I recently read this odd critique of statistics (the author calls it a critique of probability theory, but I think he doesn't understand the difference probability theory and statistics).


In this question, I'm concerned with this specific critique (I already asked another question about the remaining ones):

by hiding the causal factors of an event behind the abstraction of a “probability distribution” we deprive ourselves of the ability to identify when those causal factors change and our assumptions no longer hold (i.e. the distribution shifts). [..] For example, I may experiment with a coin and decide that it is fair when tossing it onto a wooden surface, only to discover later that the coin is magnetized and slightly biased towards heads on metallic surfaces

Isn't this backwards? Actually, statistics allowed us to understand a great deal about a physical system, without having to know the precise laws which determine the behavior of the system, similar to what happens in statistical mechanics. What am I missing here?

  • 4
    $\begingroup$ I don't think you are missing something here. It is an unusual proposition. $\endgroup$
    – usεr11852
    Apr 4 at 20:51

Mitch Gordon confesses that he doesn't exactly understand the role of probability theory in science and you should believe him. IMHO he gives adequate evidence of his confusion in the link.

If you think you may have a biased coin, a probability model for a fair coin is a hindrance to checking the coin for fairness only if you're too lazy to toss it repeatedly in an effort to find out. In fact, significant departure of the results from tossing the coin from the probability model for a fair coin would be how you would evaluate evidence that the coin might be biased.

For example, 489 Heads in 1000 tosses would not provide significant evidence of unfairness because there is about a 50:50 chance of getting a number of heads as or more different from the expected 500.

2*pbinom(489, 1000, .5)
[1] 0.50666

However, 459 heads in 1000 would provide statistically significant evidence near the 1% level either that the coin is not fair$-$or that the method of tossing is is flawed.

2*pbinom(459, 1000, .5)
[1] 0.01038813

You may find this link of interest. It mentions some thoughtful approaches to testing for randomness.

  • 2
    $\begingroup$ I like your answer overall (+1) and I agree with the general sentiment. I'd suggest a minor modification: instead than just linking to Persi Diaconis' interview, you could include a couple quotes which are particularly relevant to the topic. IMO, these two are: concerning the shaved dice, "You can't really do the physics of a bouncing, rolling solid on a rough surface," he says. "It's just too complicated." Concerning the coin flip, the message seems to be that to investigate "unrehearsed tosses -- by ordinary folk who flip coins with unpredictable speeds and heights and catch them at..." $\endgroup$
    – DeltaIV
    Apr 5 at 12:02
  • 2
    $\begingroup$ different angles -- would show that the outcome of the act was, in fact, random.", you need both physics and statistics. $\endgroup$
    – DeltaIV
    Apr 5 at 12:03

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