One Manova & Two Way Manova
Fernando Christian
2024-10-28
One Way Manova
Input Data
Data berikut merupakan data yang bersumber dari web kaggle.com terkait hasil nilai tiga tes pada mata pelajaran sejarah geografi dari beberapa siswa-siswi.
data <- read.csv("C:/Users/wartw/OneDrive/Documents/ADM/Students Annual Score in History geography subject.csv");data## Gender Test_01 Exam_01 Test_02 Exam_02 Test_03 Exam_03 Annual_Score Success
## 1 F 72.50 93.75 81.25 86.25 100.00 86.25 87.36 1
## 2 F 68.75 81.25 65.00 56.25 90.00 71.25 71.25 1
## 3 F 67.50 58.75 42.50 45.00 85.00 50.00 55.83 1
## 4 F 58.75 87.50 75.00 76.25 100.00 81.25 80.42 1
## 5 F 90.00 83.75 70.00 93.75 90.00 88.75 86.94 1
## 6 F 36.25 36.25 48.75 62.50 85.00 75.00 57.50 1
## 7 F 22.50 32.50 17.50 7.50 70.00 65.00 35.56 0
## 8 F 23.75 71.25 57.50 67.50 97.50 92.50 71.25 1
## 9 F 45.00 52.50 68.75 40.00 87.50 68.75 58.19 1
## 10 M 30.00 56.25 28.75 53.75 52.50 42.50 46.25 0
## 11 F 35.00 15.00 31.25 16.25 90.00 35.00 32.08 0
## 12 M 76.25 82.50 65.00 70.00 87.50 83.75 77.92 1
## 13 M 88.75 85.00 88.75 98.75 100.00 88.75 91.39 1
## 14 M 40.00 61.25 62.50 50.00 65.00 75.00 60.00 1
## 15 F 65.00 72.50 56.25 86.25 90.00 91.25 79.03 1
## 16 F 83.75 73.75 30.00 55.00 100.00 76.25 69.31 1
## 17 F 37.50 66.25 42.50 51.25 92.50 75.00 61.94 1
## 18 F 78.75 55.00 77.50 36.25 85.00 40.00 55.97 1
## 19 M 77.50 81.25 53.75 91.25 100.00 95.00 85.14 1
## 20 M 97.50 80.00 62.50 78.75 85.00 68.75 77.78 1
## 21 F 46.25 65.00 31.25 70.00 100.00 93.75 70.56 1
## 22 F 52.50 86.25 52.50 45.00 62.50 72.50 63.89 1
## 23 M 50.00 56.25 48.75 41.25 87.50 80.00 60.14 1
## 24 F 77.50 70.00 21.25 42.50 100.00 73.75 63.47 1
## 25 M 80.00 80.00 82.50 90.00 100.00 85.00 85.83 1
## 26 F 77.50 78.75 83.75 83.75 100.00 81.25 83.19 1
## 27 F 26.25 77.50 22.50 75.00 85.00 90.00 68.75 1
## 28 F 98.75 85.00 90.00 87.50 100.00 92.50 90.97 1
## 29 M 40.00 71.25 45.00 67.50 90.00 92.50 70.83 1
## 30 M 73.75 78.75 63.75 61.25 97.50 85.00 76.11 1
## 31 M 58.75 56.25 37.50 26.25 80.00 55.00 50.14 1
## 32 F 87.50 92.50 88.75 93.75 100.00 98.75 94.03 1
## 33 M 45.00 76.25 45.00 25.00 100.00 87.50 63.06 1
## 34 F 33.75 86.25 55.00 71.25 100.00 97.50 77.64 1
## 35 F 33.75 63.75 23.75 51.25 75.00 62.50 54.17 1
## 36 M 36.25 72.50 48.75 58.75 75.00 87.50 66.39 1
## 37 M 47.50 82.50 46.25 62.50 92.50 71.25 68.75 1
## 38 F 42.50 65.00 83.75 82.50 100.00 95.00 79.03 1
## 39 F 35.00 55.00 70.00 57.50 100.00 71.25 63.61 1
## 40 M 66.25 71.25 47.50 68.75 100.00 95.00 75.97 1
## 41 M 62.50 70.00 16.25 26.25 0.00 57.50 42.92 0
## 42 F 51.25 58.75 51.25 60.00 97.50 96.25 70.00 1
## 43 M 67.50 57.50 71.25 37.50 90.00 65.00 60.97 1
## 44 F 75.00 73.75 68.75 78.75 85.00 75.00 75.97 1
## 45 F 80.00 88.75 50.00 75.00 100.00 95.00 83.06 1
## 46 F 65.00 55.00 27.50 28.75 75.00 62.50 51.11 1
## 47 M 62.50 58.75 60.00 35.00 72.50 40.00 51.39 1
## 48 F 45.00 60.00 30.00 38.75 42.50 61.25 48.61 0
## 49 F 75.00 50.00 71.25 27.50 50.00 22.50 44.03 0
## 50 M 56.25 63.00 40.00 27.50 55.00 77.50 54.14 1
## 51 F 73.75 56.25 58.75 37.50 70.00 55.00 55.56 1
## 52 F 58.75 53.75 38.75 36.25 60.00 40.00 46.39 0
## 53 F 68.75 58.75 90.00 40.00 100.00 80.00 68.47 1
## 54 F 40.00 60.00 27.50 32.50 62.50 31.25 41.94 0
## 55 F 60.00 97.50 68.75 80.00 100.00 77.50 82.08 1
## 56 F 90.00 68.75 35.00 57.50 75.00 65.00 64.72 1
## 57 F 71.25 73.75 47.50 62.50 65.00 61.25 64.31 1
## 58 F 80.00 71.25 61.25 50.00 100.00 86.25 72.92 1
## 59 F 62.50 45.00 48.75 45.00 62.50 36.25 47.36 0
## 60 F 76.25 90.00 87.50 90.00 100.00 65.00 83.75 1
## 61 F 52.50 55.00 37.50 28.75 50.00 28.75 40.56 0
## 62 M 58.75 88.75 70.00 51.25 80.00 78.75 71.81 1
## 63 F 77.50 65.00 80.00 62.50 100.00 95.00 78.06 1
## 64 F 40.00 33.75 87.50 31.25 100.00 58.75 52.78 1
## 65 F 100.00 86.25 100.00 95.00 100.00 97.50 95.28 1
## 66 M 37.50 50.00 45.00 55.00 62.50 72.50 55.56 1
## 67 F 81.25 88.75 76.25 0.00 85.00 37.50 55.00 1
## 68 M 53.75 61.25 57.50 50.00 75.00 60.00 58.75 1
## 69 M 63.75 72.50 45.00 62.50 97.50 88.75 72.64 1
## 70 F 56.25 32.50 36.25 25.00 75.00 6.25 32.78 0
## 71 M 38.75 78.75 23.75 38.75 95.00 92.50 64.17 1
## 72 M 15.00 57.50 68.75 32.50 82.50 28.75 44.86 0
## 73 M 27.50 81.25 76.25 75.00 82.50 93.75 76.25 1
## 74 F 60.00 70.00 65.00 18.75 50.00 37.50 47.50 0
## 75 M 60.00 57.50 47.50 45.00 75.00 78.75 60.56 1
## 76 F 78.75 41.25 46.25 50.00 92.50 70.00 60.00 1
## 77 F 91.25 96.25 95.00 86.25 100.00 95.00 93.47 1
## 78 M 67.50 71.25 57.50 60.00 67.50 71.25 66.39 1
## 79 F 72.50 75.00 46.25 57.50 70.00 82.50 68.75 1
## 80 F 98.75 90.00 80.00 93.75 100.00 95.00 92.92 1
## 81 F 55.00 71.25 52.50 28.75 100.00 76.25 62.22 1
## 82 F 53.75 63.75 75.00 57.50 30.00 30.00 51.25 1
## 83 F 72.50 82.50 100.00 95.00 81.25 81.25 85.69 1
## 84 M 52.50 62.50 65.00 50.00 100.00 30.00 55.83 1
## 85 F 55.00 50.00 67.50 41.25 100.00 23.75 50.28 1
## 86 M 7.50 1.25 10.00 8.75 38.75 38.75 17.08 0
## 87 F 40.00 47.50 30.00 8.75 100.00 23.75 36.67 0
## 88 F 35.00 21.25 27.50 2.50 17.50 17.50 18.06 0
## 89 M 21.25 15.00 50.00 55.00 90.00 27.50 39.58 0
## 90 F 27.50 12.50 72.50 17.50 100.00 15.00 32.22 0
## 91 F 11.25 2.50 5.00 13.75 8.75 8.75 8.33 0
## 92 F 26.25 21.25 67.50 18.75 100.00 20.00 34.86 0
## 93 M 10.00 2.50 0.00 0.00 3.75 3.75 2.92 0
## 94 F 21.25 11.25 27.50 15.00 1.25 1.25 11.67 0
## 95 F 80.00 68.75 92.50 78.75 100.00 72.50 79.17 1
## 96 F 37.50 35.00 85.00 33.75 100.00 18.75 44.17 0
## 97 F 25.00 50.00 55.00 38.75 100.00 18.75 43.89 0
## 98 M 18.75 10.00 30.00 35.00 8.75 8.75 18.33 0
## 99 M 5.00 5.00 15.00 11.25 1.25 1.25 6.25 0
## 100 F 37.50 35.00 82.50 12.50 100.00 13.75 38.06 0
## 101 F 63.75 63.75 95.00 88.75 100.00 52.50 74.31 1
## 102 M 28.75 20.00 10.00 11.25 25.00 25.00 19.58 0
## 103 F 45.00 53.75 30.00 16.25 100.00 35.00 42.78 0
## 104 F 72.50 45.00 45.00 25.00 28.75 28.75 38.19 0
## 105 F 36.25 20.00 52.50 26.25 100.00 20.00 35.69 0
## 106 F 5.00 7.50 15.00 12.50 15.00 15.00 11.67 0
## 107 F 42.50 32.50 65.00 22.50 100.00 50.00 46.39 0
## 108 F 43.75 18.75 50.00 12.50 100.00 18.75 32.64 0
## 109 F 38.75 16.25 15.00 20.00 100.00 11.25 27.64 0
## 110 F 38.75 40.00 57.50 51.25 100.00 26.25 47.92 0
## 111 F 42.50 63.75 82.50 57.50 100.00 18.75 56.11 1
## 112 M 16.25 58.75 37.50 17.50 70.00 22.50 35.69 0
## 113 F 10.00 31.25 0.00 46.25 57.50 57.50 37.50 0
## 114 F 46.25 36.25 32.50 16.25 100.00 32.50 38.75 0
## 115 F 60.00 72.50 46.25 53.75 43.75 43.75 54.44 1
## 116 F 47.50 38.75 70.00 45.00 100.00 37.50 51.11 1
## 117 F 60.00 21.25 82.50 48.75 10.00 10.00 34.72 0
## 118 F 50.00 33.75 80.00 40.00 20.00 20.00 37.50 0
## 119 F 25.00 25.00 77.50 26.25 100.00 43.75 43.61 0
## 120 F 55.00 55.00 0.00 0.00 100.00 12.50 32.22 0
## 121 F 35.00 43.75 80.00 33.75 1.25 1.25 30.42 0
## 122 F 70.00 70.00 92.50 90.00 21.25 21.25 60.69 1
## 123 F 22.50 17.50 82.50 18.75 100.00 30.00 37.50 0
## 124 F 2.50 12.50 0.00 2.50 1.25 1.25 4.03 0
## 125 M 11.25 10.00 10.00 12.50 90.00 10.00 19.58 0
## 126 F 63.75 40.00 80.00 42.50 43.75 43.75 48.89 0
## 127 M 38.75 65.00 