A researcher wishes to see whether there is any difference i

A researcher wishes to see whether there is any difference in the weight gains of athletes following one of three special diets. Athletes are randomly assigned to three groups and placed on the diet for 6 weeks. the weight gains (in pounds) are shown here. At alpha equal to 0.05, can the researcher conclude that there is a difference in the diets? Construct an ANOVA (manually), and apply Scheffe\'s test as well. Diet A: 3, 6, 7, 4. Diet B: 10, 12, 11, 14, 8, 6. Diet C: 8, 3, 2, 5.

Solution

One factor ANOVA Mean n Std. Dev 7.071428571 5.0 4 1.83 Diet A 7.071428571 10.2 6 2.86 Diet B 7.071428571 4.5 4 2.65 Diet C 7.1 14 3.65 Total ANOVA table Source SS    df MS F    p-value Treatment 101.10 2 50.548 7.74 .0080 Error 71.83 11 6.530 Total 172.93 13 Post hoc analysis Tukey simultaneous comparison t-values (d.f. = 11) Diet C Diet A Diet B 4.5 5.0 10.2 Diet C 4.5 Diet A 5.0 0.28 Diet B 10.2 3.44 3.13                critical values for experimentwise error rate: 0.05 2.70 0.01 3.63 p-values for pairwise t-tests Diet C Diet A Diet B 4.5 5.0 10.2 Diet C 4.5 Diet A 5.0 .7871 Diet B 10.2 .0056 .0095