Philosophers of science have argued that descriptions of statistical correlations or differences in correlations do not explain anything. We will see that they are no proof of discriminational relevance either. Two examples should show immediately why discriminational relevance cannot be proved by means of a statistical correlation:
(a)  a correlation between gender and physical strength
Let us assume that (on the average) men are stronger, maybe even much stronger, than women. And let us assume that a certain type of work is much better done by a strong body (a physically strong person) than by a weak body. It will be true, then, that on the average men do or will do the work better than women. Nonetheless, the factor gender is not relevant at all in respect of the quality of the work to be performed: the factor physical strength is, and this determinant only happens to be correlated with the factor gender. To maintain that it would be relevant to distinguish people on the basis of sex with regard to this kind of job is but too familiar a case of fuzzing the factorial picture again.
(b)  a correlation between race and intelligence
Let us assume that (on the average) members of race A are more intelligent than members of race B. And furthermore, that a certain kind of work can only be done well by intelligent people, and that more intelligent people will do the job better. It is true, then, that on the average members of race A will do a better job than members of race B. But --'truth is no excuse for irrelevance'-- this does by no means prove that it would be relevant to distinguish applicants for the position vacant who belong to race A from those who belong to race B. The factor intelligence is (believed to be) relevant as a factor of distinction and this factor would only happen to be correlated with the factor race (so far as races A and B are concerned). (As has been said before: "whatever the cause of difference in average IQs, it provides no justification for racial segregation in education or any other field". )

Both examples clearly have two different aspects:
(1)  What is the relevant factor of distinction? A factor correlated herewith is not (discriminationally) relevant for being correlated with it -- as outlined above.
(2)  Is a group average relevant or individual value? A full-time post is filled with one person only, and therefore it is solely individual value that counts, whether it be the person's strength in the first example or 'er intelligence in the second one. Only individual discrimination on the basis of physical strength and intelligence respectively would be relevant in these instances; categorical discrimination founded on whatever factor would be irrelevant, when the focus is not so much the quality of work to be done in general, but to be done by one particular person in one particular position.

It is evident that where group averages are not relevant --as in the examples above-- they are still indicators of the chance that the relevant quality may be found in the individual concerned. When considering a male applicant for the first position mentioned above, the chance that he will be strong enough to do the work is bigger than when considering a female applicant (granted that our statistics are correct). Yet, this modal condition is not discriminationally relevant in itself --only the applicant's actual physical strength is. In fact, a particular male applicant may be weaker than a particular female one. That is why we shall call taking this chance itself as discriminationally relevant "a judgment of pseudofactual relevance".

Whereas statistics cannot prove discriminational relevance, it can prove discriminational irrelevance. A factor does not derive its relevance from a contingent correlation with another factor which is relevant, but if a factor is (believed to be) relevant, there must be a connection between this factor and the variable of the focus. This is so, because a relevant factor must make a difference to the occurrence of an event, or to the probability of that occurrence. However, to move from this true proposition to the belief that a factor is relevant, if there is a difference in occurrence, is even invalid in standard non-relevancy or nonrelatedness logics. Putting it informally: the fact that there is a difference is no proof that the factor concerned makes it, but if the factor concerned makes it, it must be there (if not instantaneously, then shortly after). Therefore relevant is what makes a difference with respect to a certain focus. (The reason why this definition is rather meager is simply that it must hold independently of the kind of determinants chosen.)

Any doxastic relevance can be disproved by showing that there is no difference, especially no difference in statistical correlations. This is why 'statistical relevance' is only an index of the possibility of discriminational relevance with regard to classes. If a factor is statistically irrelevant, it must also be discriminationally irrelevant, but if it is statistically relevant, it need not be discriminationally relevant. The possibility of discriminational relevancy is no actual discriminational relevancy in itself. Therefore it is not less pseudofactual than the chance of relevance, when that is mistakenly believed to be factually relevant with regard to the focus at issue.

When we say that a certain factor 'makes' a difference in respect of a certain goal and is therefore relevant, we distinguish this making from mere being or becoming. Thus, making in this sense must not be confused with producing as generally used in consequentialist considerations. A particular rule might 'produce' more gains or happiness, for instance, than losses or unhappiness for the population concerned. If so, then a (rule-)utilitarian would have to recommend that rule. But this rule might be that no-one of group G is to be allowed in certain types of public places or to attend certain kinds of official functions. (Group G may consist of, say, disabled individuals or homosexual couples.) Especially if people of group G are in the minority this might 'benefit' the majority of the population, because they would have more room available, and maybe, because they are so biased that they do not feel comfortable in the presence of such people. On this assumption the loss of freedom (and happiness) of the minority in question would on balance be outweighed by the 'gains' for the majority, and this means that such a rule would be justifiable on rule-utilitarian grounds.

But would the introduction of the rule only correspond to a difference (an increase) in utility, or would it also make this difference? If the statistics are correct, there would indeed be a correlation, namely that diminishing the number of people of group G in places of type T would increase the total utility. Yet, such a correlation does in no way demonstrate the discriminational relevance of the distinction between people belonging and not belonging to group G, even not, or particularly not, with respect to the factor utility or happiness. To make it plausible that the factor in question (such as disability or sexual preference) would be discriminationally relevant, it must at least be demonstrated too that there is a special explanatory link between this factor and happiness itself. No doubt, a majority will have more room available by excluding a minority, but this has nothing to do with the factor on the basis of which a smaller group of people or bodies is separated from a larger group of people or bodies. Any factor differentiating a smaller and a larger group would 'produce' this result. (Take, for example, all people heavier than a certain maximum weight, or all people lighter than a certain minimum weight.) That is why a utilitarian or other consequentialist who speaks of "producing" or "bringing about a certain difference" does not necessarily refer to 'making a difference' in the relevant(ist) sense. As mentioned in the previous division (section 5.3.5) this requires an additional principle or criterion of relevance.

It may be that a rule which excludes, for example, a certain minority from certain places would increase the total utility in a social system, because the majority of the people do not like the members of that minority, and feel happier when they are not around. In such a case it does seem that there is an explanatory link between the factor on the basis of which the minority is distinguished and the factor happiness by way of most people's attitudes towards the members of that minority. If these attitudes did indeed make the difference here, the relevance of the factor on the basis of which the minority is distinguished would not be pseudofactual. But the question is now whether these very attitudes themselves do not depend on nonrelevance (and/or false belief). If they are biased, they certainly do.