Paired T-Test (Matched Pair/Repeated Measure)

Comparing two Samples/Populations/Groups/Means/Values

Two-sample paired T-test is performed when two observations are made on each observational unit. There are situations where completely randomized trials do not provide better responses towards the research questions. The example in Table 7 provides a few examples of such in which the repeated measures on the same observational unit would produce a better result in support of the research questions.

Table 7. Examples for Paired/Matched Paired/Repeated Measure Experiments

Assume that a researcher is interested to compare the drivability of two similar vehicles from two different manufacturers. She hired 15 test drivers and collected the drivability performance data provided in Table 8.

Table 8. Paired T-Test Data

Step 1


Step 2


Two-sample paired T-Test can be applied as the data comes in pairs for this experimental situation. Analysis can be performed manually using the paired T-Test formula provided Equation 6.

Equation 6

Step 3


In MS Excel, manual analysis using the paired T-Test formula is provided in Table 9.

Table 9. Manual Analysis Results for Paired T-Test Using MS Excel

Analysis using the statistical function in MS excel is provided in Figure 10.

Figure 10. Two Sample Paired T-Test Analysis Results Using MS Excel

Figure 11. Two Sample Paired T-Test Analysis Results Using Minitab

Statistical Interpretation of the Results

We do not reject the null hypothesis because the p-value (0.430) is larger than the level of significance (0.05). [p-value is the observed probability of the null hypothesis to happen, which is calculated from the sample data using an appropriate method, two-sample paired T-Test in this case]

Step 4

Contextual Conclusion

Statistically, vehicle 1 and vehicle 2 are same with respect to the drivability rating by the test drivers. [rewrite the accepted hypothesis for an eighth grader without using the statistical jargon such as the p-value, level of significance, etc.]