Post Hoc, or Correlation Ain’t Causation

_{Jan 01 . 2010}

The name in Latin, post hoc ergo propter hoc, means “after this therefore because of this”. The fallacy is committed when it is assumed that because Y follows X that Y was caused by X. Also known as coincidental correlation. Correlation is not causation.

Examples

Spotify Loses $2 Billion as Stock Plummets After Neil Young’s Joe Rogan Protest
Antoinett Siu at The Wrap (January 29, 2022).

Spotify stock’s loss of value around the time of a public pressure campaign to censor Joe Rogan and his guests reflected a broader market dip.

A remarkable meteor was seen in the sky, and followed by a dreadful national calamity: a conjunction among the planets was followed by a royal marriage which issued in far-reaching consequences; and the superstitious conclude that one of the facts had some kind of causal connection with the other. We have outlived these weaknesses of past ages: but we have not outgrown the fallacies on which they proceeded. A country or college has prospered under a certain government or management, and some conclude that it was because of the government or management and oppose all projected improvements.
McCosh, The Laws of Discursive Thought, pp. 193-4.

For his 72nd birthday Wally received a cellular phone, and after three years of using it almost daily, he was diagnosed with brain cancer. Clearly, holding the phone so close to his head was responsible.
Carrick & Finsen, The Persuasive Pen, p. 196.

The standard example of the fallacy is the old Kentish peasant’s argument that Tenterden Steeple was the cause of Goodwin Sands. Sir Thomas More … had been sent down into Kent as a commissioner to inquire into the cause of the silting up of Sandwich Haven. Among those who came to his court was the oldest inhabitant, and thinking that he from his great age must at least have seen more than anybody else, More asked him what he had to say as to the cause of the sands. ‘Forsooth, sir,’ was the greybeard’s answer, ‘I am an old man: I think that Tenterden Steeple is the cause of Goodwin Sands. For I am an old man, and I may remember the building of Tenterden Steeple, and I may remember when there was no steeple at all there. And before that Tenterden Steeple was in building, there was no manner of speaking of any flats or sands that stopped the haven; and, therefore, I think that Tenterden Steeple is the cause of the destroying and decaying of Sandwich Haven.’
Minto, Logic: Inductive and Deductive, pp. 295-6.

The most vulgar form of this fallacy is that which is commonly called post hoc ergo propter hoc or cum hoc ergo propter hoc. As when it was inferred that England owed her industrial preeminence to her restrictions on commerce; as when the old school of financiers and some speculative writers maintained that the national debt was one of the causes of national prosperity; as when the excellence of the Church, of the Houses of Lords and Commons, of the procedure of the law courts, &c., were inferred from the mere fact that the country had prospered under them. In such cases as these, if it can be rendered probable by other evidence that the supposed causes have some tendency to produce the effect ascribed to them, the fact of its having been produced though only in one instance is of some value as a verification by specific experience; but in itself it goes scarcely any way at all towards establishing such a tendency since admitting the effect, a hundred other antecedents could show an equally strong title of that kind to be considered as the cause.
Mill, A System of Logic, 1900, p. 519.

A man indulges freely in wine at his club and wakes up the next morning with a splitting headache, and he attributes his indisposition to the intense mental application with which he has been prosecuting his business. The clouds are dispersed, and this is ascribed to the rising of the full moon. A man is irritable in the morning, and his relatives account for it by the fact that he got up on the left side of the bed.
Toohey, An Elementary Handbook of Logic, p. 191.

Critique

Show that the correlation is coincidental by showing that:

the effect would have occurred even if the cause did not occur, or
that the effect was caused by something other than the suggested cause. Most useful in dispelling the causal connection between two events is pointing to negative instances of the conjunction, that is, to instances when the supposed effect does not follow even though the supposed cause is present. This demonstrates that the supposed cause is at the very least not a sufficient cause of the effect.
Visit the spectacular website Spurious Correlations.

