ST 524 NCSU - Fall 2008

Homework 1 Due: September 11, 2008

1. Description A plant scientist measured the concentration of a particular virus in plant sap using ELISA (enzyme-linked immunosorbent assay) (Novy 1992). The study included 13 potato clones:: 2 commercial cultivars, 5 somatic hybrids, 5 progeny of the somatic hybrids, and one clone of Solanum etuberosum (a species related to potato). Of the 5 progeny of the somatic hybrids, two were classified as susceptible and three as resistant to the virus. The scientist wants to understand the resistance to the virus among these 13 clones. Plant sap was taken from 5 inoculated plants of each clone, for a total of 65 measurements of titer. One measurement was lost during processing of the samples. Reference : Yandell (2001)

Data

clone reps titer code type clone reps titer code type 1 1 1302 a susc 1 2 1717 a susc 8 1 361 h res 1 3 1321 a susc 8 2 113 h res 1 4 1358 a susc 8 3 338 h res 1 5 1093 a susc 8 4 283 h res 2 1 32 b etb 8 5 301 h res 2 2 12 b etb 9 1 594 i par 2 3 25 b etb 9 2 173 i par 2 4 61 b etb 9 3 526 i par 2 5 93 b etb 9 4 58 i par 3 2 1846 c cult 9 5 88 i par 3 3 1745 c cult 10 1 644 j odd 3 4 1814 c cult 10 2 680 j odd 3 5 1752 c cult 10 3 663 j odd 4 1 197 d res 10 4 780 j odd 4 2 380 d res 10 5 965 j odd 4 3 280 d res 11 1 549 k par 4 4 112 d res 11 2 603 k par 4 5 355 d res 11 3 229 k par 5 1 529 e par 11 4 398 k par 5 2 396 e par 11 5 252 k par 5 3 629 e par 12 1 1185 l susc 5 4 261 e par 12 2 1105 l susc 5 5 325 e par 12 3 1196 l susc 6 1 931 f par 12 4 949 l susc 6 2 791 f par 12 5 906 l susc 6 3 57 f par 13 1 214 m res 6 4 706 f par 13 2 351 m res 6 5 742 f par 13 3 564 m res 7 1 1361 g cult 13 4 98 m res 7 2 363 g cult 13 5 417 m res 7 3 418 g cult 7 4 579 g cult 7 5 1660 g cult

Objective: Checking assumptions. Decide whether a common residual variance is a good fit in model. 1) Write statistical linear model. 2) Run an analysis of variance in Proc GLM. Analysis of Variance Table. 3) Graph standardized residuals (StudentResid) vs predicted (mean value) for each clone. Summarize findings. 4) Run homogeneity of variance test. Use Brown-Forsythe’s and Bartlett tests. Indicate hypothesis and conclusions. Use = 0.05.

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5) Study the need to fit separate variances for each type level. 6) Select the best model to be fitted. a. Test whether a model with a common residual variance is preferred to a model with separate variances. Use a likelihood ratio test, and  = 0.05. b. Check residual plot and normality test for standardized residuals in selected model. c. Write down the final model. Test of hypothesis. Conclusions. Use = 0.05. 7) Explain any limitations to the final selected model.

2. A study will be carried out in the greenhouse on the effects of 2 methods of obtaining cuttings (M1, M2) on the growth of 5 cultivars of an ornamental shrub (V1, V2, V3, V4, V5). Identify uniquely each method by cultivar combination from T1 through T10. Use PROC PLAN to obtain: 1) a randomization plan for an CRD with 4 pots per cutting method and cultivar combination, with three cuttings per plot. These pots for 10 methods by cultivar treatment combinations will be randomly distributed along four selected benches in the greenhouse. Sketch a plan for the layout in the greenhouse indicating the position of each treatment combination. Assume each bench will contain a single row of 10 pots. 2) a randomization plan for an RCBD with 4 blocks corresponding to 4 benches in the greenhouse, and all 10 methods by cultivar treatment combinations represented once in each block. Sketch a plan for the layout in the greenhouse indicating the position of each treatment combination in each block. Assume each block will contain a single row of 'plots'.

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