Greater power of the paired t-test

When we initially applied a two-sample /-test to the first two columns of data in Table 12.1 (Section 12.2), the result was non-significant (P = 0.155), but the result of the paired /- test was clearly significant (P 0.001). This is a typical example of the greater power of the paired /-test. 

Where data form natural pairs (as in the current example), it is very frequently the case that individuals who have the highest values under the first set of experimental conditions also have the highest values under the alternative conditions. As a result, the variability in the two original sets of data is greater than that among the individual changes that occur. This is the reason why the paired /-test is more powerful (often much more powerful) than the two-sample test. 

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