Why the null hypothesis (Ho) should never be ‘accepted’?

People may have some level of difficulty in making inferences using hypothesis testing.

Let me put forth a common mistake that we do while making conclusions.

We know that when the p-value is less than the level of significance (α), we reject the null hypothesis. Commonly we take α as 0.05. So when p< 0.05, we reject the null hypothesis.

But, when the p> 0.05 we can not reject the null hypothesis.

At this point, many of us tend to say that ‘we accept the null hypothesis‘ and this statement is not correct.

Reason:

We make conclusions about the population based on a random chance that could say that Ho is true. But this random chance is at the chosen level of α. There is a possibility that some other randomly chosen sample gives a different conclusion at a different level of significance.

Thus, when p> α, we fail to reject Ho

When p is greater than α we should write the results in neutral language. For example,

Ho: Machine 1 is producing spindles with average length of 30 cm

Ha: Machine 1 is not producing spindles with average length of 30 cm

If p< 0.05, At the significance level of 0.05, we reject the null hypothesis that machine 1 is producing spindles with an average length of 30 cm. This also means that we accept (and not prove) the alternate hypothesis,  a nice explanation can be found here for this case.

When p> 0.05, at the significance level of 0.05, we can not reject the null hypothesis that machine 1 is producing spindles with an average length of 30 cm.

This simply means that at a significance level of 0.05, we can not conclude whether the machine is producing an average length of 30 cm or not.

So, we should always keep in mind that when we are not able to reject the null hypothesis, we should not conclude in any other way but in a neutral manner.

Do share in comments, your experience and other mistakes that you may have once committed/ witnessed.

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