The significance level of each hypothesis is > 2 {\displaystyle \gamma _{\alpha }} p 10.8 > Each comparison is performed at a significance level 10.8 ) p ) , s ( From Wikipedia, the free encyclopedia In statistics, Duncan's new multiple range test (MRT) is a multiple comparison procedure developed by David B. Duncan in 1955. = − p are both contained in a subset of the means which has a non-significant r r ( = p 2 3.94 ) α R . : Let us denote . α ) : r {\displaystyle {\frac {n_{2}\cdot S_{m}^{2}}{\sigma _{m}^{2}}}} = r . {\displaystyle 3vs.1:17.6-9.8=7.8>4.04(R_{4})} 2 4 21.6 = 4.04 1 2 Q .5 where σ = .5 10.8 Another solution is to perform Student's t-test of all pairs of means, and then to use FDR Controlling procedure (to control the expected proportion of incorrectly rejected null hypotheses). , and The tests are performed in the following order: the largest minus the smallest, the largest minus the second smallest, up to the largest minus the second largest; then the second largest minus the smallest, the second largest minus the second smallest, and so on, finishing with the second smallest minus the smallest. Duncan's test has been criticised as being too liberal by many statisticians including Henry Scheffé, and John W. Tukey. = 3.75 . s 20 4.13 {\displaystyle R_{(2,20,0.05)}=3.75} s , ν For (degrees of freedom for estimating the standard error). v {\displaystyle R_{(5,20,0.05)}=4.13}. Then, the observed differences between means are tested, beginning with the largest versus smallest, which would be compared with the least significant range p − n 5 3 {\displaystyle \nu } ν r ) , Else − 3.94 , ) 2 {\displaystyle 1-(0.95)^{3}=0.143}. ( ( Duncan's MRT belongs to the general class of multiple comparison procedures that use the studentized range statistic qr … R γ The result of the test is a set of subsets of means, where in each subset means have been found not to be significantly different from one another. , 2 Duncan’s Multiple Range Test was originally designed by David B. Duncan as a higher- power alternative to Newman–Keuls. ( , {\displaystyle \alpha _{p}} ) r α .1 σ p , is p 4.04 ) {\displaystyle p-2} 2.A common standard error Duncan's multiple range test does not control the familywise error rate. 5 = The test are performed sequentially, where the result of a test determines which test is performed next. 0.05 Q − m {\displaystyle r_{(2,20,0.05)}=2.95} γ = {\displaystyle r_{(p,\nu ,\alpha )}} ( p s ν 2 ( 1 = Where the shortest significant range is the significant studentized range, multiplied by the standard error. {\displaystyle R_{(5,20,0.05)}=4.13.} v H. Leon Harter, Champaigne, IL; N. Balakrishnan, McMaster University, Hamilton, Ontario, Canada; Hardback - Published Oct 27, 1997, This page was last edited on 11 May 2020, at 21:08. is the number means in the subset. 3.10 S ν p α 1 , 1 : μ , α Duncan modeled the consequences of two or more means being equal using additive loss functions within and across the pairwise comparisons. 10.8 − Tukey's range test is commonly used to compare pairs of means, this procedure controls the familywise error rate in the strong sense. 1 : According to Duncan, one should adjust the protection levels for different p-mean comparisons according to the problem discussed. ( , 0.05 2 : v 20 α r − − ( ( {\displaystyle r_{(4,20,0.05)}=3.18} 11.8 {\displaystyle p} and α 9.8 = ) > 4 .1 ) 2 > , , m . v Multiple comparisons of means allow you to examine which means are different and to estimate by how much they are different. , , has the property that Let us denote Using a known tabulation for Q, one reaches the values of α , under the hypothesis that all p population means are equal. 20 4.04 3.94 for α p ) 20 Duncan's test is commonly used in agronomy and other agricultural research. 20 3 0.05 α 1 21.6 In addition, results indicate considerable similarity in both risk and average power between Duncan's modified procedure and the Benjamini and Hochberg (1995) False discovery rate -controlling procedure, with the same weak familywise error control. = Note that different comparisons between means may differ by their significance levels- since the significance level is subject to the size of the subset of means in question. α 0.05 20 5 Duncan reasons that one has p-1 degrees of freedom for testing p ranked mean, and hence one may conduct p-1 independent tests, each with protection level , , 3.18 {\displaystyle \gamma _{2}=0.95} 3.75 ( α 100 9.8 γ .1 {\displaystyle 2vs.5:15.4-10.8=4.6>3.75(R_{2})} =

duncan's multiple range test minitab 2020