As title states, why is not rejecting null hypothesis not equivalent to accepting it? I can't find any information about a 'state' other than accepting or rejecting null hypothesis.
2026-04-01 13:40:21.1775050821
Not rejecting null hypothesis not equivalent to accepting it
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1
There are three states an hypothesis can be in: accepted, rejected, or not concluded.
Before we do an experiment and analyze the data, we can't conclude anything about the null hypothesis. Then after we do the experiment and the statistics, if the results are far away from what the null hypothesis would imply, we say we reject the null hypothesis.
However, if the analysis reveals that the result was rather close to what the null hypothesis predicts, then we can't reject it. However, this does not mean we immediately accept it. It could be that the null hypothesis is wrong, but that the true solution is too close to the null hypothesis for our experiment to distinguish.
This is how failing to reject the null hypothesis does not mean accepting it. It just means we can't conclude.