All Pairwise Comparisons among Means: Example Calculations (3 of 3)

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           lower    higher
           mean     mean        ts
G1 vs G2:  3.000    4.875     3.449
G1 vs G3:  3.000    5.000     3.679
G1 vs G4:  3.000    7.000     7.357
 
G2 vs G3:  4.875    5.000     0.230 
G2 vs G4:  4.875    7.000     3.909
 
G3 vs G4:  5.000    7.000     3.679

All are significant except for the comparison of G2 vs G3. Therefore, the Duncan's test and the Fisher's LSD yield the same results for these data. The Newman-Keuls test begins with a comparison of G1 and G4 using a critical value of 4.20. The test is significant so the comparisons G1 vs G3 and G2 vs G4 are tested using a critical value of 3.77. The comparison G1 vs G3 is not significant. This means that the comparisons of G1 vs G2 and G2 vs G3 are deemed not significant as well. The comparison of G2 vs G4 is significant, so the comparison G3 vs G4 is done using the critical value of 3.08. The comparison is significant. Two comparisons that were significant with the Fisher's LSD are not significant with the Newman-Keuls test (G1 vs G3 and G1 vs G2). The Tukey HSD uses a critical value of 4.20 for all comparisons. The only significant difference is between Group 1 and Group 4.

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