Any dependent variable of interest, such as I.Q., or academic achievement, or perceptual speed, or emotional reactivity as measured by skin resistance, or whatever, depends mainly upon a finite number of “strong” variables characteristic of the organisms studied (embodying the accumulated results of their genetic makeup and their learning histories) plus the influences manipulated by the experimenter. Upon some complicated, unknown mathematical function of this finite list of “important” determiners is then superimposed an indefinitely large number of essentially “random” factors which contribute to the intragroup variation and therefore boost the error term of the statistical significance test. In order for two groups which differ in some identified properties (such as social class, intelligence, diagnosis, racial or religious background) to differ not at all in the “output” variable of interest, it would be necessary that all determiners of the output variable have precisely the same average values in both groups, or else that their values should differ by a pattern of amounts of difference which precisely counterbalance one another to yield a net difference of zero. Now our general background knowledge in the social sciences, or, for that matter, even “common sense” considerations, makes such an exact equality of all determining variables, or a precise “accidental” counterbalanceing of them, so extremely unlikely that no psychologist or statistician would assign more than a negligibly small probability to such a state of affairs. Example: Suppose we are studying a simple perceptual-verbal task like rate of color-naming in school children, and the independent variable is father’s religious preference. Superficial consideration might suggest that these two variables would not be related, but a little thought leads one to conclude that they will almost certainly be related by some amount, however small. Consider, for instance, that a child’s reaction to any sort of school-context task will be to some extent dependent upon his social class, since the desire to please academic personnel and the desire to achieve at a performance (just because it is a task, regardless of its intrinsic interest) are both related to the kinds of sub-cultural and personality traits in the parents that lead to upward mobility, economic success, the gaining of further education, and the like. Again, since there is known to be a sex difference in colornaming, it is likely that fathers who have entered occupations more attractive to “feminine” males will (on the average) provide a somewhat more feminine fatherfigure for identification on the part of their male offspring, and that a more refined color vocabulary, making closer discriminations between similar hues, will be characteristic of the ordinary language of such a household. Further, it is known that there is a correlation between a child’s general intelligence and its father’s occupation, and of course there will be some relation, even though it may be small, between a child’s general intelligence and his color vocabulary, arising from the fact that vocabulary in general is heavily saturated with the general intelligence factor. Since religious preference is a correlate of social class, all of these social class factors, as well as the intelligence variable, would tend to influence color-naming performance. Or consider a more extreme and faint kind of relationship. It is quite conceivable that a child who belongs to a more liturgical religious denomination would be somewhat more color-oriented than a child for whom bright colors were not associated with the religious life. Everyone familiar with psychological research knows that numerous “puzzling, unexpected” correlations pop up all the time, and that it requires only a moderate amount of motivation-plus-ingenuity to construct very plausible alternative theoretical explanations for them. These armchair considerations are borne out by the finding that in psychological and sociological investigations involving very large numbers of subjects, it is regularly found that almost all correlations or differences between means are statistically significant.
In other words, for similar sorts of reasons we can expect in advance that men and women are not equally good at writing comic books, that Lutherans and Episcopalians are not equally likely to become judges, and that when they do, they are not likely to do equally well, and so on. It will be similar with any such random associations.