THE HYPOTHESIS-TESTING PROCESS

In the previous example, we used a statistical technique called the t test to test the hypothesis that two groups have the same mean in the population. We did the following:

• For each of the groups, we calculated the mean of the variable we were interested in comparing.

• We subtracted one mean from the other to determine the difference between the two.

• We calculated a t statistic by dividing the difference of the two sample means by its standard error.

• We calculated the observed significance level. This told us how often we would expect to see a difference as large as the one we observed if no difference existed between the groups in the population.

• If the observed significance level was small (less than .05), we rejected the hypothesis that the two means are equal in the population.

• Otherwise, we did not reject the null hypothesis, and we did not accept it either. We remained undecided. That is because we did not know whether no difference was present or whether our sample was simply too small to detect the difference.

This procedure is the same for tests of most hypotheses:

• You formulate a null hypothesis and its alternative.

• You calculate the probability of observing a difference of a particular magnitude in the sample when the null hypothesis is true.

• If this probability (the observed significance level) is small enough, you reject the null hypothesis.

• If the probability is not small enough, you remain undecided.

The only part of this ritual that changes for different situations is the actual statistic used to evaluate the probability of the observed difference. In the chapters that follow, we will use different types of statistics to test hypotheses that have these characteristics:

• Variables are independent.

• Several groups have the same means.

• No linear relationship exists among several variables.

If you make sure now that you understand the way hypothesis testing works, the rest of this book will be easy to understand.