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I read that the p-value is the likelihood that a number is equal to or greater than the actual observed number if the null hypothesis is correct 1 . I understand the null hypothesis means that there’s no statistical significance in a set of observations 2, and that statistical significance means that a set of observed data is due to a cause not by chance 3.

  1. Going back to the definition of the p-value above, is the p-value a number that represents the likelihood that a number is at least the actual observed number if the number is due to a cause and not due to chance?
  2. If my understanding of p-value is correct, doesn’t this mean that the p-value can overestimate a number, since it represents the likelihood a number is equal to or greater than the actual observed number if the null hypothesis is correct?
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    $\begingroup$ P-values are complicated and hard to understand. None of the three statements in your opening paragraph are correct. Your first question makes no sense as it seems to give two (unstated) definitions to "number". Same with the second question. Given this ambiguity and the presence of other simiilar questions, I voted to close. $\endgroup$
    – Harvey Motulsky
    Commented Jul 30 at 1:55

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  1. Your characterization of the p value is incorrect. For a two sided test, the correct interpretation of the p value is as follows:

The p value represents the probability of observing a test statistic at least as large in absolute value as the one we computed from these data, assuming the null hypothesis is true and all assumptions are also true.

The p value says nothing about causation and nothing about observing an effect due to chance.

  1. All estimates have error, but a p value does no tell you anything about the possible error in an estimate.
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  • $\begingroup$ Thanks. I replaced my source from investopedia to wikipedia and added an answer that i believe shows an accurate understanding of p value and null hypothesis. If the p-value represents the probability of a value being at least the actual observed value, doesn't that mean that the probability of an underestimate isn't taken into account, since the p-value only considers overestimates? $\endgroup$
    – bit
    Commented Jul 29 at 23:31
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The p-value is the probability of an extreme result, under the assumption that the null hypothesis is correct 1. A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis 1. So lower p-values are better (i.e. more accurate).

Null hypothesis, in other words, wrong hypothesis is the claim that the effect being studied does not exist (but if it does, the effect exists by chance). For example, it might state that a treatment has no effect or that two groups do not differ in a certain characteristic.

The null hypothesis can also be described as the hypothesis in which no relationship exists between two sets of data or variables being analyzed. If the null hypothesis is true, any experimentally observed effect (i.e. effect from cause and effect) is due to chance alone, hence the term "null" 2.

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  • $\begingroup$ Because all but the first two statements in this post are questionable (at best), reviewing the duplicate thread should be helpful. $\endgroup$
    – whuber ♦
    Commented Jul 30 at 13:39

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