Question 6 Split PLot design

The oats2.csv data file contains information on a split-plot design. Using lme() estimate two models with Nitrogen and Variety as factors, with no interaction effect. In the first model treat Block as a random effect. In the second model allow variety to be nested within block. Use the anova command to test whether allowing for nesting results in a statistically significant improvement in model fit.

1. Report, to four decimal places, the p-value for the anova test on whether or not nesting improves model fit(This is quiz question 8). (Marks 0.5)

Block Variety Nitrogen Yield 1 I Victory 0.0cwt 105 2 I Victory 0.2cwt 120 3 I Victory 0.4cwt 142 4 I Victory 0.6cwt 155 5 I Golden.rain 0.0cwt 110 6 I Golden.rain 0.2cwt 107 7 I Golden.rain 0.4cwt 145 8 I Golden.rain 0.6cwt 129 9 I Marvellous 0.0cwt 100 10 I Marvellous 0.2cwt 128 11 I Marvellous 0.4cwt 110 12 I Marvellous 0.6cwt 141 13 II Victory 0.0cwt 64 14 II Victory 0.2cwt 92 15 II Victory 0.4cwt 95 16 II Victory 0.6cwt 96 17 II Golden.rain 0.0cwt 72 18 II Golden.rain 0.2cwt 102 19 II Golden.rain 0.4cwt 117 20 II Golden.rain 0.6cwt 135 21 II Marvellous 0.0cwt 93 22 II Marvellous 0.2cwt 115 23 II Marvellous 0.4cwt 113 24 II Marvellous 0.6cwt 131 25 III Victory 0.0cwt 70 26 III Victory 0.2cwt 67 27 III Victory 0.4cwt 106 28 III Victory 0.6cwt 85 29 III Golden.rain 0.0cwt 65 30 III Golden.rain 0.2cwt 102 31 III Golden.rain 0.4cwt 87 32 III Golden.rain 0.6cwt 93 33 III Marvellous 0.0cwt 87 34 III Marvellous 0.2cwt 119 35 III Marvellous 0.4cwt 122 36 III Marvellous 0.6cwt 112 37 IV Victory 0.0cwt 75 38 IV Victory 0.2cwt 87 39 IV Victory 0.4cwt 81 40 IV Victory 0.6cwt 114 41 IV Golden.rain 0.0cwt 67 42 IV Golden.rain 0.2cwt 98 43 IV Golden.rain 0.4cwt 122 44 IV Golden.rain 0.6cwt 134 45 IV Marvellous 0.0cwt 72 46 IV Marvellous 0.2cwt 87 47 IV Marvellous 0.4cwt 99 48 IV Marvellous 0.6cwt 110 49 V Victory 0.0cwt 66 50 V Victory 0.2cwt 88 51 V Victory 0.4cwt 96 52 V Victory 0.6cwt 109 53 V Golden.rain 0.0cwt 80 54 V Golden.rain 0.2cwt 82 55 V Golden.rain 0.4cwt 91 56 V Golden.rain 0.6cwt 117 57 V Marvellous 0.0cwt 66 58 V Marvellous 0.2cwt 72 59 V Marvellous 0.4cwt 103 60 V Marvellous 0.6cwt 95 61 VI Victory 0.0cwt 58 62 VI Victory 0.2cwt 75 63 VI Victory 0.4cwt 110 64 VI Victory 0.6cwt 106 65 VI Golden.rain 0.0cwt 87 66 VI Golden.rain 0.2cwt 82 67 VI Golden.rain 0.4cwt 85 68 VI Golden.rain 0.6cwt 99 69 VI Marvellous 0.0cwt 94 70 VI Marvellous 0.2cwt 95 71 VI Marvellous 0.4cwt 111 72 VI Marvellous 0.6cwt 113

Question 7 MANOVA

The aminoacid.csv data file contains information on the amino acid concentration in centipede hemolymph in mg/100 ml for two amino acids.

1. The test statistic uses for the MANOVA depends on whether or not the assumptions of the model are met.Based on (i) univariate bartlett test results, and (ii) the multivariate normality tests, which test statistic would you use for the actual MANOVA test (selected when you run the summary command). Select the correct answer from the options. (This is quiz question 9). (Marks 0.5)
2. Following the MANOVA test, move to univariate testing. Based on Tukey comparisons, select the correct answer from the options. (This is quiz question 10). (Marks 0.5)

Alanine Tyrosine Sex 7 19.7 Males 7.3 20.3 Males 8 22.6 Males 8.1 23.7 Males 7.9 22 Males 6.4 18.1 Males 6.6 18.7 Males 8 21.5 Males 7.3 22.5 Females 7.7 24.9 Females 8.2 26.1 Females 8.3 27.5 Females 6.4 28.1 Females 7.1 25.8 Females 6.4 26.9 Females 8.6 25.5 Females