All Pairwise Comparisons among Means: Example Calculations (2 of 3)

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M sub i minud M sub j over squre root of MSW over n sub h

Substituting the values for nh and MSE,

           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 

The table shows the value of t for each of the six possible pairwise comparisons. For Fisher's LSD, all values of t except the comparison of Group 2 and Group 3 are above the critical value of 3.08 and are therefore significant.

Duncan's test begins with a comparison of G1 and G4 using a critical value of 3.33. The t of 7.36 is significant so G1 Vs G3 and G2 Vs G4 are tested using a critical value of 3.23. Both are significant, so all remaining comparisons are tested using a critical value of 3.08.
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