The common sense and the null hypothesis!

“You don’t accept the null hypothesis. You could only fail to reject it!”

The essence of hypothesis testing lies in this statement.

When you get a p-value that exceeds the level of significance, it means your sample hasn’t provided enough evidence for you to reject the null hypothesis.

But it doesn’t necessarily mean there is enough evidence to accept that null hypothesis.

I know! Our common sense tells us that failing to reject something means accepting it, but common sense doesn’t always work in the world of statistics. (Else, why would people roam with dice in their pockets!)

Sometimes when we fail to get significant results, it might be because our sample is imperfect.

Our sample might not be a truly random one, or our sample might be too small to meet the assumptions of the central limit theorem.

No wonder we get p-values exceeding the significance levels in such cases, preventing us from rejecting the null hypothesis.

Our next logical step would be seeing how this data was sampled or collecting more data to find enough evidence to embrace the null hypothesis.

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