55.00 58.75 100.00 65.00 63.47 1
## 128 F 51.25 60.00 67.50 58.75 52.50 52.50 57.08 1
## 129 M 63.75 48.75 80.00 45.00 100.00 81.25 65.97 1
## 130 F 32.50 32.50 0.00 11.25 26.25 26.25 22.08 0
## 131 M 51.25 43.75 27.50 28.75 41.25 41.25 38.61 0
## 132 F 90.00 40.00 57.50 21.25 23.75 23.75 37.92 0
## 133 F 68.75 47.50 87.50 42.50 53.75 53.75 55.28 1
## 134 F 61.25 91.25 72.50 68.75 86.25 86.25 79.17 1
## 135 M 77.50 43.75 70.00 60.00 72.50 72.50 63.61 1
## 136 F 47.50 15.00 0.00 13.75 53.75 53.75 29.58 0
## 137 F 80.00 81.25 75.00 93.75 83.75 83.75 84.03 1
## 138 M 40.00 40.00 35.00 26.25 100.00 12.50 36.94 0
## 139 M 57.50 61.25 62.50 35.00 100.00 75.00 62.50 1
## 140 F 76.25 62.50 80.00 57.50 36.25 36.25 56.11 1
## 141 F 67.50 71.25 75.00 75.00 83.75 83.75 76.25 1
## 142 M 56.25 76.25 97.50 75.00 100.00 65.00 76.25 1
## 143 F 55.00 72.50 60.00 61.25 55.00 55.00 60.83 1
## 144 F 40.00 47.50 65.00 40.00 33.75 33.75 42.36 0
## 145 F 55.00 38.75 12.50 28.75 100.00 40.00 42.50 0
## 146 F 23.75 37.50 10.00 26.25 100.00 11.25 31.53 0
## 147 M 42.50 46.25 57.50 35.00 35.00 35.00 40.83 0
## 148 F 83.75 70.00 35.00 78.75 62.50 62.50 67.08 1
## 149 F 71.25 63.75 80.00 66.25 76.25 76.25 71.11 1
## 150 F 60.00 38.75 55.00 28.75 35.00 35.00 39.44 0
## 151 M 32.50 3.75 42.50 3.75 1.25 1.25 10.42 0
## 152 M 55.00 51.25 40.00 0.00 26.25 26.25 30.69 0
## 153 F 80.00 70.00 100.00 66.25 71.25 71.25 74.03 1
## 154 F 97.50 76.25 100.00 76.25 68.75 68.75 78.75 1
## 155 F 52.50 65.00 0.00 46.25 66.25 66.25 52.64 1
## 156 F 47.50 21.25 72.50 18.75 6.25 6.25 24.31 0
## 157 M 55.00 40.00 55.00 57.50 35.00 35.00 45.56 0
## 158 F 73.75 36.25 65.00 60.00 40.00 40.00 50.14 1
## 159 F 67.50 26.25 15.00 18.75 26.25 26.25 27.92 0
## 160 F 51.25 38.75 65.00 13.75 100.00 32.50 42.92 0
## 161 F 70.00 61.25 60.00 33.75 100.00 31.25 53.61 1
## 162 F 30.00 21.25 67.50 40.00 0.00 0.00 24.44 0
## 163 M 43.75 41.25 70.00 22.50 100.00 35.00 45.69 0
## 164 M 28.75 63.75 47.50 12.50 27.50 27.50 34.58 0
## 165 F 51.25 15.00 55.00 7.50 11.25 11.25 20.56 0
## 166 F 97.50 100.00 0.00 77.50 62.50 62.50 71.11 1
## 167 F 60.00 62.50 72.50 28.75 41.25 41.25 48.75 0
## 168 F 85.00 82.50 80.00 57.50 45.00 45.00 64.44 1
## 169 M 28.75 21.25 42.50 28.75 20.00 20.00 25.69 0
## 170 M 63.75 53.75 25.00 43.75 26.25 26.25 40.28 0
## 171 F 46.25 32.50 15.00 21.25 35.00 35.00 30.42 0
## 172 F 95.00 78.75 97.50 95.00 100.00 91.25 91.39 1
## 173 F 67.50 71.25 87.50 57.50 65.00 65.00 67.50 1
## 174 F 67.50 53.75 52.50 0.00 55.00 55.00 43.61 0
## 175 F 38.75 30.00 45.00 41.25 100.00 47.50 46.81 0
## 176 M 47.50 68.75 90.00 51.25 25.00 25.00 50.28 1
## 177 M 73.75 82.50 0.00 78.75 78.75 78.75 70.28 1
## 178 F 71.25 93.75 80.00 91.25 100.00 72.50 85.14 1
## 179 F 90.00 87.50 95.00 88.75 86.25 86.25 88.47 1
## 180 F 57.50 42.50 60.00 21.25 100.00 36.25 46.39 0
## 181 F 35.00 23.75 30.00 23.75 100.00 56.25 41.39 0
## 182 F 66.25 53.75 95.00 86.25 45.00 45.00 64.03 1
## 183 F 63.75 76.25 72.50 46.25 100.00 63.75 67.64 1
## 184 M 52.50 33.75 27.50 26.25 30.00 30.00 32.22 0
## 185 F 5.00 77.50 60.00 63.75 52.50 52.50 56.11 1
## 186 M 5.00 47.50 32.50 13.75 61.25 61.25 38.19 0
## 187 F 42.50 47.50 27.50 18.75 27.50 27.50 31.67 0
## 188 F 52.50 77.50 57.50 65.00 60.00 60.00 63.89 1
## 189 F 85.00 88.75 92.50 81.25 100.00 81.25 86.67 1
## 190 M 83.75 95.00 77.50 72.50 100.00 81.25 84.31 1
## 191 F 30.00 50.00 17.50 10.00 100.00 32.50 36.94 0
## 192 F 68.75 40.00 72.50 15.00 27.50 27.50 37.08 0
## 193 M 65.00 66.25 77.50 68.75 52.50 52.50 63.33 1
## 194 F 66.25 48.75 40.00 12.50 50.00 0.00 30.97 0
## 195 F 26.25 51.25 0.00 31.25 31.25 31.25 31.67 0
## 196 M 85.00 100.00 92.50 63.75 83.75 83.75 84.03 1
## 197 F 62.50 28.75 17.50 26.25 22.50 22.50 28.61 0
## 198 F 67.50 66.25 60.00 22.50 100.00 43.75 54.72 1
## 199 M 60.00 60.00 27.50 20.00 31.25 31.25 37.92 0
## 200 F 70.00 66.25 67.50 26.25 100.00 30.00 53.61 1
## 201 F 20.00 36.25 35.00 37.50 17.50 17.50 28.33 0
## 202 M 66.25 42.50 52.50 13.75 23.75 23.75 33.61 0
## 203 F 65.00 50.00 45.00 36.25 100.00 32.50 49.72 0
## 204 F 92.50 95.00 95.00 87.50 75.00 75.00 86.39 1
## 205 F 71.25 63.75 85.00 85.00 60.00 60.00 70.42 1
## 206 F 65.00 36.25 37.50 18.75 100.00 33.75 42.22 0
## 207 F 77.50 58.75 22.50 42.50 100.00 42.50 54.17 1
## 208 F 61.25 47.50 72.50 52.50 46.25 46.25 52.50 1
## 209 M 25.00 32.50 0.00 17.50 30.00 30.00 23.89 0
## 210 M 33.75 56.25 10.00 17.50 100.00 48.75 43.19 0
## 211 F 56.25 40.00 97.50 22.50 46.25 46.25 46.39 0
## 212 M 66.25 53.75 12.50 25.00 52.50 52.50 43.75 0
## 213 M 35.00 38.75 0.00 37.50 23.75 23.75 28.75 0
## 214 F 27.50 7.50 0.00 7.50 0.00 0.00 6.39 0
## 215 M 17.50 48.75 67.50 62.50 40.00 40.00 47.50 0
## 216 F 0.00 61.25 0.00 0.00 0.00 0.00 13.61 0
## 217 F 51.25 26.25 65.00 18.75 40.00 40.00 36.25 0
## 218 F 25.00 18.75 85.00 26.25 37.50 37.50 34.72 0
## 219 M 30.00 18.75 45.00 16.25 37.50 37.50 28.61 0
## 220 M 31.25 38.75 70.00 47.50 100.00 41.25 50.69 1
## 221 M 26.25 55.00 37.50 40.00 36.25 36.25 40.28 0
## 222 M 23.75 25.00 0.00 13.75 32.50 32.50 22.08 0
## 223 F 50.00 75.00 100.00 83.75 51.25 51.25 69.03 1
## 224 M 32.50 43.75 45.00 20.00 100.00 50.00 45.00 0
## 225 F 23.75 25.00 82.50 13.75 16.25 16.25 25.83 0
## 226 M 53.75 58.75 75.00 40.00 58.75 58.75 55.83 1
## 227 M 50.00 52.50 60.00 13.75 13.75 13.75 31.53 0
## 228 M 53.75 76.25 60.00 40.00 45.00 45.00 53.47 1
## 229 M 55.00 50.00 85.00 31.25 100.00 51.25 56.11 1
## 230 M 35.00 47.50 0.00 0.00 0.00 26.25 20.28 0
## 231 M 26.25 46.25 42.50 22.50 42.50 42.50 37.08 0
## 232 M 38.75 60.00 87.50 63.75 43.75 43.75 56.11 1
## 233 M 25.00 31.25 32.50 7.50 0.00 0.00 15.00 0
## 234 M 35.00 92.50 90.00 73.75 68.75 68.75 73.75 1
## 235 M 32.50 20.00 62.50 30.00 22.50 22.50 29.17 0
## 236 F 81.25 39.38 56.25 31.88 86.90 36.25 48.82 0
## 237 F 90.00 46.88 57.50 41.88 90.00 45.00 56.11 1
## 238 M 43.10 15.00 16.25 0.00 0.00 0.00 9.93 0
## 239 F 26.25 9.38 21.25 7.50 39.40 2.50 13.96 0
## 240 F 71.90 38.75 73.75 20.62 72.50 11.25 39.93 0
## 241 M 58.75 21.88 18.75 15.00 11.25 6.25 19.44 0
## 242 F 81.25 17.50 48.75 18.75 55.00 16.25 32.22 0
## 243 F 41.90 10.00 36.25 2.50 16.90 13.12 16.26 0
## 244 M 46.90 15.00 17.50 5.00 26.90 0.00 14.59 0
## 245 F 71.25 25.00 32.50 14.38 66.25 15.00 30.97 0
## 246 M 40.60 26.25 16.25 16.88 6.25 33.75 24.09 0
## 247 F 53.10 23.75 6.25 12.50 5.00 0.00 15.21 0
## 248 F 68.75 28.12 18.75 6.88 10.60 10.00 20.90 0
## 249 F 79.40 45.00 32.50 31.25 83.15 21.88 43.48 0
## 250 F 55.60 32.50 33.75 3.12 35.00 0.00 21.73 0
## 251 F 78.75 22.50 32.50 18.75 53.15 18.12 31.46 0
## 252 M 51.25 22.50 40.00 8.75 31.90 6.25 22.02 0
## 253 M 47.50 21.25 23.75 20.62 62.50 16.25 27.78 0
## 254 M 3.75 4.38 37.50 29.38 65.00 16.88 23.06 0
## 255 F 83.75 30.62 40.00 22.50 76.25 34.38 41.67 0
## 256 M 40.60 28.12 37.50 14.38 73.10 30.00 32.91 0
## 257 F 83.75 45.00 75.00 43.12 93.75 47.50 58.19 1
## 258 F 81.25 14.38 27.50 10.62 61.90 31.25 31.46 0
## 259 F 28.75 20.62 21.25 8.12 9.40 2.50 13.54 0
## 260 F 60.00 23.12 35.00 11.25 33.75 