# failing to reject the null hypothesis when it is true.

This means that when the observed t-value exceeds the criticalt-value (i.e., the t-value marking that portion of the curvecontaining 5% of the area), the researcher will reject the nullhypothesis, but in doing so, he/she is taking up to a 5%chance of claiming a significant difference when none exists.

## The failure to reject does not imply the null hypothesis is true.

### 30/01/2013 · Fail to reject the null hypothesis ..

Below are copies of the objections they have lodged. As the designated authority, the Council has itself to decide whether to reject the application immediately, or allow it to proceed to a hearing. This could either be by way of a specially convened Commons and Village Green Registration Panel, or an independent Inquiry.

### fail to reject the null hypothesis or that we don't have ..

There are many applications where it is of interest to compare two independent groups with respect to their mean scores on a continuous outcome. Here we compare means between groups, but rather than generating an estimate of the difference, we will test whether the observed difference (increase, decrease or difference) is statistically significant or not. Remember, that hypothesis testing gives an assessment of statistical significance, whereas estimation gives an estimate of effect and both are important.

## If we fail to reject the null hypothesis, ..

We do not reject H_{0} because -0.96 > -2.145. We do not have statistically significant evidence at α=0.05 to show that the mean total cholesterol level is lower than the national mean in patients taking the new drug for 6 weeks. Again, because we failed to reject the null hypothesis we make a weaker concluding statement allowing for the possibility that we may have committed a Type II error (i.e., failed to reject H_{0} when in fact the drug is efficacious).

## Decide whether the null hypothesis should be rejected

Now instead of testing 1000 plant extracts, imagine that you are testing just one. If you are testing it to see if it kills beetle larvae, you know (based on everything you know about plant and beetle biology) there's a pretty good chance it will work, so you can be pretty sure that a *P* value less than 0.05 is a true positive. But if you are testing that one plant extract to see if it grows hair, which you know is very unlikely (based on everything you know about plants and hair), a *P* value less than 0.05 is almost certainly a false positive. In other words, *if you expect that the null hypothesis is probably true, a statistically significant result is probably a false positive.* This is sad; the most exciting, amazing, unexpected results in your experiments are probably just your data trying to make you jump to ridiculous conclusions. You should require a much lower *P* value to reject a null hypothesis that you think is probably true.