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Noll hypothesis - Parenting Perfect

Update: The null hypothesis is quite often known to be false before observing the data. For instance a coin (being asymmetric) is almost certainly biased; the magnitude of this bias us undoubtedly negligible, but not precisely zero, which is what the H0 for the usual test of the bias of a coin asserts. If we observe a sufficiently large number of flips, we will eventually be able to detect this miniscule deviation from exact unbiasedness. It would be odd then to accept the "null hypothesis" in this case as we know before performing the test that it is certainly false. The test is certainly still useful though as we are generally interested in whether the coin is practically biased.

Definition of null hypothesis, from the Stat Trek dictionary of statistical terms and concepts

But on that page they seem to accept their null hypothesis no matter what the p-value is. So I'm really not understanding now when to accept or reject the null hypothesis.

The Null Hypothesis in Education is Hard to Disprove | …

Cauchy's Hypothesis or Noll's theorem ..

I would suggest that it is much better to say that we "fail to reject the null hypothesis", as there are at least two reasons we might not achieve a significant result: Firstly it may be because H0 is actually true, but it might also be the case that H0 is false, but we have not collected enough data to provide sufficient evidence against it. Consider the case where we are trying to determine whether a coin is biased (H0 being that the coin is fair). If we only observe 4 coin flips, the p-value can never be less than 0.05, even if the coin is so biased it has a head on both sides, so we will always "fail to reject the null hypothesis". Clearly in that case we wouldn't want to accept the null hypothesis as it isn't true. Ideally we should perform a power analysis to find out if we can reasonably expect to be able to reject the null hypothesis when it is false, however this isn't usually nearly as straightforward as performing the test itself, which is why it is usually neglected.

Null hypothesis (abbreviated H0): The assertion that any apparent effect you see in your data does not reflect any effect in the population, but is merely the result of random fluctuations in your sample.

Null hypothesis Flashcards | Quizlet

We find that the P-value is reported as 0.77, so we should hold the noll hypothesis U=23.0.

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the null hypothesis is thus formulated so that it can be tested for possible rejection
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