15.00 25.28 0
## 261 F 60.60 37.50 57.50 32.50 81.25 30.00 44.37 0
## 262 F 51.90 35.00 26.25 18.12 42.50 20.00 29.66 0
## 263 F 50.60 32.50 45.00 21.25 50.00 17.50 32.01 0
## 264 F 24.40 22.50 23.75 13.75 34.40 10.00 19.45 0
## 265 F 24.40 17.50 40.00 10.62 31.90 8.75 18.89 0
## 266 F 73.75 24.38 21.25 27.50 43.75 20.00 31.39 0
## 267 M 73.10 35.62 40.00 17.50 73.10 21.88 37.36 0
## 268 F 60.00 14.38 25.00 15.00 55.60 7.50 23.82 0
## 269 F 41.25 25.00 57.50 34.38 51.25 10.62 32.22 0
## 270 F 73.75 24.38 32.50 27.50 75.00 20.62 36.25 0
## 271 F 63.75 32.50 35.00 11.88 36.90 13.75 27.99 0
## 272 F 78.10 28.12 48.75 16.88 68.75 15.00 35.07 0
## 273 F 65.60 23.75 26.25 21.25 57.50 13.12 29.51 0
## 274 F 75.60 38.12 51.25 20.00 78.75 25.00 41.32 0
## 275 M 21.25 16.88 16.25 0.62 26.25 2.50 11.53 0
## 276 M 70.00 18.75 27.50 10.62 36.25 9.38 23.47 0
## 277 F 68.75 16.25 45.00 21.25 62.50 20.62 32.50 0
## 278 M 27.50 5.00 25.00 26.25 72.50 17.50 24.72 0
## 279 M 72.50 16.25 45.00 21.88 80.00 18.75 34.58 0
## 280 F 85.00 42.50 86.25 36.88 67.50 38.12 52.64 1
## 281 F 86.25 43.75 70.00 40.00 100.00 43.12 56.67 1
## 282 F 61.25 15.62 33.75 13.12 75.00 18.12 29.31 0
## 283 F 8.75 5.00 47.50 21.88 32.50 18.12 19.86 0
## 284 F 87.50 36.25 80.00 26.88 100.00 36.88 51.94 1
## 285 M 45.00 4.38 20.00 6.25 25.00 13.75 15.42 0
## 286 F 25.00 8.75 42.50 5.00 20.00 23.75 18.06 0
## 287 F 78.75 26.88 73.75 33.12 65.00 28.12 43.75 0
## 288 F 92.50 43.12 90.00 48.12 100.00 36.25 59.72 1
## 289 F 28.75 8.12 20.00 18.12 40.00 13.75 18.75 0
## 290 F 95.00 43.75 100.00 49.38 100.00 44.38 63.33 1
## 291 F 40.00 16.88 66.25 19.38 80.00 24.38 34.17 0
## 292 F 70.00 41.25 65.00 39.38 50.00 35.00 46.25 0
## 293 F 37.50 12.50 55.00 18.12 87.50 30.62 33.61 0
## 294 F 58.75 5.00 38.75 27.50 25.00 23.12 25.97 0
## 295 F 98.75 43.75 86.25 44.38 100.00 30.62 58.06 1
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## 596 M 72.50 41.88 47.50 35.62 82.50 43.75 49.44 0
## 597 F 97.50 48.12 77.50 45.62 100.00 48.12 62.08 1
## 598 F 86.25 50.00 67.50 39.38 95.00 43.12 57.08 1
## 599 F 98.75 50.00 85.00 46.25 96.25 49.38 63.47 1
## 600 F 77.50 40.00 56.25 21.25 82.50 40.62 46.67 0
## 601 F 40.00 37.50 46.25 38.12 70.00 43.12 43.75 0
## 602 F 93.75 46.25 92.50 36.25 98.75 45.62 60.14 1
## 603 F 100.00 47.50 100.00 43.75 100.00 45.62 63.75 1
## 604 M 67.50 41.88 30.00 28.12 95.00 44.38 46.81 0
## 605 M 91.25 46.25 38.75 36.25 62.50 18.12 43.75 0
## 606 F 75.00 49.38 50.00 36.25 100.00 44.38 53.89 1
## 607 M 55.00 41.88 45.00 30.62 95.00 43.75 47.50 0
## 608 F 92.50 42.50 56.25 36.88 92.50 41.25 53.61 1
## 609 F 41.25 40.62 50.00 25.00 71.25 36.25 40.69 0
## 610 M 77.50 36.88 76.25 37.50 93.75 43.12 53.61 1
## 611 F 88.75 43.75 100.00 45.62 100.00 47.50 62.50 1
## 612 F 50.00 43.12 71.25 32.50 76.25 35.00 46.53 0
## 613 F 88.75 46.88 100.00 46.88 95.00 48.75 63.19 1
## 614 F 83.75 45.00 50.00 36.88 98.75 32.50 51.25 1
## 615 F 82.50 39.38 61.25 36.25 77.50 46.25 51.67 1
## 616 F 96.25 48.75 100.00 28.12 100.00 44.38 59.86 1
## 617 M 60.00 37.50 63.75 47.50 98.75 41.88 52.92 1
## 618 F 61.25 42.50 47.50 36.25 88.75 43.12 49.03 0
## 619 M 71.25 21.88 40.00 12.50 92.50 41.88 39.58 0
## 620 M 83.75 46.25 65.00 33.75 87.50 40.62 53.06 1
## 621 F 92.50 44.38 65.00 40.62 97.50 50.00 58.33 1
## 622 M 78.75 34.38 46.25 23.12 51.25 34.38 40.00 0
## 623 F 73.75 45.62 80.00 32.50 91.25 45.00 54.58 1
## 624 F 77.50 39.38 67.50 21.25 75.00 45.00 47.92 0
## 625 F 35.00 43.75 71.25 25.00 76.25 42.50 45.00 0
## 626 F 97.50 45.62 75.00 31.25 97.50 50.00 58.19 1
## 627 F 100.00 48.75 96.25 43.12 95.00 47.50 63.33 1
## 628 F 67.50 36.25 63.75 6.25 50.00 20.62 34.17 0
## 629 F 72.50 42.50 81.25 42.50 100.00 41.25 56.25 1
## 630 F 100.00 47.50 100.00 48.75 100.00 50.00 65.83 1
## 631 F 86.25 43.12 63.75 30.62 93.75 40.62 52.50 1
## 632 F 85.00 46.25 78.75 28.12 91.25 43.12 54.44 1
## 633 M 62.50 36.88 28.75 15.62 83.75 40.00 40.00 0
## 634 F 100.00 46.25 72.50 31.25 98.75 44.38 57.22 1
## X
## 1 NA
## 2 NA
## 3 NA
## 4 NA
## 5 NA
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## 630 NA
## 631 NA
## 632 NA
## 633 NA
## 634 NAMemotong Variabel yang Tidak Digunakan
Dikarenakan hanya variabel gender dan variabel tes 1, tes 2, dan tes 3 saja yang digunakan, maka variabel lainnya akan dieliminasi.
data1 <- data[,-c(3,5,7,8,9,10)];data1## Gender Test_01 Test_02 Test_03
## 1 F 72.50 81.25 100.00
## 2 F 68.75 65.00 90.00
## 3 F 67.50 42.50 85.00
## 4 F 58.75 75.00 100.00
## 5 F 90.00 70.00 90.00
## 6 F 36.25 48.75 85.00
## 7 F 22.50 17.50 70.00
## 8 F 23.75 57.50 97.50
## 9 F 45.00 68.75 87.50
## 10 M 30.00 28.75 52.50
## 11 F 35.00 31.25 90.00
## 12 M 76.25 65.00 87.50
## 13 M 88.75 88.75 100.00
## 14 M 40.00 62.50 65.00
## 15 F 65.00 56.25 90.00
## 16 F 83.75 30.00 100.00
## 17 F 37.50 42.50 92.50
## 18 F 78.75 77.50 85.00
## 19 M 77.50 53.75 100.00
## 20 M 97.50 62.50 85.00
## 21 F 46.25 31.25 100.00
## 22 F 52.50 52.50 62.50
## 23 M 50.00 48.75 87.50
## 24 F 77.50 21.25 100.00
## 25 M 80.00 82.50 100.00
## 26 F 77.50 83.75 100.00
## 27 F 26.25 22.50 85.00
## 28 F 98.75 90.00 100.00
## 29 M 40.00 45.00 90.00
## 30 M 73.75 63.75 97.50
## 31 M 58.75 37.50 80.00
## 32 F 87.50 88.75 100.00
## 33 M 45.00 45.00 100.00
## 34 F 33.75 55.00 100.00
## 35 F 33.75 23.75 75.00
## 36 M 36.25 48.75 75.00
## 37 M 47.50 46.25 92.50
## 38 F 42.50 83.75 100.00
## 39 F 35.00 70.00 100.00
## 40 M 66.25 47.50 100.00
## 41 M 62.50 16.25 0.00
## 42 F 51.25 51.25 97.50
## 43 M 67.50 71.25 90.00
## 44 F 75.00 68.75 85.00
## 45 F 80.00 50.00 100.00
## 46 F 65.00 27.50 75.00
## 47 M 62.50 60.00 72.50
## 48 F 45.00 30.00 42.50
## 49 F 75.00 71.25 50.00
## 50 M 56.25 40.00 55.00
## 51 F 73.75 58.75 70.00
## 52 F 58.75 38.75 60.00
## 53 F 68.75 90.00 100.00
## 54 F 40.00 27.50 62.50
## 55 F 60.00 68.75 100.00
## 56 F 90.00 35.00 75.00
## 57 F 71.25 47.50 65.00
## 58 F 80.00 61.25 100.00
## 59 F 62.50 48.75 62.50
## 60 F 76.25 87.50 100.00
## 61 F 52.50 37.50 50.00
## 62 M 58.75 70.00 80.00
## 63 F 77.50 80.00 100.00
## 64 F 40.00 87.50 100.00
## 65 F 100.00 100.00 100.00
## 66 M 37.50 45.00 62.50
## 67 F 81.25 76.25 85.00
## 68 M 53.75 57.50 75.00
## 69 M 63.75 45.00 97.50
## 70 F 56.25 36.25 75.00
## 71 M 38.75 23.75 95.00
## 72 M 15.00 68.75 82.50
## 73 M 27.50 76.25 82.50
## 74 F 60.00 65.00 50.00
## 75 M 60.00 47.50 75.00
## 76 F 78.75 46.25 92.50
## 77 F 91.25 95.00 100.00
## 78 M 67.50 57.50 67.50
## 79 F 72.50 46.25 70.00
## 80 F 98.75 80.00 100.00
## 81 F 55.00 52.50 100.00
## 82 F 53.75 75.00 30.00
## 83 F 72.50 100.00 81.25
## 84 M 52.50 65.00 100.00
## 85 F 55.00 67.50 100.00
## 86 M 7.50 10.00 38.75
## 87 F 40.00 30.00 100.00
## 88 F 35.00 27.50 17.50
## 89 M 21.25 50.00 90.00
## 90 F 27.50 72.50 100.00
## 91 F 11.25 5.00 8.75
## 92 F 26.25 67.50 100.00
## 93 M 10.00 0.00 3.75
## 94 F 21.25 27.50 1.25
## 95 F 80.00 92.50 100.00
## 96 F 37.50 85.00 100.00
## 97 F 25.00 55.00 100.00
## 98 M 18.75 30.00 8.75
## 99 M 5.00 15.00 1.25
## 100 F 37.50 82.50 100.00
## 101 F 63.75 95.00 100.00
## 