Week 11 - Homework 10
Mary Adepoju
11/12/2021
Week 11 - Homework
6.8 Effects of Two Different Cultural Medians
## obs timeH median
## 1 21 12 1
## 2 22 12 1
## 3 25 12 2
## 4 26 12 2
## 5 23 12 1
## 6 28 12 1
## 7 24 12 2
## 8 25 12 2
## 9 20 12 1
## 10 26 12 1
## 11 29 12 2
## 12 27 12 2
## 13 37 18 1
## 14 39 18 1
## 15 31 18 2
## 16 34 18 2
## 17 38 18 1
## 18 38 18 1
## 19 29 18 2
## 20 33 18 2
## 21 35 18 1
## 22 36 18 1
## 23 30 18 2
## 24 35 18 2## Analysis of Variance Table
##
## Response: obs
## Df Sum Sq Mean Sq F value Pr(>F)
## median 1 9.38 9.38 1.8352 0.1906172
## timeH 1 590.04 590.04 115.5057 9.291e-10 ***
## median:timeH 1 92.04 92.04 18.0179 0.0003969 ***
## Residual 20 102.17 5.11
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
The main effect, time and the interaction prove to be significant to the growth rate.
6.12 $2^2 Factorial Design
## Df Sum Sq Mean Sq F value Pr(>F)
## A4 1 0.374 0.3739 0.898 0.362
## B4 1 0.371 0.3709 0.891 0.364
## A4:B4 1 0.182 0.1823 0.438 0.521
## Residuals 12 4.994 0.4162
## hat values (leverages) are all = 0.25
## and there are no factor predictors; no plot no. 5
## 6.21 \(2^4\) Golfer Factorial Design
## replications A3 B3 C3 D3 distance
## 1 1 -1 -1 -1 -1 10.0
## 2 2 1 -1 -1 -1 18.0
## 3 3 -1 1 -1 -1 14.0
## 4 4 1 1 -1 -1 12.5
## 5 5 -1 -1 1 -1 19.0
## 6 6 1 -1 1 -1 16.0
## 7 7 -1 1 1 -1 18.5
## 8 1 1 1 1 -1 0.0
## 9 2 -1 -1 -1 1 16.5
## 10 3 1 -1 -1 1 4.5
## 11 4 -1 1 -1 1 17.5
## 12 5 1 1 -1 1 20.5
## 13 6 -1 -1 1 1 17.5
## 14 7 1 -1 1 1 33.0
## 15 1 -1 1 1 1 4.0
## 16 2 1 1 1 1 6.0
## 17 3 -1 -1 -1 -1 1.0
## 18 4 1 -1 -1 -1 14.5
## 19 5 -1 1 -1 -1 12.0
## 20 6 1 1 -1 -1 14.0
## 21 7 -1 -1 1 -1 5.0
## 22 1 1 -1 1 -1 0.0
## 23 2 -1 1 1 -1 10.0
## 24 3 1 1 1 -1 34.0
## 25 4 -1 -1 -1 1 11.0
## 26 5 1 -1 -1 1 25.5
## 27 6 -1 1 -1 1 21.5
## 28 7 1 1 -1 1 0.0
## 29 1 -1 -1 1 1 0.0
## 30 2 1 -1 1 1 0.0
## 31 3 -1 1 1 1 18.5
## 32 4 1 1 1 1 19.5
## 33 5 -1 -1 -1 -1 16.0
## 34 6 1 -1 -1 -1 15.0
## 35 7 -1 1 -1 -1 11.0
## 36 1 1 1 -1 -1 5.0
## 37 2 -1 -1 1 -1 20.5
## 38 3 1 -1 1 -1 18.0
## 39 4 -1 1 1 -1 20.0
## 40 5 1 1 1 -1 29.5
## 41 6 -1 -1 -1 1 19.0
## 42 7 1 -1 -1 1 10.0
## 43 1 -1 1 -1 1 6.5
## 44 2 1 1 -1 1 18.5
## 45 3 -1 -1 1 1 7.5
## 46 4 1 -1 1 1 6.0
## 47 5 -1 1 1 1 0.0
## 48 6 1 1 1 1 10.0
## 49 7 -1 -1 -1 -1 0.0
## 50 1 1 -1 -1 -1 16.5
## 51 2 -1 1 -1 -1 4.5
## 52 3 1 1 -1 -1 0.0
## 53 4 -1 -1 1 -1 23.5
## 54 5 1 -1 1 -1 8.0
## 55 6 -1 1 1 -1 8.0
## 56 7 1 1 1 -1 