In exercises that call for two-sample procedures, you may use either of the two approximations for the degrees of freedom that we have discussed: the value given by your software or the smaller of and . Be sure to state clearly which approximation you have used.
7.71 Satterthwaite approximation.
The degrees of freedom given by the Satterthwaite approximation are always at least as large as the smaller of and and never larger than than the sum . In Exercise 7.53 (pages 394–395), you were asked to compare the analyses with and without a very low decibel reading in the low-intensity group. Redo those analyses and make a table showing the sample sizes and , the standard deviations and , and the Satterthwaite degrees of freedom for each of these analyses. Based on these results, suggest when the Satterthwaite degrees of freedom will be closer to the smaller of and and when it will be closer to .
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7.71
When the standard deviations are similar, the Satterthwaite DF are closer to . When one standard deviation is much larger, the Satterthwaite DF is closer to the smaller of and .