If we fail to reject (i.e., \"accept\") the null hypothesis, does this mean that

Question

If we fail to reject (i.e., "accept") the null hypothesis, does this mean that we have proved it to be true beyond alt doubt? Explain your answer Yes, if we fail to reject the null we have found evidence that the null is true beyond all doubt. Yes, it suggests that the evidence is sufficient to merit rejecting the alternative hypothesis beyond all doubt. No, it suggests that the evidence is not sufficient to merit rejecting the null hypothesis. No, it suggests that the null hypothesis is true only some of the time.

Explanation / Answer

Null hypothesis are never accepted. We either reject them or fail to reject them. The distinction between “acceptance” and “failure to reject” is best understood in terms of confidence intervals. Failing to reject a hypothesis means a confidence interval contains a value of “no difference”. However, the data may also be consistent with differences of practical importance. Hence, failing to reject H0 does not mean that we have shown that there is no difference (accept H0).

If we don’t reject the null hypothesis, we don’t conclude that it’s true. We simply recognize that the null hypothesis is a possibility (it’s something that we could observe).

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