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# What is test statistic Why do you have to know the distribution of a test statistic?

Updated: 4/28/2022 Wiki User

10y ago

Suppose you have a theory about some random variable and you want to check if your theory is correct. You take some observations and summarise them using a test statistic. This may be their mean, maximum, a measure of spread - whatever. You want to check if the result that you got is consistent with your theory.

You face a problem, though. Because the variable has a random element to it, it is always possible that the result that you got was pure chance. So you work out what the probability distribution of that test statistics would be IF your theory (hypothesis) were true. You use this distribution and the value of your test statistic to decide how likely your result was if your hypothesis were true.

If that probability is very small, you conclude that your theory is not reasonable and you reject your hypothesis. Otherwise, you continue with the assumption that your theory is not unreasonable. Wiki User

10y ago   Earn +20 pts  