Longer hemlines are showing up in fashion designs for spring 2008, indicating that U.S. economic woes could worsen. ... [T]he hemline theory has proved correct at times. Hemlines were short in the Roaring Twenties but fell before the 1929 stock-market crash. In the '60s miniskirts were en vogue, and stocks rose. In the summer of 2006, designers showed short hems for spring, and in May the Standard & Poor's 500 Index hit a seven-year high.("Hemline Theory," Time 170 No. 13 (24 September 2007), 19.)
Unless some kind of causal mechanism is hypothesized and tested, several observations of similar conjunctions of events are insufficient evidence for prediction of future connections.
Normally, one would simply label a prediction based on the theory that shorter hemlines are a causal predictor of a better economy and longer hemlines are causally related to a poorer economy (as reflected in the performance of the U.S. stock market), as a case of the fallacy of false cause or non causa pro causa. In particular, as stated in the Time excerpt above, the fallacy would seem to be the more specific post hoc ergo propter hoc--the fallacy of arguing that one kind of event was caused by another kind of event merely because the second kind occurred after the first kind of event.
Yet, what is the precise distinction between an "accidental" constant conjunction of events and and an "empirically necessary" or causal connection between events? Supposing that there were no disconfirming instances of this observed conjunction, how many confirming instances of a change in hemlines and the relevant kinds of consequent stock market movement are sufficient to conclude that there is a causal connection between these kind of events?
On the one hand, first and foremost, the problem of event-description is paramount. Just as it is arguable that the various instances of changes in hemlines are not similar enough to describe these various instances of these events as the same kind of events, so likewise it is arguable that the various instances of changes in the stock market are not similar enough to describe those kinds of events as the same kind of events. But notice how, with a bit of effort, we could tailor our definitions to cover just those cases of hemline change and just those relevant stock market movements in such a way that there could be no logically-possible counterexamples. (For example, this is how Alexander Fleming in his famous paper described the discovery that penicillin is effective against penicillin-susceptible bacteria. If penicillin weren't so effective, then the bacteria would not have been penicillin-susceptible.)
These kinds of uses of the heuristic of affirming consequential results in a general statement are a common practice for hypothesis-generation by research scientists. In the case of hemline theories, if we were able to define hemline lengths and stock market movement in such a manner that these events were empirically or logically necessarily connected, then we would presumably not have a viable testable theory. If a future event conforming to our definitions were somehow to unexpectedly disconfirm our theory because of an error in formulation, then we could always revise the theory to exclude that event. Whenever the revision becomes patently viciously circular, the so-called causal theory would, in all good conscience, have to be abandoned.
On the other hand, presuming we could construct reasonably neutral definitions of our key terms of hemline lengths and stock market movements, then, of course, our first task would be to try to falsify the theory by using something like Mill's Methods.
But, again, suppose we were to find there are no disconfirming instances? Does the fact that hemline lengths and stock market movements belong to different categories of events, as stated in ordinary language, permit us to conclude causal irrelevancy? Although there surely are specific reasons based on the entrenchment of past language use for assuming there is no causal or necessary connection, that, in itself, does not allow us to conclude that a fallacy has occurred solely on that account. After all, proposed new theories, by their very nature, are not grounded in the ordinary implications of the use of the words themselves.
Assuming that we could select data to show there are no disconfirming instances, how then can we justify calling the hemline theory a case of post hoc ergo propter hoc? The answer has to do with the burden of proof. If we claim an argument is fallacious, we have not thereby proved the conclusion false--we have only claimed the conclusion does not follow from the proposed premises. Therefore, the fallacy of false cause, in this case, is accurately noted, because no cogent or testable causal mechanism is proposed to account for the conjunction of events.
This too-short analysis, of course, does not disprove the hemline theory from a statistical point of view. One can always theorize about the probabilities of coincidence. But that is a whole different subject.