102 M 28.75 10.00 25.00
## 103 F 45.00 30.00 100.00
## 104 F 72.50 45.00 28.75
## 105 F 36.25 52.50 100.00
## 106 F 5.00 15.00 15.00
## 107 F 42.50 65.00 100.00
## 108 F 43.75 50.00 100.00
## 109 F 38.75 15.00 100.00
## 110 F 38.75 57.50 100.00
## 111 F 42.50 82.50 100.00
## 112 M 16.25 37.50 70.00
## 113 F 10.00 0.00 57.50
## 114 F 46.25 32.50 100.00
## 115 F 60.00 46.25 43.75
## 116 F 47.50 70.00 100.00
## 117 F 60.00 82.50 10.00
## 118 F 50.00 80.00 20.00
## 119 F 25.00 77.50 100.00
## 120 F 55.00 0.00 100.00
## 121 F 35.00 80.00 1.25
## 122 F 70.00 92.50 21.25
## 123 F 22.50 82.50 100.00
## 124 F 2.50 0.00 1.25
## 125 M 11.25 10.00 90.00
## 126 F 63.75 80.00 43.75
## 127 M 38.75 55.00 100.00
## 128 F 51.25 67.50 52.50
## 129 M 63.75 80.00 100.00
## 130 F 32.50 0.00 26.25
## 131 M 51.25 27.50 41.25
## 132 F 90.00 57.50 23.75
## 133 F 68.75 87.50 53.75
## 134 F 61.25 72.50 86.25
## 135 M 77.50 70.00 72.50
## 136 F 47.50 0.00 53.75
## 137 F 80.00 75.00 83.75
## 138 M 40.00 35.00 100.00
## 139 M 57.50 62.50 100.00
## 140 F 76.25 80.00 36.25
## 141 F 67.50 75.00 83.75
## 142 M 56.25 97.50 100.00
## 143 F 55.00 60.00 55.00
## 144 F 40.00 65.00 33.75
## 145 F 55.00 12.50 100.00
## 146 F 23.75 10.00 100.00
## 147 M 42.50 57.50 35.00
## 148 F 83.75 35.00 62.50
## 149 F 71.25 80.00 76.25
## 150 F 60.00 55.00 35.00
## 151 M 32.50 42.50 1.25
## 152 M 55.00 40.00 26.25
## 153 F 80.00 100.00 71.25
## 154 F 97.50 100.00 68.75
## 155 F 52.50 0.00 66.25
## 156 F 47.50 72.50 6.25
## 157 M 55.00 55.00 35.00
## 158 F 73.75 65.00 40.00
## 159 F 67.50 15.00 26.25
## 160 F 51.25 65.00 100.00
## 161 F 70.00 60.00 100.00
## 162 F 30.00 67.50 0.00
## 163 M 43.75 70.00 100.00
## 164 M 28.75 47.50 27.50
## 165 F 51.25 55.00 11.25
## 166 F 97.50 0.00 62.50
## 167 F 60.00 72.50 41.25
## 168 F 85.00 80.00 45.00
## 169 M 28.75 42.50 20.00
## 170 M 63.75 25.00 26.25
## 171 F 46.25 15.00 35.00
## 172 F 95.00 97.50 100.00
## 173 F 67.50 87.50 65.00
## 174 F 67.50 52.50 55.00
## 175 F 38.75 45.00 100.00
## 176 M 47.50 90.00 25.00
## 177 M 73.75 0.00 78.75
## 178 F 71.25 80.00 100.00
## 179 F 90.00 95.00 86.25
## 180 F 57.50 60.00 100.00
## 181 F 35.00 30.00 100.00
## 182 F 66.25 95.00 45.00
## 183 F 63.75 72.50 100.00
## 184 M 52.50 27.50 30.00
## 185 F 5.00 60.00 52.50
## 186 M 5.00 32.50 61.25
## 187 F 42.50 27.50 27.50
## 188 F 52.50 57.50 60.00
## 189 F 85.00 92.50 100.00
## 190 M 83.75 77.50 100.00
## 191 F 30.00 17.50 100.00
## 192 F 68.75 72.50 27.50
## 193 M 65.00 77.50 52.50
## 194 F 66.25 40.00 50.00
## 195 F 26.25 0.00 31.25
## 196 M 85.00 92.50 83.75
## 197 F 62.50 17.50 22.50
## 198 F 67.50 60.00 100.00
## 199 M 60.00 27.50 31.25
## 200 F 70.00 67.50 100.00
## 201 F 20.00 35.00 17.50
## 202 M 66.25 52.50 23.75
## 203 F 65.00 45.00 100.00
## 204 F 92.50 95.00 75.00
## 205 F 71.25 85.00 60.00
## 206 F 65.00 37.50 100.00
## 207 F 77.50 22.50 100.00
## 208 F 61.25 72.50 46.25
## 209 M 25.00 0.00 30.00
## 210 M 33.75 10.00 100.00
## 211 F 56.25 97.50 46.25
## 212 M 66.25 12.50 52.50
## 213 M 35.00 0.00 23.75
## 214 F 27.50 0.00 0.00
## 215 M 17.50 67.50 40.00
## 216 F 0.00 0.00 0.00
## 217 F 51.25 65.00 40.00
## 218 F 25.00 85.00 37.50
## 219 M 30.00 45.00 37.50
## 220 M 31.25 70.00 100.00
## 221 M 26.25 37.50 36.25
## 222 M 23.75 0.00 32.50
## 223 F 50.00 100.00 51.25
## 224 M 32.50 45.00 100.00
## 225 F 23.75 82.50 16.25
## 226 M 53.75 75.00 58.75
## 227 M 50.00 60.00 13.75
## 228 M 53.75 60.00 45.00
## 229 M 55.00 85.00 100.00
## 230 M 35.00 0.00 0.00
## 231 M 26.25 42.50 42.50
## 232 M 38.75 87.50 43.75
## 233 M 25.00 32.50 0.00
## 234 M 35.00 90.00 68.75
## 235 M 32.50 62.50 22.50
## 236 F 81.25 56.25 86.90
## 237 F 90.00 57.50 90.00
## 238 M 43.10 16.25 0.00
## 239 F 26.25 21.25 39.40
## 240 F 71.90 73.75 72.50
## 241 M 58.75 18.75 11.25
## 242 F 81.25 48.75 55.00
## 243 F 41.90 36.25 16.90
## 244 M 46.90 17.50 26.90
## 245 F 71.25 32.50 66.25
## 246 M 40.60 16.25 6.25
## 247 F 53.10 6.25 5.00
## 248 F 68.75 18.75 10.60
## 249 F 79.40 32.50 83.15
## 250 F 55.60 33.75 35.00
## 251 F 78.75 32.50 53.15
## 252 M 51.25 40.00 31.90
## 253 M 47.50 23.75 62.50
## 254 M 3.75 37.50 65.00
## 255 F 83.75 40.00 76.25
## 256 M 40.60 37.50 73.10
## 257 F 83.75 75.00 93.75
## 258 F 81.25 27.50 61.90
## 259 F 28.75 21.25 9.40
## 260 F 60.00 35.00 33.75
## 261 F 60.60 57.50 81.25
## 262 F 51.90 26.25 42.50
## 263 F 50.60 45.00 50.00
## 264 F 24.40 23.75 34.40
## 265 F 24.40 40.00 31.90
## 266 F 73.75 21.25 43.75
## 267 M 73.10 40.00 73.10
## 268 F 60.00 25.00 55.60
## 269 F 41.25 57.50 51.25
## 270 F 73.75 32.50 75.00
## 271 F 63.75 35.00 36.90
## 272 F 78.10 48.75 68.75
## 273 F 65.60 26.25 57.50
## 274 F 75.60 51.25 78.75
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## 282 F 61.25 33.75 75.00
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## 308 M 72.50 52.50 42.50
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## 312 F 41.25 50.00 67.50
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## 314 M 40.00 42.50 42.50
## 315 F 52.50 63.75 90.00
## 316 F 67.50 60.00 87.50
## 317 M 75.60 72.50 90.00
## 318 F 20.60 60.00 100.00
## 319 F 38.10 45.00 10.00
## 320 M 49.40 42.50 100.00
## 321 F 29.40 50.00 95.00
## 322 F 44.40 37.50 100.00
## 323 F 45.00 30.00 100.00
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## 325 F 51.90 65.00 95.00
## 326 F 55.60 77.50 60.00
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## 328 F 63.75 55.00 42.50
## 329 F 48.75 42.50 100.00
## 330 F 71.90 35.00 100.00
## 331 F 20.00 5.00 10.00
## 332 M 46.90 5.00 2.50
## 333 F 61.90 70.00 90.00
## 334 M 41.25 30.00 0.00
## 335 F 53.10 55.00 100.00
## 336 F 82.50 100.00 100.00
## 337 F 62.50 62.50 95.00
## 338 F 66.90 47.50 100.00
## 339 M 61.25 12.50 100.00
## 340 F 98.75 97.50 100.00
## 341 M 60.60 62.50 100.00
## 342 F 81.90 100.00 0.00
## 343 M 25.00 22.50 60.00
## 344 F 88.75 77.50 100.00
## 345 F 79.40 50.00 100.00
## 346 F 61.90 80.00 100.00
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## 348 M 86.25 30.00 25.00
## 349 F 49.40 97.50 100.00
## 350 F 53.75 75.00 100.00
## 351 M 46.90 37.50 100.00
## 352 F 60.00 95.00 95.00
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## 355 F 68.75 30.00 100.00
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## 359 F 76.25 80.00 80.00
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## 361 M 50.00 47.50 15.00
## 362 F 93.75 100.00 95.00
## 363 F 100.00 87.50 100.00
## 364 F 91.25 95.00 80.00
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## 366 M 72.50 77.50 100.00
## 367 M 62.50 62.50 0.00
## 368 M 42.50 50.00 0.00
## 369 F 61.25 0.00 100.00
## 370 F 47.50 72.50 12.50
## 371 M 55.00 60.00 70.00
## 372 F 66.25 0.00 100.00
## 373 F 91.25 85.00 100.00
## 374 M 40.00 60.00 80.00
## 375 F 92.50 65.00 100.00
## 376 F 77.50 70.00 100.00
## 377 F 100.00 100.00 90.00
## 378 F 77.50 87.50 22.50
## 379 M 80.00 47.50 90.00
## 380 F 76.25 62.50 100.00
## 381 F 45.00 72.50 100.00
## 382 F 31.25 0.00 35.00
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## 385 F 67.50 12.50 90.00
