Hypothesis Testing Using Test Statistics or Using Probabilities
There are two ways we can conduct a hypothesis test. Iwill illustrate with an example from the normal distribution assuminga two tailed test.
Using a Test Statistic
We have a null distributionanda single observationWe findSupposewe are conducting a 5% test. We find a test statistic andcorresponding to 5% – assuming a two tailed test - bycalculatingandlooking up the corresponding value ofinthe normal distribution table, we findIfthe value of z we found usingisbigger than this we reject the null hypothesis.
Using a Probability
We have a null distributionanda single observationWe findSupposewe are conducting a 5% test. Everything so far is as it was above.But now, instead of finding the test statistic corresponding to 5% -assuming a two tailed test – we use the calculated value of z tofind a probability. If the probability we find is less than 2.5%-sincewe are conducting a two tailed test - we reject the nullhypothesis.
Things to Remember
Big test statistic implies reject null hypothesis and small teststatistic implies do not reject null hypothesis.
Small probability implies reject null hypothesis and bigprobability implies do not reject null hypothesis.
The test statistic is related to the probability of the nullhypothesis being true – if the test statistic is large theprobability of the null hypothesis being true is small, so reject thenull hypothesis - if the test statistic is small the probability ofthe null hypothesis being true is large so do not reject the nullhypothesis.