# the null hypothesis is not rejected when it is false c.

A false negative is where **a negative test result is wrong**. In other words, you get a negative test result, but you *should* have got a positive test result. For example, you might take a pregnancy test and it comes back as negative (not pregnant). However, you are in fact, pregnant. The false negative with a pregnancy test could be due to taking the test too early, using diluted urine, or checking the results too soon. Just about every medical test comes with the risk of a false negative. For example, a test for cancer might come back negative, when in reality you actually have the disease. False negatives can also happen in other areas, like:

## the research hypothesis is not rejected when it is false722-1

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

Here are three experiments to illustrate when the different approaches to statistics are appropriate. In the first experiment, you are testing a plant extract on rabbits to see if it will lower their blood pressure. You already know that the plant extract is a diuretic (makes the rabbits pee more) and you already know that diuretics tend to lower blood pressure, so you think there's a good chance it will work. If it does work, you'll do more low-cost animal tests on it before you do expensive, potentially risky human trials. Your prior expectation is that the null hypothesis (that the plant extract has no effect) has a good chance of being false, and the cost of a false positive is fairly low. So you should do frequentist hypothesis testing, with a significance level of 0.05.

### rejecting the null hypothesis when it is false.

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.