Studies have found an association between individuals’ socioeconomic background (SEB) and achieved level of education or socioeconomic position even when adjusting for cognitive ability [e.g. 1, 2]. Some researchers have explained this association with negative social expectations and discrimination against people from humbler origins and favoritism of the highborn. The persistence of this association when adjusting for cognitive ability has been interpreted to mean that higher cognitive ability is required from someone with a lower SEB in order to achieve the same level of education or socioeconomic position as someone with a higher SEB, or alternatively that high SEB can compensate for a lack in cognitive ability [1, 3, 4]. However, other studies have found that when adjusting for achieved socioeconomic position, a positive association between SEB and cognitive ability as well as achieved level of education can be observed [5,6,7,8,9,10]. If using the same logic as above, a contradictory interpretation would emerge: higher cognitive ability is required from individuals with high SEB in order to achieve the same socioeconomic position as someone with lower SEB, i.e. there is societal discrimination against the highborn.
An alternative explanation, which could account for the above-mentioned seemingly contradictory associations, is residual confounding. Confounding in a statistical analysis occurs when a variable (Z) influences both the dependent variable (Y) and the independent variable (X) [11]. It is common to adjust for potential confounding variables by including them as covariates in an analysis, in order to reduce the risk of spurious associations. However, the influence of the confounding variable may not be fully attenuated by such adjustment [12,13,14,15,16]. Residual confounding refers to confounding which remains despite adjustment. The impact of residual confounding is increased by higher true degree of confounding, larger sample size, and higher reliability in the measurements of X and Y, while it is attenuated by a high reliability in the measurement of Z [12,13,14,15,16]. With these factors in place, even if entities/individuals have the same value on observed Z they will tend to differ in their true Z and this may result in an association between observed X and observed Y even if adjusting for observed Z. For example, even if achieved socioeconomic position or level of education has been rated as the same, the actual/true position or level may be higher for those with high SEB compared to those with lower SEB. Similarly, even if observed cognitive ability is the same, true ability may tend to be higher for those with high SEB. This could explain why high SEB is associated with a higher achieved socioeconomic position and level of education, even when adjusting for observed ability.
The expected standardized effect of measured SEB on true cognitive ability when adjusting for measured cognitive ability is given by Eq. (1) (see “Appendix” for derivation). Assuming that cognitive ability is not measured completely without reliability (rTrCA,CA ≠ 0) and that the correlation between observed ability and SEB does not equal unity (rCA,SEB ≠ 1), we see that the effect of observed SEB on true cognitive ability when adjusting for observed ability is expected to be zero only if the correlation between observed cognitive ability and SEB equals zero (rCA,SEB = 0) or if cognitive ability is measured with perfect reliability (rTrCA,CA = 1). Consequently, observed SEB is expected to be associated with whatever true cognitive ability is associated with, e.g. achieved level of education, even when adjusting for measured cognitive ability. It should be noted that in the present context, the term “reliability” should be interpreted more broadly than just, for example, homogeneity. If some research participants would not take the measurement of cognitive ability seriously, e.g. due to low motivation, this could actually strengthen the correlations between scores on subtests and, consequently, the homogeneity of the tests. However, such lack of earnestness among some participants would tend to weaken the correlation between true and measured cognitive ability.
$$E|{\beta}_{SEB,TrCA.CA}|=\frac{{r}_{CA,SEB}\times (1-{r}_{TrCA,CA}^{2})}{{r}_{TrCA,CA}\times (1-{r}_{CA,SEB}^{2})}$$
(1)
According to a “discrimination hypothesis”, a positive association between SEB and achieved level of education is expected to persist when adjusting for cognitive ability [1, although they do not use the term “discrimination hypothesis”]. However, when adjusting for achieved level of education, the discrimination hypothesis predicts a negative association between SEB and cognitive ability, indicating that higher ability was required from those with lower SEB in order to achieve the same level of education as those with higher SEB. We propose the competing “residual confounding hypothesis”, which implies that any two of cognitive ability, SEB, and achieved level of education will be positively associated even when adjusting for the third, due to imperfect measurement. Furthermore, the discrimination hypothesis predicts that a difference score between achieved level of education and cognitive ability (both variables standardized) will be positively associated with SEB. This difference score is a measure of the degree to which participants are, in a manner of speaking, more educated than intelligent. The residual confounding hypothesis does not imply any association between the difference score and SEB.
Aims
This study aimed to investigate:
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whether the discrimination hypothesis or the residual confounding hypothesis is best supported by empirical data.
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whether, in the present case, reversing the predictors and outcomes yields a viable test of the logic of inference.
To the best of our knowledge, this is the first explicit investigation of the possibility that adjusted associations between SEB, cognitive ability, and achieved level of education may be due to residual confounding rather than discrimination.