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## 387 F 72.50 100.00 75.00
## 388 F 67.50 42.50 100.00
## 389 F 95.00 100.00 100.00
## 390 F 93.75 85.00 90.00
## 391 M 75.00 75.00 42.50
## 392 M 97.50 0.00 20.00
## 393 F 76.25 72.50 100.00
## 394 F 61.25 75.00 95.00
## 395 F 17.50 30.00 70.00
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## 397 M 33.75 57.50 15.00
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## 399 M 43.75 35.00 80.00
## 400 F 50.00 42.50 85.00
## 401 F 61.25 77.50 100.00
## 402 M 0.00 30.00 60.00
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## 404 F 66.25 50.00 90.00
## 405 F 70.00 67.50 80.00
## 406 M 41.25 60.00 100.00
## 407 F 92.50 100.00 100.00
## 408 F 53.75 60.00 90.00
## 409 M 52.50 0.00 35.00
## 410 F 95.00 80.00 15.00
## 411 F 20.00 25.00 100.00
## 412 F 12.50 22.50 100.00
## 413 F 71.25 57.50 100.00
## 414 F 91.25 90.00 42.50
## 415 F 45.00 72.50 100.00
## 416 F 62.50 0.00 90.00
## 417 F 80.00 65.00 100.00
## 418 F 87.50 65.00 95.00
## 419 M 57.50 42.50 85.00
## 420 M 47.50 40.00 100.00
## 421 F 62.50 82.50 7.50
## 422 F 60.00 40.00 70.00
## 423 F 73.75 90.00 90.00
## 424 M 37.50 30.00 90.00
## 425 F 66.25 77.50 100.00
## 426 M 62.50 55.00 22.50
## 427 M 25.00 37.50 100.00
## 428 F 37.50 0.00 0.00
## 429 F 51.25 55.00 7.50
## 430 F 82.50 87.50 100.00
## 431 F 100.00 100.00 100.00
## 432 F 48.75 45.00 12.50
## 433 M 32.50 42.50 90.00
## 434 M 72.50 62.50 0.00
## 435 M 0.00 7.50 5.00
## 436 F 67.50 23.75 5.00
## 437 M 41.25 11.25 81.25
## 438 F 67.50 57.50 5.00
## 439 F 72.50 10.00 5.00
## 440 M 60.00 28.75 5.00
## 441 F 87.50 100.00 100.00
## 442 F 87.50 72.50 95.00
## 443 F 87.50 82.50 92.50
## 444 M 0.00 0.00 5.00
## 445 F 90.00 27.50 5.00
## 446 M 82.50 91.25 70.00
## 447 F 85.00 12.50 5.00
## 448 F 70.00 31.25 5.00
## 449 F 72.50 46.25 5.00
## 450 M 70.00 33.75 32.50
## 451 F 20.00 2.50 5.00
## 452 F 52.50 35.00 31.25
## 453 M 87.50 32.50 67.50
## 454 M 71.25 67.50 55.00
## 455 F 67.50 37.50 5.00
## 456 F 58.75 12.50 5.00
## 457 F 55.00 27.50 5.00
## 458 F 50.00 17.50 5.00
## 459 F 85.00 47.50 80.00
## 460 F 62.50 42.50 70.00
## 461 F 85.00 60.00 60.00
## 462 F 80.00 61.25 5.00
## 463 M 62.50 28.75 5.00
## 464 F 62.50 36.25 5.00
## 465 F 95.00 90.00 90.00
## 466 M 62.50 20.00 5.00
## 467 F 12.50 20.00 5.00
## 468 F 77.50 53.75 5.00
## 469 M 42.50 52.50 5.00
## 470 F 81.25 72.50 5.00
## 471 F 77.50 77.50 5.00
## 472 F 57.50 40.00 5.00
## 473 M 70.00 57.50 40.00
## 474 M 45.00 25.00 5.00
## 475 F 86.25 40.00 5.00
## 476 F 82.50 68.75 5.00
## 477 F 100.00 68.75 90.00
## 478 F 55.00 31.25 5.00
## 479 F 100.00 100.00 100.00
## 480 M 57.50 0.00 5.00
## 481 F 72.50 57.50 5.00
## 482 F 46.25 37.50 5.00
## 483 F 78.75 63.75 5.00
## 484 M 55.00 0.00 40.00
## 485 F 52.50 42.50 5.00
## 486 F 100.00 97.50 100.00
## 487 F 60.00 50.00 71.25
## 488 M 87.50 42.50 5.00
## 489 F 26.25 25.00 52.50
## 490 F 50.00 35.00 5.00
## 491 F 61.25 88.75 75.00
## 492 F 60.00 2.50 5.00
## 493 F 63.75 20.00 5.00
## 494 F 95.00 77.50 75.00
## 495 F 26.25 41.25 5.00
## 496 F 76.25 81.25 86.25
## 497 F 45.00 43.75 5.00
## 498 F 95.00 95.00 5.00
## 499 F 71.25 28.75 75.00
## 500 M 80.00 40.00 5.00
## 501 F 58.75 60.00 65.00
## 502 F 60.00 7.50 5.00
## 503 F 58.75 0.00 5.00
## 504 F 97.50 87.50 5.00
## 505 F 72.50 21.25 5.00
## 506 F 72.50 53.75 25.00
## 507 M 95.00 40.00 43.75
## 508 F 60.00 15.00 35.00
## 509 F 57.50 17.50 60.00
## 510 M 38.75 50.00 37.50
## 511 F 68.75 23.75 5.00
## 512 M 100.00 100.00 100.00
## 513 M 33.75 37.50 65.00
## 514 M 62.50 33.75 92.50
## 515 F 76.25 61.25 57.50
## 516 M 58.75 63.75 70.00
## 517 M 81.25 33.75 60.00
## 518 F 97.50 100.00 100.00
## 519 F 81.25 96.25 100.00
## 520 F 56.25 67.50 82.50
## 521 M 63.75 41.25 72.50
## 522 F 100.00 100.00 100.00
## 523 F 86.25 58.75 65.00
## 524 M 46.25 48.75 60.00
## 525 M 71.25 65.00 52.50
## 526 M 43.75 35.00 57.50
## 527 F 100.00 70.00 85.00
## 528 M 100.00 55.00 65.00
## 529 F 87.50 100.00 70.00
## 530 F 88.75 100.00 75.00
## 531 F 95.00 98.75 95.00
## 532 M 67.50 60.00 52.50
## 533 F 73.75 32.50 52.50
## 534 F 98.75 100.00 72.50
## 535 F 82.50 80.00 52.50
## 536 F 62.50 57.50 77.50
## 537 F 81.25 100.00 95.00
## 538 M 67.50 57.50 77.50
## 539 F 83.75 70.00 97.50
## 540 M 81.25 40.00 83.75
## 541 F 91.25 38.75 100.00
## 542 F 72.50 25.00 87.50
## 543 F 85.00 87.50 98.75
## 544 M 41.25 30.00 71.25
## 545 F 96.25 90.00 98.75
## 546 M 70.00 60.00 78.75
## 547 F 52.50 40.00 92.50
## 548 M 58.75 48.75 80.00
## 549 F 96.25 50.00 92.50
## 550 F 61.25 56.25 92.50
## 551 F 90.00 53.75 97.50
## 552 M 33.75 15.00 72.50
## 553 F 81.25 101.25 100.00
## 554 F 97.50 100.00 87.50
## 555 M 56.25 41.25 52.50
## 556 F 85.00 67.50 87.50
## 557 M 33.75 27.50 5.00
## 558 F 98.75 100.00 100.00
## 559 F 60.00 36.25 5.00
## 560 F 87.50 75.00 95.00
## 561 M 56.25 73.75 97.50
## 562 M 100.00 37.50 97.50
## 563 F 82.50 98.75 100.00
## 564 F 62.50 73.75 95.00
## 565 F 71.25 78.75 68.75
## 566 F 98.75 98.75 95.00
## 567 F 45.00 43.75 80.00
## 568 F 78.75 73.75 80.00
## 569 M 68.75 77.50 88.75
## 570 F 75.00 100.00 96.25
## 571 F 95.00 100.00 100.00
## 572 F 61.25 71.25 77.50
## 573 F 80.00 81.25 90.00
## 574 M 11.25 67.50 83.75
## 575 F 72.50 63.75 85.00
## 576 F 100.00 100.00 100.00
## 577 M 87.50 95.00 95.00
## 578 M 31.25 42.50 66.25
## 579 F 76.25 80.00 97.50
## 580 M 53.75 33.75 15.00
## 581 F 86.25 67.50 100.00
## 582 F 90.00 50.00 100.00
## 583 M 52.50 21.25 81.25
## 584 F 90.00 81.25 91.25
## 585 F 82.50 100.00 100.00
## 586 F 93.75 77.50 92.50
## 587 F 90.00 50.00 100.00
## 588 M 62.50 23.75 65.00
## 589 F 73.75 52.50 68.75
## 590 F 88.75 50.00 83.75
## 591 M 67.50 42.50 75.00
## 592 F 96.25 65.00 82.50
## 593 F 100.00 56.25 100.00
## 594 F 87.50 68.75 81.25
## 595 M 88.75 62.50 96.25
## 596 M 72.50 47.50 82.50
## 597 F 97.50 77.50 100.00
## 598 F 86.25 67.50 95.00
## 599 F 98.75 85.00 96.25
## 600 F 77.50 56.25 82.50
## 601 F 40.00 46.25 70.00
## 602 F 93.75 92.50 98.75
## 603 F 100.00 100.00 100.00
## 604 M 67.50 30.00 95.00
## 605 M 91.25 38.75 62.50
## 606 F 75.00 50.00 100.00
## 607 M 55.00 45.00 95.00
## 608 F 92.50 56.25 92.50
## 609 F 41.25 50.00 71.25
## 610 M 77.50 76.25 93.75
## 611 F 88.75 100.00 100.00
## 612 F 50.00 71.25 76.25
## 613 F 88.75 100.00 95.00
## 614 F 83.75 50.00 98.75
## 615 F 82.50 61.25 77.50
## 616 F 96.25 100.00 100.00
## 617 M 60.00 63.75 98.75
## 618 F 61.25 47.50 88.75
## 619 M 71.25 40.00 92.50
## 620 M 83.75 65.00 87.50
## 621 F 92.50 65.00 97.50
## 622 M 78.75 46.25 51.25
## 623 F 73.75 80.00 91.25
## 624 F 77.50 67.50 75.00
## 625 F 35.00 71.25 76.25
## 626 F 97.50 75.00 97.50
## 627 F 100.00 96.25 95.00
## 628 F 67.50 63.75 50.00
## 629 F 72.50 81.25 100.00
## 630 F 100.00 100.00 100.00
## 631 F 86.25 63.75 93.75
## 632 F 85.00 78.75 91.25
## 633 M 62.50 28.75 83.75
## 634 F 100.00 72.50 98.75Mengubah Variabel Character Menjadi Numerik
Dikarenakan pada variabel gender masih bersifat character, maka dilakukan perubahan character pada variabel gender menjadi numerik dengan taraf 1 dan 2.
