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In discussions of probability we often find ourselves saying that we can make an event more likely or less likely. It feels wordy, like there should be a single word for that. I don't mean "preclude" or "necessitate." I mean a change of probability that doesn't reach 0% or 100%. For example, we might say:

If we increase the sample size, we [decrease the probability of] certain kinds of error. If we decrease the sample size, we [increase the probability of] certain kinds of error.

What goes in that bracketed space? Not "rarify," which means something else; and not "preclude," which we can never seem to accomplish.

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    So you want a word for "the alteration of probability"? Or do you want one that specifies whether it is a decrease or it is an increase in probability? – Hank Mar 2 '17 at 20:04
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    Based on what you say in your question, this is simply "altering the probability", and many synonyms to "alter" would work as well. – Canis Lupus Mar 2 '17 at 20:08
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    Perhaps "inhibit". – StoneyB Mar 2 '17 at 20:09
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    If we increase the sample size, we reduce statistical error through smoothening. – Yosef Baskin Mar 2 '17 at 20:10
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    Yes, I will. The fact that after a few hours your have received multiple divergent answers is the first clue. The second clue is that you have not provided any feedback that would help bring those answers into focus on what you are requesting. Specific to your question, do you want something that describes "more less likely or less likely" (from your title), "more or less likely" (from your question), or "less likely" (from your example)? If you want to get a good answer, sometimes you will have to tend to your question or it will wither. – Canis Lupus Mar 3 '17 at 14:21
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A possibility is mitigate

Make (something bad) less severe, serious, or painful.

This doesn't apply in the general case of reducing probability, but when you're talking specifically about an adverse condition, reducing its probability also tends to reduce its severity, and I think I've seen the word used in contexts like your example.

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What about reduce? The Oxford Dictionary defines it as:

  1. Make smaller or less in amount, degree, or size.

If we want to be technical (of course we do) it doesn't explicitly carry the implication that it's less probable, just that it happens less, but this distinction is commonly glossed over.

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If we increase the sample size, we militate against certain kinds of error.

According to Cambridge Dictionary:

militate against sthg: to make something less likely to happen or succeed

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"If we increase the sample size, we minimise (reduce to the smallest possible amount, extent, or degree, OED) certain kinds of error.

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If we increase the sample size, we avert the occurrence certain kinds of error.

avert the occurrence: to keep from happening; prevent TFD

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The OED actually contains words for this:

disprobabilize, v.

rare
trans. To deprive of probability, render improbable.

probabilize, v.

trans. To make probable or likely.

probabilify, v.

Philos.
trans. To make probable, give probability to.

("disprobabilize, v.", "probabilize, v.", & "probabilify, v." OED Online. Oxford University Press, December 2016.)

Only the first is marked as rare(!), and the latter two (along with alternate spelling probablize) have all been updated with attestations into the 21st century.

So, for your example, you theoretically could say:

If we increase the sample size, we disprobabilize certain kinds of error. If we decrease the sample size, we probabilify/probabilize certain kinds of error.

To my ear, however, they all sound goofy enough to probablize you sounding like you made them up on the spot and disprobabilize a serious reception. The fact that such unwieldy words needed to be coined also probabilifies the absence of better alternatives.

  • I must say that this is my favorite response so far, for (and despite) all the reasons you give. But I'm afraid these words would probabilify a lot of giggling and confusion in class. – Chaim Mar 3 '17 at 18:41
  • @Chaim I completely agree. I hadn't heard of any of these until I went looking for an answer to your question, but now I am thinking I might occasionally sprinkle these in conversation and in my own classes, just for the pleasure of their "mouth feel"...and being able to follow up with "It's in the OED! Look it up!" – 1006a Mar 3 '17 at 18:59

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