Tukey Test Demo

The Tukey test may follow an ANOVA test but it is not dependent upon it. The six waves used in this example are shown below.

data1data2data3data4data5data6
40.1156.0262.9826.5938.6741.1
41.5838.7126.8424.2639.0916.48
36.8139.9137.625.5836.2629.9
30.0133.748.3233.3433.8837.04
31.6735.4238.5622.2628.3829.62
33.2926.6434.7431.5147.1839.29
37.148.0123.3219.6834.6624.69
39.7940.0639.54

To run the Tukey and the Neuman-Keuls tests execute the following command:

  StatsTukeyTest/T=1/Q/NK data1,data2,data3,data4,data5,data6

The results are displayed in the Tukey Test table:

PairDIFFSEqq.05_39_6Concl.Tpq.5_39_pConcl.NK
data2_vs_data414.53932.945264.936514.23697064.236970
data2_vs_data68.6152.945262.925044.23697154.043921
data2_vs_data13.979282.945261.351084.23697143.794851
data2_vs_data52.56752.845390.9023374.23697133.445461
data2_vs_data30.7224992.845390.2539194.23697122.860521
data3_vs_data413.81682.945264.69124.23697054.043920
data3_vs_data67.89252.945262.679734.23697143.794851
data3_vs_data13.256792.945261.105774.23697133.445461
data3_vs_data51.8452.845390.6484184.23697122.860521
data5_vs_data411.97182.945264.064774.23697143.794850
data5_vs_data66.04752.945262.05334.23697133.445461
data5_vs_data11.411782.945260.4793424.23697122.860521
data1_vs_data410.563.041853.471574.23697133.445460
data1_vs_data64.635713.041851.523984.23697122.860521
data6_vs_data45.924293.041851.947594.23697122.860521

The table shows the statistics for each possible pair in both the Tukey and Neuman-Keuls tests. The conclusions in both cases apply to H0: the mean values of the two members of the pair are equal. Note that both tests have the same statistic q. The difference between the tests is manifested in the critical values: the Neuman-Keuls test uses a more sensitive critical value that is based on the difference between the ranks of the two members of the pair. As a result, the Neuman-Keuls test for data1 vs data4 rejects H0 while the Tukey test accepts it.