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 Statistical hypothesis testing

Much of statistical reasoning was developed in the context of quality control where you need a definite yes or no answer from every analysis. Do you accept or reject the batch? The logic used to obtain the answer is called hypothesis testing.

First, define a threshold P value before you do the experiment. Ideally, you should set this value based on the relative consequences of missing a true difference or falsely finding a difference. In practice, the threshold value (called alpha) is almost always set to 0.05 (an arbitrary value that has been widely adopted).

Next, define the null hypothesis. If you are comparing two means, the null hypothesis is that the two populations have the same mean. When analyzing an experiment, the null hypothesis is usually the opposite of the experimental hypothesis. Your experimental hypothesis -- the reason you did the experiment -- is that the treatment changes the mean. The null hypothesis is that two populations have the same mean (or that the treatment has no effect).

Now, perform the appropriate statistical test to compute the P value.

If the P value is less than the threshold, state that you “reject the null hypothesis” and that the difference is “statistically significant”.

If the P value is greater than the threshold, state that you “do not reject the null hypothesis” and that the difference is “not statistically significant”. You cannot conclude that the null hypothesis is true. All you can do is conclude that you don't have sufficient evidence to reject the null hypothesis.