8.0
## 57 1 -1 -1 -1 1 4.5
## 58 2 1 -1 -1 1 18.0
## 59 3 -1 1 -1 1 14.5
## 60 4 1 1 -1 1 10.0
## 61 5 -1 -1 1 1 0.0
## 62 6 1 -1 1 1 17.5
## 63 7 -1 1 1 1 6.0
## 64 1 1 1 1 1 19.5
## 65 2 -1 -1 -1 -1 18.0
## 66 3 1 -1 -1 -1 16.0
## 67 4 -1 1 -1 -1 5.5
## 68 5 1 1 -1 -1 10.0
## 69 6 -1 -1 1 -1 7.0
## 70 7 1 -1 1 -1 36.0
## 71 1 -1 1 1 -1 15.0
## 72 2 1 1 1 -1 16.0
## 73 3 -1 -1 -1 1 8.5
## 74 4 1 -1 -1 1 0.0
## 75 5 -1 1 -1 1 0.5
## 76 6 1 1 -1 1 9.0
## 77 7 -1 -1 1 1 3.0
## 78 1 1 -1 1 1 41.5
## 79 2 -1 1 1 1 39.0
## 80 3 1 1 1 1 6.5
## 81 4 -1 -1 -1 -1 3.5
## 82 5 1 -1 -1 -1 7.0
## 83 6 -1 1 -1 -1 8.5
## 84 7 1 1 -1 -1 36.0
## 85 1 -1 -1 1 -1 8.0
## 86 2 1 -1 1 -1 4.5
## 87 3 -1 1 1 -1 6.5
## 88 4 1 1 1 -1 10.0
## 89 5 -1 -1 -1 1 13.0
## 90 6 1 -1 -1 1 41.0
## 91 7 -1 1 -1 1 14.0
## 92 1 1 1 -1 1 21.5
## 93 2 -1 -1 1 1 10.5
## 94 3 1 -1 1 1 6.5
## 95 4 -1 1 1 1 0.0
## 96 5 1 1 1 1 15.5
## 97 6 -1 -1 -1 -1 24.0
## 98 7 1 -1 -1 -1 16.0
## 99 1 -1 1 -1 -1 0.0
## 100 2 1 1 -1 -1 0.0
## 101 3 -1 -1 1 -1 0.0
## 102 4 1 -1 1 -1 4.5
## 103 5 -1 1 1 -1 1.0
## 104 6 1 1 1 -1 4.0
## 105 7 -1 -1 -1 1 6.5
## 106 1 1 -1 -1 1 18.0
## 107 2 -1 1 -1 1 5.0
## 108 3 1 1 -1 1 7.0
## 109 4 -1 -1 1 1 10.0
## 110 5 1 -1 1 1 32.5
## 111 6 -1 1 1 1 18.5
## 112 7 1 1 1 1 8.0## Warning in halfnormal.lm(model5): halfnormal not recommended for models with
## more residual df than model df##
## Significant effects (alpha=0.05, Lenth method):## [1] e70 e81 e91 A3
Factor A = length 10ft = -1 30ft = 1
Factor B = Type of Putter mallet = -1 cavity-back = 1
Factor C = Break of Putter Straight = -1 Breaking = 1
Factor D = Slope of Putt level = -1 downhill = 1
6.36 \(2^4\) Factorial Design
##
## Significant effects (alpha=0.05, Lenth method):## [1] A2 B2 A2:B2 A2:B2:C2
## Df Sum Sq Mean Sq F value Pr(>F)
## A2 1 159.83 159.83 1563.061 1.84e-10 ***
## B2 1 36.09 36.09 352.937 6.66e-08 ***
## C2 1 0.78 0.78 7.616 0.02468 *
## A2:B2 1 18.30 18.30 178.933 9.33e-07 ***
## A2:C2 1 1.42 1.42 13.907 0.00579 **
## B2:C2 1 0.84 0.84 8.232 0.02085 *
## A2:B2:C2 1 1.90 1.90 18.556 0.00259 **
## Residuals 8 0.82 0.10
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## hat values (leverages) are all = 0.5
## and there are no factor predictors; no plot no. 5
a. The significant main effects are A and B. The significant interactions effects are AB, ABC.
b. The model is inadequate because the normal probability plot is not desirable because the plot has some curviture to it.
