Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

<-- Previous | Newer --> | Current: 983456888 Dick Beldin at Thu, 01 Mar 2001 14:28:08 +0000.

# Testing_Hypotheses

```back to [[Statistical Theory]] -- [[Applied Statistics]]

Many researchers wish to test a '''statistical hypothesis''' with their data. There are several prerequisites which should be accomplished before the data is at hand.
#The hypothesis must be stated in mathematical/statistical terms that make it possible to calculate the probability of possible sample assuming the hypothesis is correct. For example, ''The mean response to treatment being tested is equal to the mean response to the placebo in the control group. Both response have the [[Normal Distribution]] with the unknown means and the same known [[Standard Deviation]].''
#A test [[Statistic]] must be chosen that will summarize the information in the sample that is relevant to the hypothesis. In the example given above, it might be the numerical difference between the two sample means.
#The distribution of the test statistic is used to calculate the probability sets of possible values (usually an interval or union of intervals). In this example, the difference between sample means would have a normal distribution with a standard deviation equal to the common standard deviation times the factor '''1/sqrt(n1) + 1/sqrt(n2)''' where n1 and n2 are the sample sizes.
#Among all the sets of possible values, we must choose one that we think represents the most extreme evidence '''against''' the hypothesis. That is called the '''critical region''' of the test statistic. The probability of the test statistic falling in the critical region when the hypothesis is correct is called the '''alpha''' value (or '''size''') of the test.
#After the data is available, the test statistic is calculated and we determine whether it is inside the critical region.
#If the test statistic is inside the critical region, then our conclusion is either
*The hypothesis is incorrect ''or''
*An event of probability less than or equal to ''alpha'' has occurred.

----
[[Dick Beldin]]
```