data1$Gender <- ifelse(data1$Gender == "M", 1, 2);data1## Gender Test_01 Test_02 Test_03
## 1 2 72.50 81.25 100.00
## 2 2 68.75 65.00 90.00
## 3 2 67.50 42.50 85.00
## 4 2 58.75 75.00 100.00
## 5 2 90.00 70.00 90.00
## 6 2 36.25 48.75 85.00
## 7 2 22.50 17.50 70.00
## 8 2 23.75 57.50 97.50
## 9 2 45.00 68.75 87.50
## 10 1 30.00 28.75 52.50
## 11 2 35.00 31.25 90.00
## 12 1 76.25 65.00 87.50
## 13 1 88.75 88.75 100.00
## 14 1 40.00 62.50 65.00
## 15 2 65.00 56.25 90.00
## 16 2 83.75 30.00 100.00
## 17 2 37.50 42.50 92.50
## 18 2 78.75 77.50 85.00
## 19 1 77.50 53.75 100.00
## 20 1 97.50 62.50 85.00
## 21 2 46.25 31.25 100.00
## 22 2 52.50 52.50 62.50
## 23 1 50.00 48.75 87.50
## 24 2 77.50 21.25 100.00
## 25 1 80.00 82.50 100.00
## 26 2 77.50 83.75 100.00
## 27 2 26.25 22.50 85.00
## 28 2 98.75 90.00 100.00
## 29 1 40.00 45.00 90.00
## 30 1 73.75 63.75 97.50
## 31 1 58.75 37.50 80.00
## 32 2 87.50 88.75 100.00
## 33 1 45.00 45.00 100.00
## 34 2 33.75 55.00 100.00
## 35 2 33.75 23.75 75.00
## 36 1 36.25 48.75 75.00
## 37 1 47.50 46.25 92.50
## 38 2 42.50 83.75 100.00
## 39 2 35.00 70.00 100.00
## 40 1 66.25 47.50 100.00
## 41 1 62.50 16.25 0.00
## 42 2 51.25 51.25 97.50
## 43 1 67.50 71.25 90.00
## 44 2 75.00 68.75 85.00
## 45 2 80.00 50.00 100.00
## 46 2 65.00 27.50 75.00
## 47 1 62.50 60.00 72.50
## 48 2 45.00 30.00 42.50
## 49 2 75.00 71.25 50.00
## 50 1 56.25 40.00 55.00
## 51 2 73.75 58.75 70.00
## 52 2 58.75 38.75 60.00
## 53 2 68.75 90.00 100.00
## 54 2 40.00 27.50 62.50
## 55 2 60.00 68.75 100.00
## 56 2 90.00 35.00 75.00
## 57 2 71.25 47.50 65.00
## 58 2 80.00 61.25 100.00
## 59 2 62.50 48.75 62.50
## 60 2 76.25 87.50 100.00
## 61 2 52.50 37.50 50.00
## 62 1 58.75 70.00 80.00
## 63 2 77.50 80.00 100.00
## 64 2 40.00 87.50 100.00
## 65 2 100.00 100.00 100.00
## 66 1 37.50 45.00 62.50
## 67 2 81.25 76.25 85.00
## 68 1 53.75 57.50 75.00
## 69 1 63.75 45.00 97.50
## 70 2 56.25 36.25 75.00
## 71 1 38.75 23.75 95.00
## 72 1 15.00 68.75 82.50
## 73 1 27.50 76.25 82.50
## 74 2 60.00 65.00 50.00
## 75 1 60.00 47.50 75.00
## 76 2 78.75 46.25 92.50
## 77 2 91.25 95.00 100.00
## 78 1 67.50 57.50 67.50
## 79 2 72.50 46.25 70.00
## 80 2 98.75 80.00 100.00
## 81 2 55.00 52.50 100.00
## 82 2 53.75 75.00 30.00
## 83 2 72.50 100.00 81.25
## 84 1 52.50 65.00 100.00
## 85 2 55.00 67.50 100.00
## 86 1 7.50 10.00 38.75
## 87 2 40.00 30.00 100.00
## 88 2 35.00 27.50 17.50
## 89 1 21.25 50.00 90.00
## 90 2 27.50 72.50 100.00
## 91 2 11.25 5.00 8.75
## 92 2 26.25 67.50 100.00
## 93 1 10.00 0.00 3.75
## 94 2 21.25 27.50 1.25
## 95 2 80.00 92.50 100.00
## 96 2 37.50 85.00 100.00
## 97 2 25.00 55.00 100.00
## 98 1 18.75 30.00 8.75
## 99 1 5.00 15.00 1.25
## 100 2 37.50 82.50 100.00
## 101 2 63.75 95.00 100.00
## 102 1 28.75 10.00 25.00
## 103 2 45.00 30.00 100.00
## 104 2 72.50 45.00 28.75
## 105 2 36.25 52.50 100.00
## 106 2 5.00 15.00 15.00
## 107 2 42.50 65.00 100.00
## 108 2 43.75 50.00 100.00
## 109 2 38.75 15.00 100.00
## 110 2 38.75 57.50 100.00
## 111 2 42.50 82.50 100.00
## 112 1 16.25 37.50 70.00
## 113 2 10.00 0.00 57.50
## 114 2 46.25 32.50 100.00
## 115 2 60.00 46.25 43.75
## 116 2 47.50 70.00 100.00
## 117 2 60.00 82.50 10.00
## 118 2 50.00 80.00 20.00
## 119 2 25.00 77.50 100.00
## 120 2 55.00 0.00 100.00
## 121 2 35.00 80.00 1.25
## 122 2 70.00 92.50 21.25
## 123 2 22.50 82.50 100.00
## 124 2 2.50 0.00 1.25
## 125 1 11.25 10.00 90.00
## 126 2 63.75 80.00 43.75
## 127 1 38.75 55.00 100.00
## 128 2 51.25 67.50 52.50
## 129 1 63.75 80.00 100.00
## 130 2 32.50 0.00 26.25
## 131 1 51.25 27.50 41.25
## 132 2 90.00 57.50 23.75
## 133 2 68.75 87.50 53.75
## 134 2 61.25 72.50 86.25
## 135 1 77.50 70.00 72.50
## 136 2 47.50 0.00 53.75
## 137 2 80.00 75.00 83.75
## 138 1 40.00 35.00 100.00
## 139 1 57.50 62.50 100.00
## 140 2 76.25 80.00 36.25
## 141 2 67.50 75.00 83.75
## 142 1 56.25 97.50 100.00
## 143 2 55.00 60.00 55.00
## 144 2 40.00 65.00 33.75
## 145 2 55.00 12.50 100.00
## 146 2 23.75 10.00 100.00
## 147 1 42.50 57.50 35.00
## 148 2 83.75 35.00 62.50
## 149 2 71.25 80.00 76.25
## 150 2 60.00 55.00 35.00
## 151 1 32.50 42.50 1.25
## 152 1 55.00 40.00 26.25
## 153 2 80.00 100.00 71.25
## 154 2 97.50 100.00 68.75
## 155 2 52.50 0.00 66.25
## 156 2 47.50 72.50 6.25
## 157 1 55.00 55.00 35.00
## 158 2 73.75 65.00 40.00
## 159 2 67.50 15.00 26.25
## 160 2 51.25 65.00 100.00
## 161 2 70.00 60.00 100.00
## 162 2 30.00 67.50 0.00
## 163 1 43.75 70.00 100.00
## 164 1 28.75 47.50 27.50
## 165 2 51.25 55.00 11.25
## 166 2 97.50 0.00 62.50
## 167 2 60.00 72.50 41.25
## 168 2 85.00 80.00 45.00
## 169 1 28.75 42.50 20.00
## 170 1 63.75 25.00 26.25
## 171 2 46.25 15.00 35.00
## 172 2 95.00 97.50 100.00
## 173 2 67.50 87.50 65.00
## 174 2 67.50 52.50 55.00
## 175 2 38.75 45.00 100.00
## 176 1 47.50 90.00 25.00
## 177 1 73.75 0.00 78.75
## 178 2 71.25 80.00 100.00
## 179 2 90.00 95.00 86.25
## 180 2 57.50 60.00 100.00
## 181 2 35.00 30.00 100.00
## 182 2 66.25 95.00 45.00
## 183 2 63.75 72.50 100.00
## 184 1 52.50 27.50 30.00
## 185 2 5.00 60.00 52.50
## 186 1 5.00 32.50 61.25
## 187 2 42.50 27.50 27.50
## 188 2 52.50 57.50 60.00
## 189 2 85.00 92.50 100.00
## 190 1 83.75 77.50 100.00
## 191 2 30.00 17.50 100.00
## 192 2 68.75 72.50 27.50
## 193 1 65.00 77.50 52.50
## 194 2 66.25 40.00 50.00
## 195 2 26.25 0.00 31.25
## 196 1 85.00 92.50 83.75
## 197 2 62.50 17.50 22.50
## 198 2 67.50 60.00 100.00
## 199 1 60.00 27.50 31.25
## 200 2 70.00 67.50 100.00
## 201 2 20.00 35.00 17.50
## 202 1 66.25 52.50 23.75
## 203 2 65.00 45.00 100.00
## 204 2 92.50 95.00 75.00
## 205 2 71.25 85.00 60.00
## 206 2 65.00 37.50 100.00
## 207 2 77.50 22.50 100.00
## 208 2 61.25 72.50 46.25
## 209 1 25.00 0.00 30.00
## 210 1 33.75 10.00 100.00
## 211 2 56.25 97.50 46.25
## 212 1 66.25 12.50 52.50
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## 246 1 40.60 16.25 6.25
## 247 2 53.10 6.25 5.00
## 248 2 68.75 18.75 10.60
## 249 2 79.40 32.50 83.15
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## 252 1 51.25 40.00 31.90
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## 265 2 24.40 40.00 31.90
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## 281 2 86.25 70.00 100.00
## 282 2 61.25 33.75 75.00
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## 285 1 45.00 20.00 25.00
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## 431 2 100.00 100.00 100.00
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## 450 1 70.00 33.75 32.50
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## 492 2 60.00 2.50 5.00
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## 550 2 61.25 56.25 92.50
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## 552 1 33.75 15.00 72.50
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## 555 1 56.25 41.25 52.50
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## 559 2 60.00 36.25 5.00
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## 562 1 100.00 37.50 97.50
## 563 2 82.50 98.75 100.00
## 564 2 62.50 73.75 95.00
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## 566 2 98.75 98.75 95.00
## 567 2 45.00 43.75 80.00
## 568 2 78.75 73.75 80.00
## 569 1 68.75 77.50 88.75
## 570 2 75.00 100.00 96.25
## 571 2 95.00 100.00 100.00
## 572 2 61.25 71.25 77.50
## 573 2 80.00 81.25 90.00
## 574 1 11.25 67.50 83.75
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## 576 2 100.00 100.00 100.00
## 577 1 87.50 95.00 95.00
## 578 1 31.25 42.50 66.25
## 579 2 76.25 80.00 97.50
## 580 1 53.75 33.75 15.00
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## 582 2 90.00 50.00 100.00
## 583 1 52.50 21.25 81.25
## 584 2 90.00 81.25 91.25
## 585 2 82.50 100.00 100.00
## 586 2 93.75 77.50 92.50
## 587 2 90.00 50.00 100.00
## 588 1 62.50 23.75 65.00
## 589 2 73.75 52.50 68.75
## 590 2 88.75 50.00 83.75
## 591 1 67.50 42.50 75.00
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## 593 2 100.00 56.25 100.00
## 594 2 87.50 68.75 81.25
## 595 1 88.75 62.50 96.25
## 596 1 72.50 47.50 82.50
## 597 2 97.50 77.50 100.00
## 598 2 86.25 67.50 95.00
## 599 2 98.75 85.00 96.25
## 600 2 77.50 56.25 82.50
## 601 2 40.00 46.25 70.00
## 602 2 93.75 92.50 98.75
## 603 2 100.00 100.00 100.00
## 604 1 67.50 30.00 95.00
## 605 1 91.25 38.75 62.50
## 606 2 75.00 50.00 100.00
## 607 1 55.00 45.00 95.00
## 608 2 92.50 56.25 92.50
## 609 2 41.25 50.00 71.25
## 610 1 77.50 76.25 93.75
## 611 2 88.75 100.00 100.00
## 612 2 50.00 71.25 76.25
## 613 2 88.75 100.00 95.00
## 614 2 83.75 50.00 98.75
## 615 2 82.50 61.25 77.50
## 616 2 96.25 100.00 100.00
## 617 1 60.00 63.75 98.75
## 618 2 61.25 47.50 88.75
## 619 1 71.25 40.00 92.50
## 620 1 83.75 65.00 87.50
## 621 2 92.50 65.00 97.50
## 622 1 78.75 46.25 51.25
## 623 2 73.75 80.00 91.25
## 624 2 77.50 67.50 75.00
## 625 2 35.00 71.25 76.25
## 626 2 97.50 75.00 97.50
## 627 2 100.00 96.25 95.00
## 628 2 67.50 63.75 50.00
## 629 2 72.50 81.25 100.00
## 630 2 100.00 100.00 100.00
## 631 2 86.25 63.75 93.75
## 632 2 85.00 78.75 91.25
## 633 1 62.50 28.75 83.75
## 634 2 100.00 72.50 98.75Uji Normalitas Multivariat
Dilakukan uji normalitas multivariat dengan mardia’s test untuk mengetahui apakah data berdistribusi normal atau tidak.
library(MVN)## Warning: package 'MVN' was built under R version 4.3.3test = mvn(data1, mvnTest = "mardia", univariateTest = "SW", multivariatePlot = "qq");test
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 165.407615723809 6.7529984547935e-25 NO
## 2 Mardia Kurtosis -4.28086360776005 1.86169437461636e-05 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk Gender 0.5813 <0.001 NO
## 2 Shapiro-Wilk Test_01 0.9773 <0.001 NO
## 3 Shapiro-Wilk Test_02 0.9745 <0.001 NO
## 4 Shapiro-Wilk Test_03 0.8469 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## Gender 634 1.690852 0.4625073 2.000 1 2.00 1 2 -0.8239900
## Test_01 634 61.606940 23.2752818 62.500 0 100.00 45 80 -0.3506773
## Test_02 634 54.538644 27.0240861 56.250 0 101.25 35 75 -0.1424219
## Test_03 634 66.607177 34.1249751 78.125 0 100.00 40 100 -0.6876709
## Kurtosis
## Gender -1.3231199
## Test_01 -0.5097632
## Test_02 -0.7841503
## Test_03 -0.9599264Berdasarkan hasil uji normalitas multivariat di atas dapat disimpulkan bahwa data multivariat tidak berdistribusi normal.
