Armstrong and Woodley argue that the documented rise in measured IQs is a result of test-takers applying rule-based approaches to tests, resulting in an increase similar to that seen in re-testing. They're arguing that in large part, it is a testing artifact. They make several predictions about what we should observe if their rule-based model is correct. For instance, that measures of crystallized intelligence (i.e. vocabulary) should not rise or not rise as robustly, and they haven't; that most obviously rule-based tests (like Raven's progressive matrices) should show the strongest effect (they do); and that we should expect the gains to appear when countries undergo demographic transition including standardized education, and the rate of increase should correspond to the rate of the transition.
To this last point, it's worth pointing out that there are many other less interesting medical explanations for why intelligence might actually be rising. Specifically, lower parasite load due to public sanitation and better nutrition in early childhood are very good candidates for why the Flynn-type gains are most pronounced in Europe, Japan and Korea in the periods when they were observed. It's hard to make the argument that lower parasite load leads to better cognitive strategies to game tests. It's also not surprising that if bombs are falling around your school and then they stop, the people tested after they stop may perform better - especially since even non-warfare jet and traffic noise has been shown to locally impair reading comprehension in students.
A second, neglected question is whether the abstract rule-based thinking required for the re-testing-type gains actually correlates to some other outcome, like personal or national per capita income, or life satisfaction. If the Flynn effect doesn't represent an increase in g but does correlate with economic growth, do we care that much?
References
Armstrong EL and Woodley MA. The rule-dependence model explains the commonalities between the Flynn effect and IQ gains via retesting. Learning and Individual Differences, Volume 29, January 2014, Pages 41–49.
Eppig C, Fincher CL, Thornhill R. Parasite prevalence and the worldwide distribution of cognitive ability. Intelligence 39 (2011) 155–160.
Haines MM, Stansfeld SA, Job RF, Berglund B, Head J. Chronic aircraft noise exposure, stress responses, mental health and cognitive performance in school children. Psychol Med. 2001 Feb;31(2):265-77.
Consciousness and how it got to be that way
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Other than rule-based testing knowledge gained, could increased scholasticism in general due to increases in literacy (as claimed by David Marks) be at work? Furthermore - how did the distributions change, if they did change, in the study cited? "If increasing literacy were really explaining a number of seemingly different IQ trends, then you would expect to see a few things. First, within a population you should expect increased education of literacy skills to be associated with an increase in the average IQ of that population. Second, IQ gains should be most pronounced in the lower half of the IQ bell curve since this is the section of the population that prior to the education would have obtained relatively lower scores due to their inability to comprehend the intelligence test's instructions. With increased literacy, you should expect to see a change in the skewness of the IQ distribution from positive to negative as a result of higher rates of literacy in the lower half of the IQ distribution (but very little change in the top half of the distribution). You should also expect to see differences on the particular intelligence test subscales, with increased literacy showing the strongest effects on verbal tests of intelligence and minimal differences on other tests of intelligence. If all these predictions hold up, there would be support for the notion that secular IQ gains and race differences are not different phenomena but have a common origin in literacy." From: https://www.psychologytoday.com/us/blog/beautiful-minds/201008/the-flynn-effect-and-iq-disparities-among-races-ethnicities-and-nations
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