Note: The problem numbering below may not reflect actual numbering in DGE.
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1 Stat664 Year 1999 DGE Note: The problem numbering below may not reflect actual numbering in DGE. 1. For a balanced one-way random effect model, (a) write down the model and assumptions; (b) write down the OV table including SS (sums of squares), DF (degrees of freedom), MS (mean squares), E[MS] (expected mean squares), and F (F ratio); (c) verify the formula you ve written above for E[M between ]. 2. The surface finish of metal parts made on four machines is being studied. n experiment is conducted in which each machine is run by three different operators and two specimens from each operator are collected and tested. Because of the location of the machines, different operators are used on each machine, and the operators are chosen at random. The data are shown in the following table. Machine 1 Machine 2 Machine 3 Machine 4 Operator There are four sets of computer output given in the ppendix, only one is proper for the analysis of this problem. nalyze the data using the correct computer output. 3. Briefly state the three principles of planning experiment: randomization, blocking, and replication. State also their importance in planning experiment. 4. Six factorial treatments are compared in a 6 6 Latin square. The six treatment combinations 11, 12, 13, 21, 22, and 23 of factors and B correspond to the Latin letters, B, C, D, E, and F, respectively. What are the degrees of freedom of the following NOV table? Briefly describe how the SS for the B-interaction is computed. column (day) row (replicate)
2 NOV source df row column treatment combination main effect main effect B B-interaction error total 35 2
3 ppendix Computer output #1 Dependent Variable: FINISH Model Error Source DF Type I SS Square F Value Pr > F MCHINE OPERTOR(MCHINE) MCHINE OPERTOR(MCHINE) lpha= 0.05 df= 12 MSE= 84.5 Critical Value of T= 2.18 Least Significant Difference= s with the same letter are not significantly different. T Grouping N MCHINE B B B Computer output #2 C
4 Dependent Variable: FINISH Model Error Source DF Type I SS Square F Value Pr > F MCHINE OPERTOR MCHINE OPERTOR lpha= 0.05 df= 18 MSE= Critical Value of T= 2.10 Least Significant Difference= s with the same letter are not significantly different. Computer output #3 T Grouping N MCHINE B B B C C C Dependent Variable: FINISH Model Error
5 Source DF Type I SS Square F Value Pr > F MCHINE OPERTOR(MCHINE) MCHINE OPERTOR(MCHINE) Tests of Hypotheses using the Type III MS for OPERTOR(MCHINE) as an error term MCHINE lpha= 0.05 df= 8 MSE= Critical Value of T= 2.31 Least Significant Difference= s with the same letter are not significantly different. Computer output #4 T Grouping N MCHINE B B B B B Dependent Variable: FINISH Model Error
6 Source DF Type I SS Square F Value Pr > F MCHINE OPERTOR MCHINE OPERTOR Tests of Hypotheses using the Type III MS for OPERTOR as an error term MCHINE lpha= 0.05 df= 2 MSE= Critical Value of T= 4.30 Least Significant Difference= s with the same letter are not significantly different. T Grouping N MCHINE
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