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In computer science, all-pairs testing or pairwise testing is a combinatorial method of software testing that, for each pair of input parameters to a system (typically, a software algorithm), tests all possible discrete combinations of those parameters.
The following example will illustrate why: Let us assume one is truly interested, as Duncan suggested, only with the correct ranking of subsets of size 4 or below. Let us also assume that one performs the simple pairwise comparison with a protection level =. Given an overall set of 100 means, let us look at the null hypotheses of the test:
Kemeny–Young calculations are usually done in two steps. The first step is to create a matrix or table that counts pairwise voter preferences. The second step is to test all possible rankings, calculate a score for each such ranking, and compare the scores. Each ranking score equals the sum of the pairwise counts that apply to that ranking.
Their method was a general one, which considered all kinds of pairwise comparisons. [7] Tukey's and Scheffé's methods allow any number of comparisons among a set of sample means. On the other hand, Dunnett's test only compares one group with the others, addressing a special case of multiple comparisons problem—pairwise comparisons of ...
We could then calculate the sample means within the treated and untreated groups of subjects, and compare these means to each other. In a "paired difference analysis", we would first subtract the pre-treatment value from the post-treatment value for each subject, then compare these differences to zero. See also paired permutation test.
The model is named after Ralph A. Bradley and Milton E. Terry, [3] who presented it in 1952, [4] although it had already been studied by Ernst Zermelo in the 1920s. [1] [5] [6] Applications of the model include the ranking of competitors in sports, chess, and other competitions, [7] the ranking of products in paired comparison surveys of consumer choice, analysis of dominance hierarchies ...
When the pairwise comparisons are as numerous as those in our example, specialized AHP software can help in making them quickly and efficiently. We will assume that the Jones family has access to such software, and that it allows the opinions of various family members to be combined into an overall opinion for the group.
If only a fixed number of pairwise comparisons are to be made, the Tukey–Kramer method will result in a more precise confidence interval. In the general case when many or all contrasts might be of interest, the Scheffé method is more appropriate and will give narrower confidence intervals in the case of a large number of comparisons.