Example of Paired tmain topic interpreting results session command see also
Example of Paired tA shoe company wants to compare two materials, A and B, for use on the soles of boys' shoes. In this example, each of ten boys in a study wore a special pair of shoes with the sole of one shoe made from Material A and the sole on the other shoe made from Material B. The sole types were randomly assigned to account for systematic differences in wear between the left and right foot. After three months, the shoes are measured for wear.
For these data, you would use a paired design rather than an unpaired design. A paired t-procedure would probably have a smaller error term than the corresponding unpaired procedure because it removes variability that is due to differences between the pairs. For example, one boy may live in the city and walk on pavement most of the day, while another boy may live in the country and spend much of his day on unpaved surfaces.
1 Open the worksheet EXH_STAT.MTW.
2 Choose Stat > Basic Statistics > Paired t.
3 Choose Each sample is in a column.
4 In Sample 1, enter Mat-A. In Sample 2, enter Mat-B. Click OK.
Session window output
Paired T-Test and CI: Mat-A, Mat-B
Paired T for Mat-A - Mat-B
N Mean StDev SE Mean Mat-A 10 10.630 2.451 0.775 Mat-B 10 11.040 2.518 0.796 Difference 10 -0.410 0.387 0.122
95% CI for mean difference: (-0.687, -0.133) T-Test of mean difference = 0 (vs ≠ 0): T-Value = -3.35 P-Value = 0.009 |
The confidence interval for the mean difference between the two materials does not include zero, which suggests a difference between them. The small p-value (p = 0.009) further suggests that the data are inconsistent with H0: m d = 0, that is, the two materials do not perform equally. Specifically, Material B (mean = 11.04) performed better than Material A (mean = 10.63) in terms of wear over the three month test period.
Compare the results from the paired procedure with those from an unpaired, two-sample t-test (Stat > Basic Statistics > 2-Sample t). The results of the paired procedure led us to believe that the data are not consistent with H0 (t = -3.35; p = 0.009). The results of the unpaired procedure (not shown) are quite different, however. An unpaired t-test results in a t-value of -0.37, and a p-value of 0.72. Based on such results, we would fail to reject the null hypothesis and would conclude that there is no difference in the performance of the two materials.
In the unpaired procedure, the large amount of variance in shoe wear between boys (average wear for one boy was 6.50 and for another 14.25) obscures the somewhat less dramatic difference in wear between the left and right shoes (the largest difference between shoes was 1.10). This is why a paired experimental design and subsequent analysis with a paired t-test, where appropriate, is often much more powerful than an unpaired approach.