##
## Significant effects (alpha=0.05, Lenth method):## [1] A2 B2 A2:B2:C2
## Df Sum Sq Mean Sq F value Pr(>F)
## A2 1 10.572 10.572 1994.556 6.98e-11 ***
## B2 1 1.580 1.580 298.147 1.29e-07 ***
## C2 1 0.001 0.001 0.124 0.73386
## A2:B2 1 0.010 0.010 1.839 0.21207
## A2:C2 1 0.025 0.025 4.763 0.06063 .
## B2:C2 1 0.000 0.000 0.054 0.82223
## A2:B2:C2 1 0.064 0.064 12.147 0.00826 **
## Residuals 8 0.042 0.005
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Df Sum Sq Mean Sq F value Pr(>F)
## A2 1 10.572 10.572 962.9 1.41e-13 ***
## B2 1 1.580 1.580 143.9 2.09e-08 ***
## Residuals 13 0.143 0.011
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## hat values (leverages) are all = 0.5
## and there are no factor predictors; no plot no. 5
The significant interaction effects after the transformation are A, B, and ABC.
d.
6.39 \(2^5\) Factorial Design
##
## Significant effects (alpha=0.05, Lenth method):## [1] D1 E1 A1:D1 A1 D1:E1 B1:E1 A1:B1 A1:B1:E1
##
## [9] A1:E1 A1:D1:E1
## Df Sum Sq Mean Sq F value Pr(>F)
## A1 1 83.56 83.56 57.233 1.14e-06 ***
## B1 1 0.06 0.06 0.041 0.841418
## D1 1 285.78 285.78 195.742 2.16e-10 ***
## E1 1 153.17 153.17 104.910 1.97e-08 ***
## A1:B1 1 48.93 48.93 33.514 2.77e-05 ***
## A1:D1 1 88.88 88.88 60.875 7.66e-07 ***
## B1:D1 1 0.01 0.01 0.004 0.950618
## A1:E1 1 33.76 33.76 23.126 0.000193 ***
## B1:E1 1 52.71 52.71 36.103 1.82e-05 ***
## D1:E1 1 61.80 61.80 42.328 7.24e-06 ***
## A1:B1:D1 1 3.82 3.82 2.613 0.125501
## A1:B1:E1 1 44.96 44.96 30.794 4.40e-05 ***
## A1:D1:E1 1 26.01 26.01 17.815 0.000650 ***
## B1:D1:E1 1 0.05 0.05 0.035 0.854935
## A1:B1:D1:E1 1 5.31 5.31 3.634 0.074735 .
## Residuals 16 23.36 1.46
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## hat values (leverages) are all = 0.5
## and there are no factor predictors; no plot no. 5
a. The significant main effects are A,D,E. There are significant interaction effects: AD, DE, AB, ABE, AE, ADE.
b. The residual plots do not show any violations to the assumptions of normalness and constance variance.
c. The non-significant factor is Factor C. When you remove Factor C from the experiment, it is now a 2^4 factorial design. After looking at the ANOVA table, same factors are significant.
## Df Sum Sq Mean Sq F value Pr(>F)
## A1 1 83.56 83.56 57.233 1.14e-06 ***
## B1 1 0.06 0.06 0.041 0.841418
## D1 1 285.78 285.78 195.742 2.16e-10 ***
## E1 1 153.17 153.17 104.910 1.97e-08 ***
## A1:B1 1 48.93 48.93 33.514 2.77e-05 ***
## A1:D1 1 88.88 88.88 60.875 7.66e-07 ***
## B1:D1 1 0.01 0.01 0.004 0.950618
## A1:E1 1 33.76 33.76 23.126 0.000193 ***
## B1:E1 1 52.71 52.71 36.103 1.82e-05 ***
## D1:E1 1 61.80 61.80 42.328 7.24e-06 ***
## A1:B1:D1 1 3.82 3.82 2.613 0.125501
## A1:B1:E1 1 44.96 44.96 30.794 4.40e-05 ***
## A1:D1:E1 1 26.01 26.01 17.815 0.000650 ***
## B1:D1:E1 1 0.05 0.05 0.035 0.854935
## A1:B1:D1:E1 1 5.31 5.31 3.634 0.074735 .
## Residuals 16 23.36 1.46
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1