- A researcher wishes to see whether there is any difference inthe weight gains of athletes following one of three special diets.Athletes are randomly assigned to three groups and placed on thediet for 6 weeks. The weight gains (in pounds) are shown here. At α= 0.05, can the researcher conclude that there is a difference inthe diets?
DietAÂ Â Â Â Â Â Â Â Â Â Â Â DietBÂ Â Â Â Â Â Â Â Â Â Â Â DietCÂ Â Â Â Â Â Â Â Â Â Â Â Total
                       3                     10                  8
6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 12Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 3
7Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 11Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2
4Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 14Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5
                                   8
                                   6
the critical value = 3.98
Conclusion:
Analysis of Variance Summary Table
P-value
Source                            Sum of Squares      D.F.   Mean Square F ratio p-value
Betweengroups                     Â
Within                           Â
SSBÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â SSWÂ Â Â
MSB =SSBk-1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â MSW=SSWN-k
F =MSBMSW
ANOVA 1 TUKEY B
                                   ID        N
                                   ____________________________
                                   3          4      4.50
                                       ____________________________
                                  1         4         5.00            Â
                                   ____________________________
                                   2         6                                 10.17
                                   _____________________________
                                   Sig.                .954              1.00
