Consider a balanced incomplete block design (BIBD) with k treatments of effects T,...,k, n blocks, each...

 

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Consider a balanced incomplete block design (BIBD) with k treatments of effects T,...,k, n blocks, each treatment appearing in p blocks, s treatments observed in each block, and A pairs of treatments available in each block. The null hypothesis is H == tk. (a) Let D denote the Durbin-Skillings-Mack test statistic for general alternatives in BIBD. Prove E[D]=k-1. (b) The following table presents the data {X} in a BIBD: [8] Treatment Block 1 2 3 4 5 1 21 15 17 - 28 2 25 19 35 32 3 39 32 35 44 - 4 - 22 16 24 30 5 38 34 45 42 Test Ho against general alternatives by the p-value of the test based on D. [8] (c) Decide the differences between treatment effects 71,..., Ts based on the data in part (b) by the Skillings-Mack two-sided all-treatment multiple comparison procedure for BIBD with a 0.1, using R to find relevant 90.1 [4] Consider a balanced incomplete block design (BIBD) with k treatments of effects T,...,k, n blocks, each treatment appearing in p blocks, s treatments observed in each block, and A pairs of treatments available in each block. The null hypothesis is H == tk. (a) Let D denote the Durbin-Skillings-Mack test statistic for general alternatives in BIBD. Prove E[D]=k-1. (b) The following table presents the data {X} in a BIBD: [8] Treatment Block 1 2 3 4 5 1 21 15 17 - 28 2 25 19 35 32 3 39 32 35 44 - 4 - 22 16 24 30 5 38 34 45 42 Test Ho against general alternatives by the p-value of the test based on D. [8] (c) Decide the differences between treatment effects 71,..., Ts based on the data in part (b) by the Skillings-Mack two-sided all-treatment multiple comparison procedure for BIBD with a 0.1, using R to find relevant 90.1 [4]