the most accomplished people in the world (such as a Nobel Prize winning scientists, billionaire CEO, world famous musician, or beloved president of a country). On this scale from 0 to 100, where would what you have accomplished thus far in your life fall (according to the standards of the people in your country)?"

Time use discrepancy is measured by subtracting actual self-reported use of time from the ideal time that participants reported they spent on different activities such as exercising, sleeping, reading, spending time with friends and family etc. The absolute values of these discrepancies for each specific activity were then summed to obtain the total time use discrepancy score. Higher score indicates higher mismatch between ideal and actual time use, i.e., more time spent in unwanted ways.

Note: In the plots below, we fitted a blue line that illustrates the relationship between IQ and other variables using the LOESS method (specifically quadratic local regression with tricube weight function) which is a non-parametric regression method that fits a smooth curve to data without assuming a specific model (such as linear or quadratic).

Note: Time use discrepancy is measured by subtracting actual from the ideal time that participants reported they spent on different activities such as exercising, sleeping, reading, spending time with friends and family etc. The absolute values of these discrepancies for each specific activity were then summed to obtain the total time use discrepancy score. Higher score indicates higher mismatch between ideal and actual time use, i.e., more time spent in ways other than ideal.

What do the other studies say?

One of the largest studies (Brown et al., 2021) that investigated whether the effects of IQ on various outcomes are linear (meaning similar irrespective of the IQ level) or curvilinear (meaning stronger at some and weaker at different levels of IQ) conducted on a large sample of US and UK citizens (n = 48,558) concluded that, whenever there was an effect of IQ on an outcome, it was almost exclusively linear, with all nonlinear effects being practically insignificant in magnitude. Although we found some differences in correlations across the three groups (i.e., the low, average and high IQ groups),these differences were quite small and practically negligible, with the exception of our good employee score. In this sense, despite some popular voices against the linearity hypothesis, our data are mostly in line with the latest findings in the literature.

As additional notes, Jauk et al., 2013 found no threshold effect for creative achievement, whereas they do find thresholds for ideational originality (IQ=100) and ideational fluency (IQ=85) beyond which further IQ seemed to have little effect. Robertson et al., 2010, on the other hand pushed the idea to its limits testing whether there was a link between cognitive ability and outcomes for those in the top 1% of cognitive ability. They found that even in this very elite group "individual differences in general cognitive ability level...lead to differences in educational, occupational, and creative outcomes decades later." This is the graph they provide of outcomes versus age 13 SAT math scores:

source

Takeaways

• To the extent IQ predicted variables that we tested, the effects were similar across the whole range of IQ scores (i.e. nor particularly stronger on the left side of the distribution)

• The only notable exception to this was the good employee self-report score for which IQ was indeed more predictive on the left side of the distribution, meaning in lower IQ group

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