Such a comparison would be a dependent or related comparison, in that we have the same individuals but different conditions between the first and second sampling period. Both types of comparisons involve the t-test of population means. What we assume in this test is that the two samples are random samples, and that the difference between the two means is normally distributed. These hypotheses I have given you are for the two-tailed test. Calculating the test statistic If repeated sample means from a population have a t distribution, then it follows that the difference between repeated pairs of sample means taken from a population , or from two population means, have a t distribution.
Example Let s continue the example of lithium levels in psychiatric patients.
Suppose we have a sample of both male and female patients. Comparing the critical value to the table value, we find that the critical is less than the table, therefore we cannot reject the null hypothesis, and conclude that there is no difference in the mean weight of cranberries from the two bogs. B. Dependent sample Recall that the null hypothesis for the paired test is that the average difference among the pairs is that the average difference among the pairs is equal to zero. To calculate the average difference, we must first calculate the difference for each value in the sample. For example, when determining whether or not MCAT scores differed between an April and an August test for students who had taken the Kaplan test prep in between, we would have to determine the difference in MCAT score for each student between the two dates.