Paired t

Test of the Differences - Hypotheses

  

When you use the paired t-procedures, you are really trying to decide which of two opposing hypotheses seem to be true, based on your sample data:

·    H0 (the null hypothesis): That the mean of the differences in the population is equal to the chosen reference value (usually zero)

- or -

·    H1 (the alternative hypothesis): That the mean of the differences in the population is not equal to the chosen reference value. (By default, H1 is nondirectional. However, a directional hypothesis can be specified instead.)

Example Output

Paired T for Before - After

 

             N    Mean  StDev  SE Mean

Before      15  74.667  3.478    0.898

After       15  72.333  3.200    0.826

Difference  15   2.333  3.352    0.866

 

 

95% CI for mean difference: (0.477, 4.190)

T-Test of mean difference = 0 (vs ≠ 0): T-Value = 2.70  P-Value = 0.017

Interpretation

In the heart rate example, you have heart rates for a sample of people measured before and after an exercise program, and you want to know the following: Based on the sample data, is it likely that the heart rates both before and after the exercise program are the same? In other words, is the mean difference between before and after measurements equal to zero? Thus, your hypotheses are H0, the mean difference = 0, and H1, the mean difference ≠ 0.