Memotong Data Pengamatan
Dikarenakan data multivariat tidak berdistribusi normal, maka akan dilakukan pemotongan data dengan harapan data akan berdistribusi normal. Data amatan dipotong menjadi 46 data dari 634 data yaitu dari data amatan ke-30 dan data amatan ke-75.
data_fix <- data1[c(30:75),];data_fix## Gender Test_01 Test_02 Test_03
## 30 1 73.75 63.75 97.5
## 31 1 58.75 37.50 80.0
## 32 2 87.50 88.75 100.0
## 33 1 45.00 45.00 100.0
## 34 2 33.75 55.00 100.0
## 35 2 33.75 23.75 75.0
## 36 1 36.25 48.75 75.0
## 37 1 47.50 46.25 92.5
## 38 2 42.50 83.75 100.0
## 39 2 35.00 70.00 100.0
## 40 1 66.25 47.50 100.0
## 41 1 62.50 16.25 0.0
## 42 2 51.25 51.25 97.5
## 43 1 67.50 71.25 90.0
## 44 2 75.00 68.75 85.0
## 45 2 80.00 50.00 100.0
## 46 2 65.00 27.50 75.0
## 47 1 62.50 60.00 72.5
## 48 2 45.00 30.00 42.5
## 49 2 75.00 71.25 50.0
## 50 1 56.25 40.00 55.0
## 51 2 73.75 58.75 70.0
## 52 2 58.75 38.75 60.0
## 53 2 68.75 90.00 100.0
## 54 2 40.00 27.50 62.5
## 55 2 60.00 68.75 100.0
## 56 2 90.00 35.00 75.0
## 57 2 71.25 47.50 65.0
## 58 2 80.00 61.25 100.0
## 59 2 62.50 48.75 62.5
## 60 2 76.25 87.50 100.0
## 61 2 52.50 37.50 50.0
## 62 1 58.75 70.00 80.0
## 63 2 77.50 80.00 100.0
## 64 2 40.00 87.50 100.0
## 65 2 100.00 100.00 100.0
## 66 1 37.50 45.00 62.5
## 67 2 81.25 76.25 85.0
## 68 1 53.75 57.50 75.0
## 69 1 63.75 45.00 97.5
## 70 2 56.25 36.25 75.0
## 71 1 38.75 23.75 95.0
## 72 1 15.00 68.75 82.5
## 73 1 27.50 76.25 82.5
## 74 2 60.00 65.00 50.0
## 75 1 60.00 47.50 75.0Uji Normalitas Multivariat
Setelah dilakukan pemotongan data amatan, maka akan dilakukan uji normalitas multivariat kembali apakah data sudah berdistribusi normal atau tidak.
test1 = mvn(data_fix, mvnTest = "mardia", univariateTest = "SW", multivariatePlot = "qq");test1
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 28.4505000215713 0.0991566372504572 YES
## 2 Mardia Kurtosis -0.645115750127456 0.518852177871912 YES
## 3 MVN <NA> <NA> YES
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk Gender 0.6196 <0.001 NO
## 2 Shapiro-Wilk Test_01 0.9893 0.9453 YES
## 3 Shapiro-Wilk Test_02 0.9795 0.5863 YES
## 4 Shapiro-Wilk Test_03 0.8430 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## Gender 46 1.608696 0.4934352 2.000 1.00 2 1.000 2.000 -0.43098956
## Test_01 46 58.777174 18.0844645 60.000 15.00 100 45.000 73.125 -0.09959429
## Test_02 46 56.005435 20.3981541 53.125 16.25 100 41.250 70.000 0.13671718
## Test_03 46 80.271739 21.1162672 82.500 0.00 100 70.625 100.000 -1.32244887
## Kurtosis
## Gender -1.8531258
## Test_01 -0.4695586
## Test_02 -0.8669970
## Test_03 2.4110727Berdasarkan hasil uji normalitas multivariat di atas dapat disimpulkan bahwa data multivariat sudah berdistribusi normal.
Uji Homogenitas
Dilakukan uji homogenitas dengan uji box M untuk melihat apakah varians antarvariabel bersifat homogen atau tidak.
library(biotools)## Warning: package 'biotools' was built under R version 4.3.3## Loading required package: MASS## ---
## biotools version 4.2data_fix1 <- data_fix[,-1]
grup <- data_fix$Gender
head(grup)## [1] 1 1 2 1 2 2boxM(data = data_fix1, grouping = grup)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data_fix1
## Chi-Sq (approx.) = 6.1346, df = 6, p-value = 0.4083Berdasarkan hasil uji homogenitas multivariat di atas dapat disimpulkan bahwa dengan taraf signifikansi 5%. data bersifat heterogen dikarenakan p-value (0,4083) < alpha (0,05).
Uji One Way Manova
Setelah asumsi normal dan heterogen terpenuhi, maka dilakukan uji one way manova untuk menguji apakah ada perbedaan rata-rata dari lebih dari satu variabel dependen secara simultan berdasarkan satu variabel independen kategoris.
owm = manova(cbind(data_fix$Test_01,
data_fix$Test_02,
data_fix$Test_03) ~ data_fix$Gender)
summary(owm)## Df Pillai approx F num Df den Df Pr(>F)
## data_fix$Gender 1 0.11816 1.8759 3 42 0.1483
## Residuals 44Berdasarkan uji one way anova tersebut, didapatkan p-value (0,1483) > alpha (0,05). Dapat disimpulkan bahwa dengan taraf siginifikansi 5%, variabel gender tidak berpengaruh terhadap hasil nilai tiga tes pada mata pelajaran sejarah geografi dari beberapa siswa-siswi.
Two Way Manova
Input Data
Data berikut merupakan data yang bersumber dari web kaggle.com terkait hasil metode diet yang dilakukan selama enam minggu
data2 <- read.csv("C:/Users/wartw/OneDrive/Documents/ADM/Diet.csv");data2## gender Diet weight weight6weeks
## 1 M B 60 60.0
## 2 M B 103 103.0
## 3 F A 58 54.2
## 4 F A 60 54.0
## 5 F A 64 63.3
## 6 F A 64 61.1
## 7 F A 65 62.2
## 8 F A 66 64.0
## 9 F A 67 65.0
## 10 F A 69 60.5
## 11 F A 70 68.1
## 12 F A 70 66.9
## 13 F A 72 70.5
## 14 F A 72 69.0
## 15 F A 72 68.4
## 16 F A 82 81.1
## 17 F B 58 60.1
## 18 F B 58 56.0
## 19 F B 59 57.3
## 20 F B 61 56.7
## 21 F B 62 55.0
## 22 F B 63 62.4
## 23 F B 63 60.3
## 24 F B 63 59.4
## 25 F B 65 62.0
## 26 F B 66 64.0
## 27 F B 68 63.8
## 28 F B 68 63.3
## 29 F B 76 72.7
## 30 F B 77 77.5
## 31 F C 60 53.0
## 32 F C 62 56.4
## 33 F C 64 60.6
## 34 F C 65 58.2
## 35 F C 66 58.2
## 36 F C 67 61.6
## 37 F C 67 60.2
## 38 F C 69 61.8
## 39 F C 70 63.0
## 40 F C 70 62.7
## 41 F C 72 71.1
## 42 F C 72 64.4
## 43 F C 73 68.9
## 44 F C 75 68.7
## 45 F C 76 71.0
## 46 M A 71 71.6
## 47 M A 72 70.9
## 48 M A 74 69.5
## 49 M A 78 73.9
## 50 M A 80 71.0
## 51 M A 80 77.6
## 52 M A 83 79.1
## 53 M A 85 81.5
## 54 M A 87 81.9
## 55 M A 88 84.5
## 56 M B 71 66.8
## 57 M B 75 72.6
## 58 M B 75 69.2
## 59 M B 76 72.5
## 60 M B 78 72.7
## 61 M B 78 76.3
## 62 M B 79 73.6
## 63 M B 79 72.9
## 64 M B 79 71.1
## 65 M B 80 81.4
## 66 M B 80 75.7
## 67 M C 71 68.5
## 68 M C 73 72.1
## 69 M C 76 72.5
## 70 M C 78 77.5
## 71 M C 78 75.2
## 72 M C 78 69.4
## 73 M C 79 74.5
## 74 M C 83 80.2
## 75 M C 84 79.9
## 76 M C 85 79.7
## 77 M C 87 77.8
## 78 M C 88 81.9Mengubah Variabel Character Menjadi Numerik
Dikarenakan pada variabel gender dan Diet masih bersifat character, maka dilakukan perubahan character pada variabel gender menjadi numerik dengan taraf 1 dan 2 dan variabel Diet menjadi 1 dan 2, serta mengubah variabel weight dari integer ke numerik.
data2$gender <- ifelse(data2$gender == "M", 1, 2)
data2$Diet <- ifelse(data2$Diet == "A", 1, 2)
data2$weight <- as.numeric(data2$weight)
str(data2)## 'data.frame': 78 obs. of 4 variables:
## $ gender : num 1 1 2 2 2 2 2 2 2 2 ...
## $ Diet : num 2 2 1 1 1 1 1 1 1 1 ...
## $ weight : num 60 103 58 60 64 64 65 66 67 69 ...
## $ weight6weeks: num 60 103 54.2 54 63.3 61.1 62.2 64 65 60.5 ...Membuat Data Frame
Setelah mengubah semua variabel menjadi numerik, selanjutnya membuat data frame.
data3 <- data.frame(c(data2$gender),
c(data2$Diet),
c(data2$weight),
c(data2$weight6weeks));data3## c.data2.gender. c.data2.Diet. c.data2.weight. c.data2.weight6weeks.
