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.
| data1 | data2 | data3 | data4 | data5 | data6 |
| 40.11 | 56.02 | 62.98 | 26.59 | 38.67 | 41.1 |
| 41.58 | 38.71 | 26.84 | 24.26 | 39.09 | 16.48 |
| 36.81 | 39.91 | 37.6 | 25.58 | 36.26 | 29.9 |
| 30.01 | 33.7 | 48.32 | 33.34 | 33.88 | 37.04 |
| 31.67 | 35.42 | 38.56 | 22.26 | 28.38 | 29.62 |
| 33.29 | 26.64 | 34.74 | 31.51 | 47.18 | 39.29 |
| 37.1 | 48.01 | 23.32 | 19.68 | 34.66 | 24.69 |
| 39.79 | 40.06 | 39.54 |
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:
| Pair | DIFF | SE | q | q.05_39_6 | Concl.T | p | q.5_39_p | Concl.NK |
| data2_vs_data4 | 14.5393 | 2.94526 | 4.93651 | 4.23697 | 0 | 6 | 4.23697 | 0 |
| data2_vs_data6 | 8.615 | 2.94526 | 2.92504 | 4.23697 | 1 | 5 | 4.04392 | 1 |
| data2_vs_data1 | 3.97928 | 2.94526 | 1.35108 | 4.23697 | 1 | 4 | 3.79485 | 1 |
| data2_vs_data5 | 2.5675 | 2.84539 | 0.902337 | 4.23697 | 1 | 3 | 3.44546 | 1 |
| data2_vs_data3 | 0.722499 | 2.84539 | 0.253919 | 4.23697 | 1 | 2 | 2.86052 | 1 |
| data3_vs_data4 | 13.8168 | 2.94526 | 4.6912 | 4.23697 | 0 | 5 | 4.04392 | 0 |
| data3_vs_data6 | 7.8925 | 2.94526 | 2.67973 | 4.23697 | 1 | 4 | 3.79485 | 1 |
| data3_vs_data1 | 3.25679 | 2.94526 | 1.10577 | 4.23697 | 1 | 3 | 3.44546 | 1 |
| data3_vs_data5 | 1.845 | 2.84539 | 0.648418 | 4.23697 | 1 | 2 | 2.86052 | 1 |
| data5_vs_data4 | 11.9718 | 2.94526 | 4.06477 | 4.23697 | 1 | 4 | 3.79485 | 0 |
| data5_vs_data6 | 6.0475 | 2.94526 | 2.0533 | 4.23697 | 1 | 3 | 3.44546 | 1 |
| data5_vs_data1 | 1.41178 | 2.94526 | 0.479342 | 4.23697 | 1 | 2 | 2.86052 | 1 |
| data1_vs_data4 | 10.56 | 3.04185 | 3.47157 | 4.23697 | 1 | 3 | 3.44546 | 0 |
| data1_vs_data6 | 4.63571 | 3.04185 | 1.52398 | 4.23697 | 1 | 2 | 2.86052 | 1 |
| data6_vs_data4 | 5.92429 | 3.04185 | 1.94759 | 4.23697 | 1 | 2 | 2.86052 | 1 |
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.
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