Approximate k-Ratio t Tests for Diffierences between Unequally Replicated Treatmentsl
Approximate k-Ratio t Tests for Diffierences between Unequally Replicated Treatmentsl
复制标题
不均匀重复处理之间差异的近似 k 比检验
作者：
D. B. Duncan;J. Godbold
k-Ratio t tests have been developedfor tests of allpairwise diXerences andpractically all contrasts among n equally replicated means. In place of choosing an oe, these new t tests depend on choosing an error-seriousness ratio k. They depend also on the overall data through the betweentreatments F ratio and its degrees offreedom q andf: This paper extends these k-ratio t tests to cases with unequally replicated means or with treatment estimates which are heteroscedastic and correlated. The critical t value t(k, F, q, f) is the same except that in the test of each di0Jerence d = Xi-xj, for example, the overall F and q are replaced by an 'e%Jective' F ratio Fij with an e%Jective qij based on a simple approximation due to Satterthwaite (1946). The rule is thus not completely optimum as is true in the Bayes sense for the nale for equal replications. It does, however, have virtually the same adaptive dependence on the data through the efJective F ratio. This allows it to be anything from extremely cautious and conservative to being quite powerful and sensitive according to the intuitive needs, thus avoiding serious objections to the comparable oe-level multiple comparisons rules.