Commentary

It has been argued, in the same manner, that when two things are constantly observed to accompany one another, the one must depend upon the other. Thence, for ex. in natural science, classes have been formed from two properties which have been found to exist together in certain animals or plants; and it has been asserted that one must depend upon the other, and that therefore every object possessed of one must have both. Some time after, a new being has been discovered possessed of one of these properties and not of the other, and the whole theory falls to the ground. Nothing has contributed more to the overthrow of physiological systems, than the discovery of so man anomalous animals and plants in New Holland.
Bentham, Outline of a New System of Logic, pp. 254-5.

A common kind of covariation is one in which the relationship is real but it is not possible to be sure which of the variables is the cause and which the effect. In some of these instances cause and effect may change places from time to time or indeed both may be cause and effect at the same time. A correlation between income and ownership of stocks might be of that kind. The more money you make, the more stock you buy, and the more stock you buy, the more income you get; it is not accurate to say simply that one has produced the other.
Darrell Huff, How to Lie with Statistics (W. W. Norton & Company.), pp. 91-92.

So correlation alone is never enough to establish causation. Of course, in some cases, it is obvious which thing causes the other: the rising river doesn’t make it rain, and roosters don’t cause the sun to rise. But even in these cases, it isn’t the mere correlation of the events that tells us which is which. If all we knew about roosters and sunrises was that roosters crow at sunrise, we wouldn’t be able to say which caused which, or if something else caused them both to happen together, or if it were only a coincidence.
Gregory, A Crash Course in Logic, p. 22.

On the Enigmatic Notion of Causality…

It is not easy to offer an analysis of the fallacy of post hoc, because there is no widespread agreement on how to analyze the concept of causation. Consequently, no established theory of what, precisely, is wrong about post hoc reasoning can be offered at present.
Woods & Walton, Argument, p. 83.

On the difficulty of discerning causal connections…

False Cause, or Post hoc ergo propter hoc, is almost openly beyond the reach of Formal analysis. For it consists in asserting a causal connexion which is false, and mistaking a sequence for a consequence. But seeing that a mere sequence of events is all that we ever start from in our search for causal connexion (true or false), that ‘events,’ sequences, and ’causes’ are of all of them selections of our making, and that the risk of arguing from sequences to consequences has to be taken by all inferences good or bad, it is clear that no Formal criticism of this ‘fallacy’ is attainable. Before denouncing it logicians should have exhibited a little sympathy with the concrete difficulties of science, the history of which shows that the ‘true’ ’cause’ has been slowly discriminated from the ‘false’ only by its success. And rightly; for how was any one to tell a priori and merely from his prepossessions as to what were ‘true causes,’ and without long watching and experimentation and manifold mistakes, that there existed differences in the efficacy of ‘heavenly bodies’ so enormous that whereas the sun controlled all terrestrial processes, the moon affected only the tides, and the planets and the stars nothing at all (to speak of), and that therefore the influence of the moon on the weather and of the planets on individual lives were ‘false causes,’ and astrology was no a ‘science’ but a ‘superstition’? The ex post facto verdict of logic is merely an idle insult to the vanquished in the struggle for existence of scientific theories.
Schiller, Formal Logic, pp. 362-3.

On causal fallacies as a universal human proclivity…

The general name used to describe the first class of fallacies which are due to this particular form of mental sluggishness is post hoc, ergo propter hoc. Two events occur in close conjunction with each other, and it is then assumed without further investigation that they are related to each other as cause and effect. Many popular superstitions are examples of this fallacy. Some project begun on Friday turns.out disastrously, and it is inferred that some causal relation existed between the fate of the enterprise, and the day on which it was begun. Or thirteen persons sit down to dinner together, and some one dies before the year is out. It is to be noticed that such beliefs are supported by the tendency, to which we referred in the last section, to observe only the instances in which the supposed effect follows, and to neglect the negative cases, or cases of failure. ‘Fortune favours fools,’ we exclaim when we hear of any piece of good luck happening to any one not noted for his wisdom. But we fail to take account of the more usual fate of the weak-minded. The belief that the full moon in rising disperses the clouds, which was also quoted earlier, is a good example of post hoc, propter hoc. … The tendency to neglect negative instances was given by Bacon as the most striking example of the ‘ Idols of the Tribe’ (Idola tribus), i.e. of the species of fallacies to which the whole tribe or race of men are subject.
Creighton, An Introductory Logic, p. 310.