## 1 1 2 60 60.0
## 2 1 2 103 103.0
## 3 2 1 58 54.2
## 4 2 1 60 54.0
## 5 2 1 64 63.3
## 6 2 1 64 61.1
## 7 2 1 65 62.2
## 8 2 1 66 64.0
## 9 2 1 67 65.0
## 10 2 1 69 60.5
## 11 2 1 70 68.1
## 12 2 1 70 66.9
## 13 2 1 72 70.5
## 14 2 1 72 69.0
## 15 2 1 72 68.4
## 16 2 1 82 81.1
## 17 2 2 58 60.1
## 18 2 2 58 56.0
## 19 2 2 59 57.3
## 20 2 2 61 56.7
## 21 2 2 62 55.0
## 22 2 2 63 62.4
## 23 2 2 63 60.3
## 24 2 2 63 59.4
## 25 2 2 65 62.0
## 26 2 2 66 64.0
## 27 2 2 68 63.8
## 28 2 2 68 63.3
## 29 2 2 76 72.7
## 30 2 2 77 77.5
## 31 2 2 60 53.0
## 32 2 2 62 56.4
## 33 2 2 64 60.6
## 34 2 2 65 58.2
## 35 2 2 66 58.2
## 36 2 2 67 61.6
## 37 2 2 67 60.2
## 38 2 2 69 61.8
## 39 2 2 70 63.0
## 40 2 2 70 62.7
## 41 2 2 72 71.1
## 42 2 2 72 64.4
## 43 2 2 73 68.9
## 44 2 2 75 68.7
## 45 2 2 76 71.0
## 46 1 1 71 71.6
## 47 1 1 72 70.9
## 48 1 1 74 69.5
## 49 1 1 78 73.9
## 50 1 1 80 71.0
## 51 1 1 80 77.6
## 52 1 1 83 79.1
## 53 1 1 85 81.5
## 54 1 1 87 81.9
## 55 1 1 88 84.5
## 56 1 2 71 66.8
## 57 1 2 75 72.6
## 58 1 2 75 69.2
## 59 1 2 76 72.5
## 60 1 2 78 72.7
## 61 1 2 78 76.3
## 62 1 2 79 73.6
## 63 1 2 79 72.9
## 64 1 2 79 71.1
## 65 1 2 80 81.4
## 66 1 2 80 75.7
## 67 1 2 71 68.5
## 68 1 2 73 72.1
## 69 1 2 76 72.5
## 70 1 2 78 77.5
## 71 1 2 78 75.2
## 72 1 2 78 69.4
## 73 1 2 79 74.5
## 74 1 2 83 80.2
## 75 1 2 84 79.9
## 76 1 2 85 79.7
## 77 1 2 87 77.8
## 78 1 2 88 81.9Uji Normalitas Multivariat
Dilakukan uji normalitas multivariat dengan mardia’s test untuk mengetahui apakah data berdistribusi normal atau tidak.
library(MVN)
test2 <- mvn(data3, mvnTest = "mardia", univariateTest = "SW", multivariatePlot = "qq");test2
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 39.4150303277646 0.00591792969937303 NO
## 2 Mardia Kurtosis 0.033505972746442 0.973271102944795 YES
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk c.data2.gender. 0.6326 <0.001 NO
## 2 Shapiro-Wilk c.data2.Diet. 0.5803 <0.001 NO
## 3 Shapiro-Wilk c.data2.weight. 0.9692 0.0554 YES
## 4 Shapiro-Wilk c.data2.weight6weeks. 0.9580 0.0115 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## c.data2.gender. 78 1.551282 0.5005824 2.00 1 2 1.00 2.000
## c.data2.Diet. 78 1.692308 0.4645258 2.00 1 2 1.00 2.000
## c.data2.weight. 78 72.525641 8.7233443 72.00 58 103 66.00 78.000
## c.data2.weight6weeks. 78 68.680769 8.9245038 68.95 53 103 61.85 73.825
## Skew Kurtosis
## c.data2.gender. -0.2022628 -1.9840351
## c.data2.Diet. -0.8173592 -1.3487243
## c.data2.weight. 0.4928322 0.3909745
## c.data2.weight6weeks. 0.6474563 1.1188360Berdasarkan hasil uji normalitas multivariat di atas dapat disimpulkan bahwa data multivariat tidak berdistribusi normal.
Memotong Data Pengamatan
Dikarenakan data multivariat tidak berdistribusi normal, maka akan dilakukan pemotongan data dengan harapan data akan berdistribusi normal. Data amatan dipotong menjadi 56 data dari 78 data yaitu dari data amatan ke-5 dan data amatan ke-60
data_fix2 <- data3[c(5:60),];data_fix2## c.data2.gender. c.data2.Diet. c.data2.weight. c.data2.weight6weeks.
## 5 2 1 64 63.3
## 6 2 1 64 61.1
## 7 2 1 65 62.2
## 8 2 1 66 64.0
## 9 2 1 67 65.0
## 10 2 1 69 60.5
## 11 2 1 70 68.1
## 12 2 1 70 66.9
## 13 2 1 72 70.5
## 14 2 1 72 69.0
## 15 2 1 72 68.4
## 16 2 1 82 81.1
## 17 2 2 58 60.1
## 18 2 2 58 56.0
## 19 2 2 59 57.3
## 20 2 2 61 56.7
## 21 2 2 62 55.0
## 22 2 2 63 62.4
## 23 2 2 63 60.3
## 24 2 2 63 59.4
## 25 2 2 65 62.0
## 26 2 2 66 64.0
## 27 2 2 68 63.8
## 28 2 2 68 63.3
## 29 2 2 76 72.7
## 30 2 2 77 77.5
## 31 2 2 60 53.0
## 32 2 2 62 56.4
## 33 2 2 64 60.6
## 34 2 2 65 58.2
## 35 2 2 66 58.2
## 36 2 2 67 61.6
## 37 2 2 67 60.2
## 38 2 2 69 61.8
## 39 2 2 70 63.0
## 40 2 2 70 62.7
## 41 2 2 72 71.1
## 42 2 2 72 64.4
## 43 2 2 73 68.9
## 44 2 2 75 68.7
## 45 2 2 76 71.0
## 46 1 1 71 71.6
## 47 1 1 72 70.9
## 48 1 1 74 69.5
## 49 1 1 78 73.9
## 50 1 1 80 71.0
## 51 1 1 80 77.6
## 52 1 1 83 79.1
## 53 1 1 85 81.5
## 54 1 1 87 81.9
## 55 1 1 88 84.5
## 56 1 2 71 66.8
## 57 1 2 75 72.6
## 58 1 2 75 69.2
## 59 1 2 76 72.5
## 60 1 2 78 72.7Uji Normalitas Multivariat
Setelah dilakukan pemotongan data amatan, maka akan dilakukan uji normalitas multivariat kembali apakah data sudah berdistribusi normal atau tidak.
test3 <- mvn(data_fix2, mvnTest = "mardia", univariateTest = "SW", multivariatePlot = "qq");test3
## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 24.3744260936431 0.226418978367029 YES
## 2 Mardia Kurtosis -1.48599971667034 0.137279195941051 YES
## 3 MVN <NA> <NA> YES
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk c.data2.gender. 0.5532 <0.001 NO
## 2 Shapiro-Wilk c.data2.Diet. 0.6198 <0.001 NO
## 3 Shapiro-Wilk c.data2.weight. 0.9737 0.2587 YES
## 4 Shapiro-Wilk c.data2.weight6weeks. 0.9654 0.1084 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## c.data2.gender. 56 1.732143 0.4468505 2.0 1 2.0 1.000 2.000
## c.data2.Diet. 56 1.607143 0.4928054 2.0 1 2.0 1.000 2.000
## c.data2.weight. 56 70.375000 7.2452179 70.0 58 88.0 65.000 75.000
## c.data2.weight6weeks. 56 66.530357 7.4585380 64.7 53 84.5 60.975 71.025
## Skew Kurtosis
## c.data2.gender. -1.0204642 -0.9751146
## c.data2.Diet. -0.4270635 -1.8496961
## c.data2.weight. 0.4433259 -0.3852176
## c.data2.weight6weeks. 0.4720432 -0.4898212Berdasarkan hasil uji normalitas multivariat di atas dapat disimpulkan bahwa data multivariat sudah berdistribusi normal.
Uji Homogenitas
Dilakukan uji homogenitas dengan uji box M untuk melihat apakah varians antarvariabel bersifat homogen atau tidak.
library(biotools)
data_p1 <- data_fix2[,-1]
grup1 <- data_fix2$c.data2.gender.
boxM(data = data_p1, grouping = grup1)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data_p1
## Chi-Sq (approx.) = 2.3066, df = 6, p-value = 0.8895data_p2 <- data_fix2[,-2]
grup2 <- data_fix2$c.data2.Diet.
boxM(data = data_p2, grouping = grup2)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data_p2
## Chi-Sq (approx.) = 4.001, df = 6, p-value = 0.6765Berdasarkan hasil uji homogenitas multivariat di atas dapat disimpulkan bahwa dengan taraf signifikansi 5%. pada variabel gender data bersifat heterogen dikarenakan p-value (0,8895) < alpha (0,05) dan pada variabel Diet data bersifat heterogen dikarenakan p-value (0,6765) > alpha (0,05).
Uji Two Way Manova
Setelah asumsi normal dan heterogen terpenuhi, maka dilakukan uji two way manova untuk menguji apakah ada perbedaan rata-rata dari lebih dari satu variabel dependen secara simultan berdasarkan dua variabel independen kategoris.
gender1 <- as.factor(data_fix2$c.data2.gender.);gender1## [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [39] 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## Levels: 1 2Diet1 <- as.factor(data_fix2$c.data2.Diet.);Diet1## [1] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [39] 2 2 2 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2
## Levels: 1 2twm <- manova(cbind(data_fix2$c.data2.weight.,
data_fix2$c.data2.weight6weeks.) ~ gender1 * Diet1, data = data_fix2);twm## Call:
## manova(cbind(data_fix2$c.data2.weight., data_fix2$c.data2.weight6weeks.) ~
## gender1 * Diet1, data = data_fix2)
##
## Terms:
## gender1 Diet1 gender1:Diet1 Residuals
## resp 1 1254.4811 127.7040 10.6301 1494.3098
## resp 2 1253.8323 247.1078 3.1058 1555.5926
## Deg. of Freedom 1 1 1 52
##
## Residual standard errors: 5.360665 5.469483
## Estimated effects may be unbalancedsummary(twm)## Df Pillai approx F num Df den Df Pr(>F)
## gender1 1 0.46460 22.1277 2 51 1.206e-07 ***
## Diet1 1 0.15394 4.6397 2 51 0.01408 *
## gender1:Diet1 1 0.01208 0.3119 2 51 0.73342
## Residuals 52
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Berdasarkan uji two way manova di atas didapatkan variabel gender dan variabel Diet berpengaruh signifikan terhadap variabel lainnya.
Uji Lanjut
Dikarenakan variabel gender dan variabel Diet berpengaruh signfikan, maka akan dilakukan uji lanjut untuk mengetahui variabel gender dan variabel Diet berpengaruh signifikan terhadap variabel apa.
summary.aov(twm)## Response 1 :
## Df Sum Sq Mean Sq F value Pr(>F)
## gender1 1 1254.48 1254.48 43.6543 2.093e-08 ***
## Diet1 1 127.70 127.70 4.4439 0.03986 *
## gender1:Diet1 1 10.63 10.63 0.3699 0.54570
## Residuals 52 1494.31 28.74
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response 2 :
## Df Sum Sq Mean Sq F value Pr(>F)
## gender1 1 1253.83 1253.83 41.9128 3.41e-08 ***
## Diet1 1 247.11 247.11 8.2603 0.005857 **
## gender1:Diet1 1 3.11 3.11 0.1038 0.748586
## Residuals 52 1555.59 29.92
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Berdasarkan uji lanjut di atas didapatkan :
Variabel weight :
gender : p-value < alpha (0,05), variabel gender berpengaruh signifikan terhadap variabel weight.
Diet : p-value < alpha (0,05), variabel Diet berpengaruh signifikan terhadap variabel weight.
gender & Diet : p-value > alpha (0,05), variabel gender & Diet tidak berpengaruh signifikan terhadap variabel weight.
Variabel weight6weeks :
gender : p-value < alpha (0,05), variabel gender berpengaruh signifikan terhadap variabel weight6weeks.
Diet : p-value < alpha (0,05), variabel Diet berpengaruh signifikan terhadap variabel weight6weeks.
gender & Diet : p-value > alpha (0,05), variabel gender & Diet tidak berpengaruh signifikan terhadap variabel weight6weeks.