Is a p-value could be equal to zero (0)?

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Expert Solution

It will be the case that if you observed a sample that's impossible under the null (and if the statistic is able to detect that), you can get a p-value of exactly zero.

That can happen in real world problems. For example, if you do an Anderson-Darling test of goodness of fit of data to a standard uniform with some data outside that range - e.g. where your sample is (0.430, 0.712, 0.885, 1.08) - the p-value is actually zero (but a Kolmogorov-Smirnov test by contrast would give a p-value that isn't zero, even though we can rule it out by inspection).

Likelihood ratio tests will likewise give a p-value of zero if the sample is not possible under the null

The interpretation of small p-values varies by context.Fisher (1925) himself said there was

‘‘No practical importance whether p is .01 or .000001’’ (p. 89) and in the contexts he worked (and I work) this is true. However, if you are in some branches of physics different criteria are used for discoveries and there is some discussion in other disciplines implementing some of the thresholds used in physics. So, my "answer" is that it would be worth knowing the context to provide more useful answers. If you were announcing the discovery of the Higgs boson you would do something different than if you happiness correlated with the weather.

ThankYou for the question. Glad to help you.

orchestra answered 1 year ago

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