This blog attempts to highlight one of the central conceptual issues facing the field of psychology today, which is the relation between the “individual” and the “aggregate.” The individual refers to the specific person, you, me, your spouse, your child, etc. The aggregate refers to a group, and especially group averages and statistical comparisons made based on those group averages. The central conceptual issue at hand can be phrased in terms of a question: what do aggregate data actually say, exactly, about specific individuals?
This question is central because much of mainstream psychology has adopted the assumption that one can simply apply aggregate truths to the individual. In other words, psychology essentially assumes that each individual (you, me, whomever) is explained by the “average” at the level of the aggregate. However, as has been spelled out in a series of powerful papers by Dr. Jim Lamiell, this assumption is seriously suspect.
Let’s begin by noting how common aggregate analyses are. They are everywhere when you look for them. That is, the design of much research goes something like this: Group A is compared with Group B on some variable, which could either be a natural category (e.g. gender) or a treatment intervention (e.g. cognitive behavior therapy compared with psychodynamic therapy). The dependent variable means and standard deviations of the two groups are reported, and a test of significance shows the difference between the means to be unlikely as the product of chance, upon which the claim is made that there is a general and lawful relationship between the group difference and the outcome difference. This procedure of inference is so common that it can be considered the way mainstream psychologists derive “truths” about their subject matter.
For clarity, let’s work with a specific example. Not long ago a popular Psychology Today blog reported on research that showed that fathers who had daughters showed a decrease in their support for traditional gender roles compared to fathers who had sons (and men without children). In one such study providing support for this claim, researchers analyzed gender attitudes in over two thousand men and women over time both before and after becoming a parent, and based on the data they gathered, they concluded that “having a daughter (vs. having a son) causes men to reduce their support for traditional gender roles, but a female child has no such effect among women” (Fitzgibbons & Malhotra, 2011, p. 209).
I recall noticing this finding when it was reported on PT because it did not resonate with me personally (although I was not particularly surprised that it was true at the level of the aggregate). A bit of background offers a context as to why. My first child, Sydney, is a daughter (now fifteen). What caught my attention is that I personally would be very surprised if MY attitudes toward gender roles were more traditional 17 years ago, prior to her birth. Why? Because fifteen to seventeen years ago I was on the tail end of my deep immersion in—and devoted commitment to—a strong feminist ideology. Although I still consider myself a feminist, I have “softened a bit” since that time regarding my knee-jerk reaction against any kind of gendered ideology. As a function of this personal history, although I would currently score very low on the scale the researchers used to measure traditional gender role ideology, I would likely have scored even lower prior to the birth of my daughter.
One interpretation of the facts above would be simply to say that I “am an exception to the rule” discovered by the researchers. After all, most men have not been deeply immersed in feminist ideology just prior to the birth of their first daughter, so my unique history then might have created conditions that resulted in the exception of the rule.
But this interpretation gives rise to the question of what exactly is the rule and to whom, exactly, does it apply? To answer this, let’s first take a look at the precise data the authors used to make the claim that when fathers have daughters it influences their ideas about gender. The authors report on the aggregate differences for the 1000+ men who took the measure before and after having a child. For men who had a girl, the mean pre-post difference on the scale was 0.65 of a point on the scale. So, the “rule” generated from the aggregate analysis is that for fathers having daughters, their self-reported endorsement of gendered roles decreases just over a half a point on the scale the authors used.
Yet finding an aggregate change of 0.65 of a point on this scale does NOT mean that all the men or even most of the men moved 0.65 of a point. Interestingly, we can KNOW that NONE of the men actually changed 0.65 of a point. Why? Because the scale is scored in whole numbers, thus the smallest difference that could be measured is a change of 1.0 point on the scale. This reality makes concrete a point that Dr. James Lamiell makes over and over in his writing, which is that aggregate differences DO NOT warrant claims to knowledge about all individuals within the aggregate. Indeed, what is found for the aggregate might actually represent something that applies to no one. He writes:
“But as far as we can justifiably claim to know on the basis of the statistical 'rule,' every single individual in the designated population could be an exception to the statistical 'rule.' In other words, the problem is not that the aggregate 'rule' won't apply to every one. The problem is that the aggregate rule cannot knowably be said to apply to any one. The rule quite literally applies to no one.”
In short, average differences between groups DO NOT necessarily reveal causal forces that apply uniformly to individuals. Indeed, the “average man,” who is supposedly revealed in aggregate differences, is essentially a mathematical fiction. Interestingly, this point has been known for a very long time. In 1867, the philosopher and mathematician Moritz Wilhelm Drobisch (1802-1896) wrote:
“It is only through a great failure of understanding [that] the mathematical fiction of an average man . . . [can] be elaborated as if all individuals . . . possess a real part of whatever obtains for this average person” (Drobisch, 1867, quoted in Porter,1986, p. 171).
Ultimately, exactly what aggregate results tell us and their implications for individuals is an extremely complicated issue, with many different angles and caveats. The most important take home point from this blog is to be reminded that one CANNOT glibly apply findings from the aggregate to the individual. It is a point that mainstream psychology has too long been in denial about.
References
Shafer, Emily Fitzgibbons and Neil Malhotra. 2011. "The effect of a child's sex on support for traditional gender roles." Social Forces 90:209-222.
Porter, T. M. (1986). The rise of statistical thinking 1892-1900. Princeton: Princeton University Press.
Recommended Readings by Jim Lamiell
Lamiell, J. T. (2003). Beyond individual and group differences: Human individuality, scientific psychology, and William Stern’s critical personalism. Thousand Oaks, CA: Sage Publications.
Lamiell, J. T. (2000). A periodic table of personality elements: The “Big Five” and trait “psychology” in critical perspective. Journal of Theoretical and Philosophical Psychology, 20, 1-24.
Lamiell, J. T. (1998). ‘Nomothetic and ‘idiographic’: Contrasting Windelband’s understanding with contemporary usage. Theory and Psychology, 8, 23-28
Lamiell, J. T. (1981). Toward an idiothetic psychology of personality. American Psychologist, 36, 276-289.