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C.1 Within- vs. Between-Group Variation

C.1 Within- vs. Between-Group Variation

Suppose 12 recent college graduates are assigned to three groups: 4 subjects to an exercise group (I), 4 subjects to a drug treatment group (II), and 4 subjects to a control group (III). Ages, pulse rates, diastolic blood pressures, and triglyceride measurements are taken after 8 weeks in the study, with the following results:

  1. Age (years)

    The age measurements are the same for all 12 subjects. Clearly, there is no variation among the group means and, therefore, no difference among groups with respect to age.



  2. Pulse Rates (beats/min.)

    The pulse rate measurements are the same for all 4 subjects within each group, but the measurements vary across groups. Observation of these data without further analysis would likely lead to the conclusion of a difference in mean pulse rates among the three groups.



  3. Diastolic BP (mm Hg)

    Diastolic blood pressure measurements show a variation both within and among groups. Within-group measurements vary by no more than 2 mm Hg, while the variation among the group means is as much as 14 mm. Because the among-group variation is large compared to the withingroup variation, you would likely think that there is a difference among groups in mean diastolic blood pressure.



  4. Triglycerides (mg/dl)

    The triglyceride measurements show considerable variation both within and among groups. Because the variation within groups no longer allows our intuition to distinguish among groups, it is not clear whether a group effect exists.




  

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