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

The probability of a type II error depends on the way the null hypothesis is false.

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.

A Type I error is committed when one accepts the null hypothesis when it is false.
On the other hand, since the null hypothesis is always rejected, the probability of failing to reject it when it is false is 0, that is, =0.

False Alarm Hypothesis of Food Allergy - News Medical

Having said that, there's one key concept from Bayesian statistics that is important for all users of statistics to understand. To illustrate it, imagine that you are testing extracts from 1000 different tropical plants, trying to find something that will kill beetle larvae. The reality (which you don't know) is that 500 of the extracts kill beetle larvae, and 500 don't. You do the 1000 experiments and do the 1000 frequentist statistical tests, and you use the traditional significance level of PPPP value, after all), so you have 25 false positives. So you end up with 525 plant extracts that gave you a P value less than 0.05. You'll have to do further experiments to figure out which are the 25 false positives and which are the 500 true positives, but that's not so bad, since you know that most of them will turn out to be true positives.

If, for example, the null hypothesis says two population means are equal, the alternative says the means are unequal.

Imran Nazar Hosein & his false Hypothesis - Home | …

The likelihood of a hypothesis being true or false moves up and down a 'ladder' as more and more experiments on the hypothesis are published. The probability that the scientific community considers the hypothesis to be true can become so high that researchers do not study the hypothesis any further - it will be taken for granted and perceived as a fact. The model shows that you have to publish a certain percentage of negative results (often 20-30 %) in order to ensure that hypotheses that are false do not end up being regarded as facts.

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False positives and false negatives - Wikipedia

The relative costs of false positives and false negatives, and thus the best P value to use, will be different for different experiments. If you are screening a bunch of potential sex-ratio-changing treatments and get a false positive, it wouldn't be a big deal; you'd just run a few more tests on that treatment until you were convinced the initial result was a false positive. The cost of a false negative, however, would be that you would miss out on a tremendously valuable discovery. You might therefore set your significance value to 0.10 or more for your initial tests. On the other hand, once your sex-ratio-changing treatment is undergoing final trials before being sold to farmers, a false positive could be very expensive; you'd want to be very confident that it really worked. Otherwise, if you sell the chicken farmers a sex-ratio treatment that turns out to not really work (it was a false positive), they'll sue the pants off of you. Therefore, you might want to set your significance level to 0.01, or even lower, for your final tests.