Two-sample t test versus matched pairs t test. Consider the following data set. The data were actually collected in pairs, and each row represents a pair.
|
Group 1
|
Group 2
|
|
48.86
|
48.88
|
|
50.60
|
52.63
|
|
51.02
|
52.55
|
|
47.99
|
50.94
|
|
54.20
|
53.02
|
|
50.66
|
50.66
|
|
45.91
|
47.78
|
|
48.79
|
48.44
|
|
47.76
|
48.92
|
|
51.13
|
51.63
|
(a) Suppose that we ignore the fact that the data were collected in pairs and mistakenly treat this as a two-sample problem. Compute the sample mean and variance for each group. Then compute the two-sample t statistic, degrees of freedom, and P-value.
(b) Now analyze the data in the proper way. Compute the sample mean and variance of the differences. Then compute the t statistic, degrees of freedom, and P-value.
(c) Describe the differences in the two test results.