1. Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Multiple Comparisons of Means Rejection of H o does not imply that all of k means are different from one another. H o : μ 2 1 = μ 2 2 = μ 2 3 = μ 2 4 = μ 2 5 H a : μ 2 1 ≠ μ 2 2 ≠ … The problem is that it is generally invalid to employ multiple t-tests to examine all possible pairs of means. … But there are statistical test to do so referred to as “multiple comparison tests”.

2. Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Multiple Comparisons of Means Nobody agrees on the best test to use. However there are two test that are most often used: Tukey’s test Student-Newman-Keuls test (SNK) There is also a third which you might see – a Duncan’s test (in older literature) or a Duncan’s multiple-range test.

3. Special Topics 504: Practical Methods in Analyzing Animal Science Experiments Multiple Comparisons of Means Five different levels of probiotic treatments are tested on 25 g trout in a 4 week feeding trial. H o : μ 2 1 = μ 2 2 = μ 2 3 = μ 2 4 = μ 2 5 Ha: Mean growth rates are not the same in all five diets. Trt1Trt2Trt3Trt4Trt5 28.239.646.341.056.3 33.240.842.144.154.1 36.437.943.546.459.4 34.637.148.840.262.7 29.143.643.738.660.0 31.042.440.136.357.3