when accept a false null hypothesis is called

when accept a false null hypothesis is called

There is no probability that the null hypothesis is true or false because there is no element of chance. For instance, if you are investigating whether a potential mine has a gold concentration greater than that of a break-even mine, the null hypothesis that your potential mine has a gold concentration no greater than that of a break-even mine is either true or false; you simply do not know which. Because the gold is already in the ground, there is no probability associated with these two cases (in a frequentist sense), and consequently, there is no chance because everything is already determined. Only our own uncertainty about the null hypothesis remains.

null hypothesis

This lack of knowledge about the null hypothesis is why we need to conduct a statistical test: we wish to draw conclusions about the null hypothesis using our data. Specifically, we must determine whether we will act as though the null hypothesis is true or false. Based on the results of our hypothesis test, we will either embrace or reject the null hypothesis. If we adopt the null hypothesis, we assert that our data are consistent with it, recognizing that other hypotheses may also be consistent with the data. When we reject the null hypothesis, we assert that our data are so unexpected that they contradict the null hypothesis.

Our decision will alter our conduct. If we reject the null hypothesis, we will act as if it is false, despite the fact that we do not know whether this is the case. If we adopt the null hypothesis, we will act as if it is true, despite the fact that we have not demonstrated its veracity. It is impossible to determine whether the null hypothesis is true or false, regardless of the outcome of our statistical test. In other words, we do not and will never prove or disprove null hypotheses; we never demonstrate that they are true or false.

We operate in a world where hypotheses are either true or false, but we cannot determine which. We want to conduct statistical tests that enable us to make decisions (accept or reject), and we want these decisions to be accurate.

There are four potential scenarios, as there are two possibilities for the null hypothesis (true or false) and two for our decision (accept or reject). Accepting a true null hypothesis and rejecting a false null hypothesis are the two correct decisions. The other two instances are incorrect. A type I error is committed if we reject a genuine null hypothesis. Accepting a false null hypothesis constitutes a type II fallacy.