- “If our actions are caused by chance…” (source)
- “How can you tell whether this deviation was due to chance?” (source)
- “A difference among samples that is due to random variation (chance) is called sampling error.” (source)
- “In normal English, ‘significant’ means important, while in Statistics ‘significant’ means probably true (not due to chance).” (source)
- “Such alternative explanations may be due to the effects of chance (random error)…” (source
- “The difference between two groups is statistically significant if it can not be explained by chance alone.” (source)
- “A significance test will help us decide if the observed difference between two sample proportions is the result of pure chance…” (source)
We needn’t continue; the gist is clear.
Chance is not a cause; it is not a physical thing; it cannot be operative; it is not a measurable property. If you think it is, I challenge you to collect a bucket of it and bring it our way. If that is too much to carry, make it a thimbleful. Or tell us how it can be seen, felt, heard, smelt (yes, smelt), or touched. Or show us just how, by what precise mechanism, the property of chance carries out its nefarious duties.
Saying events are “due to chance” is a holdover from the days when if a cause was unknown it was ascribed to fairies, pixies, or spirits. It’s the same now, except that chance is sort of vague mystical entity, a dangerous creature not to be stared at, nor sought. Its presence can be felt; it is just as real as any vaporous apparition, and as vexing as a poltergeist. Chance is always destructive of knowledge in a demonically playful way, operating always behind a cloak. It never sleeps.
It’s true that the old (and not yet deceased) frequentist view of probability requires chance (or Chance) to be real; probability is (somehow) created in the wake of Chance. Chance is the being, to a frequentist, which fiddles with the coin as it is spinning, causing it to land heads. Busy man, Chance. Think of all those quarks it has to spin.
But even Bayesians who should know better use the same words. A guess is that this is so because Bayesians were first trained as frequentists and that it is difficult to leave behind fully a bad upbringing. If true, the solution is to eschew frequentist training—which should be done in any case.
What is real definition of chance? Since probability (also not real) is just a measure of uncertainty, chance is a synonym for unknown cause. Try it in the sentences above and you’ll see that they usually become tautological or nonsensical.
“How can you tell whether this deviation was caused by something unknown?” Well, it’s when we don’t know what the cause was. “The difference between two groups is statistically significant if it can not be explained by a cause we don’t know about.” Say that three times fast. “A difference among samples that is due to an unknown cause is called sampling error.” This one works, except for the unfortunate word error, which implies a mistake has been made.
Chance always means “I don’t know how that happened.” This does not imply that somebody doesn’t know why it happened, thought that could be true sometimes (e.g. quantum effects). Coin flips are great examples. Most times the initial conditions are of such complexity that predicting the outcome is too difficult, especially for most civilians. But the measurements can be done. The same flip which for one man is “random”, i.e. “caused by chance”, i.e. “caused by he knows not what”, is for the next man perfectly predictable.
Incidentally, my favorite bad example in today’s list is the one which begins “In normal English…” signaling that in statistics we will be using abnormal language. Too true. The unintentional additional hilarity of getting the (frequentist) theory wrong, I leave you to work out for yourself.
Update In comments some expressed a habit of saying “by chance”. Break it. To say a thing comes to be (known) by something is to say it either caused by it, or is part of the cause of it. Webster by: “With, as means, way, process, etc.; through means of; with aid of; through; through the act or agency of” Chance.
If pressed for a cause, admit ignorance up to the point of probability and then say, “But my uncertainty in the thing is expressed by this & such probability.”
Example 1: Something caused the coin to land heads; I don’t enough to say what; but given the evidence we discussed, the probability of a heads is 1/2.
Example 2: Something caused the observed minor differences between patient groups; I don’t know what; but given the evidence of the study, the probability of a difference is only 1/2.