The Davis dataset appears to be a portion of data reported by: Davis, C. & Cowles, M. (1991). Body image and exercise: A study of relationships and comparisons between physically active men and women. Sex Roles, 25, 33-44.
library(car) # calling the library lets you use the data and functions in it
library(psych) # for descriptive stats##
## Attaching package: 'psych'## The following object is masked from 'package:car':
##
## logitDavis # prints the dataset from the package 'car'## sex weight height repwt repht
## 1 M 77 182 77 180
## 2 F 58 161 51 159
## 3 F 53 161 54 158
## 4 M 68 177 70 175
## 5 F 59 157 59 155
## 6 M 76 170 76 165
## 7 M 76 167 77 165
## 8 M 69 186 73 180
## 9 M 71 178 71 175
## 10 M 65 171 64 170
## 11 M 70 175 75 174
## 12 F 166 57 56 163
## 13 F 51 161 52 158
## 14 F 64 168 64 165
## 15 F 52 163 57 160
## 16 F 65 166 66 165
## 17 M 92 187 101 185
## 18 F 62 168 62 165
## 19 M 76 197 75 200
## 20 F 61 175 61 171
## 21 M 119 180 124 178
## 22 F 61 170 61 170
## 23 M 65 175 66 173
## 24 M 66 173 70 170
## 25 F 54 171 59 168
## 26 F 50 166 50 165
## 27 F 63 169 61 168
## 28 F 58 166 60 160
## 29 F 39 157 41 153
## 30 M 101 183 100 180
## 31 F 71 166 71 165
## 32 M 75 178 73 175
## 33 M 79 173 76 173
## 34 F 52 164 52 161
## 35 F 68 169 63 170
## 36 M 64 176 65 175
## 37 F 56 166 54 165
## 38 M 69 174 69 171
## 39 M 88 178 86 175
## 40 M 65 187 67 188
## 41 F 54 164 53 160
## 42 M 80 178 80 178
## 43 F 63 163 59 159
## 44 M 78 183 80 180
## 45 M 85 179 82 175
## 46 F 54 160 55 158
## 47 M 73 180 NA NA
## 48 F 49 161 NA NA
## 49 F 54 174 56 173
## 50 F 75 162 75 158
## 51 M 82 182 85 183
## 52 F 56 165 57 163
## 53 M 74 169 73 170
## 54 M 102 185 107 185
## 55 M 64 177 NA NA
## 56 M 65 176 64 172
## 57 F 66 170 65 NA
## 58 M 73 183 74 180
## 59 M 75 172 70 169
## 60 M 57 173 58 170
## 61 M 68 165 69 165
## 62 M 71 177 71 170
## 63 M 71 180 76 175
## 64 F 78 173 75 169
## 65 M 97 189 98 185
## 66 F 60 162 59 160
## 67 F 64 165 63 163
## 68 F 64 164 62 161
## 69 F 52 158 51 155
## 70 M 80 178 76 175
## 71 F 62 175 61 171
## 72 M 66 173 66 175
## 73 F 55 165 54 163
## 74 F 56 163 57 159
## 75 F 50 166 50 161
## 76 F 50 171 NA NA
## 77 F 50 160 55 150
## 78 F 63 160 64 158
## 79 M 69 182 70 180
## 80 M 69 183 70 183
## 81 F 61 165 60 163
## 82 M 55 168 56 170
## 83 F 53 169 52 175
## 84 F 60 167 55 163
## 85 F 56 170 56 170
## 86 M 59 182 61 183
## 87 M 62 178 66 175
## 88 F 53 165 53 165
## 89 F 57 163 59 160
## 90 F 57 162 56 160
## 91 M 70 173 68 170
## 92 F 56 161 56 161
## 93 M 84 184 86 183
## 94 M 69 180 71 180
## 95 M 88 189 87 185
## 96 F 56 165 57 160
## 97 M 103 185 101 182
## 98 F 50 169 50 165
## 99 F 52 159 52 153
## 100 F 55 155 NA 154
## 101 F 55 164 55 163
## 102 M 63 178 63 175
## 103 F 47 163 47 160
## 104 F 45 163 45 160
## 105 F 62 175 63 173
## 106 F 53 164 51 160
## 107 F 52 152 51 150
## 108 F 57 167 55 164
## 109 F 64 166 64 165
## 110 F 59 166 55 163
## 111 M 84 183 90 183
## 112 M 79 179 79 171
## 113 F 55 174 57 171
## 114 M 67 179 67 179
## 115 F 76 167 77 165
## 116 F 62 168 62 163
## 117 M 83 184 83 181
## 118 M 96 184 94 183
## 119 M 75 169 76 165
## 120 M 65 178 66 178
## 121 M 78 178 77 175
## 122 M 69 167 73 165
## 123 F 68 178 68 175
## 124 F 55 165 55 163
## 125 M 67 179 NA NA
## 126 F 52 169 56 NA
## 127 F 47 153 NA 154
## 128 F 45 157 45 153
## 129 F 68 171 68 169
## 130 F 44 157 44 155
## 131 F 62 166 61 163
## 132 M 87 185 89 185
## 133 F 56 160 53 158
## 134 F 50 148 47 148
## 135 M 83 177 84 175
## 136 F 53 162 53 160
## 137 F 64 172 62 168
## 138 F 62 167 NA NA
## 139 M 90 188 91 185
## 140 M 85 191 83 188
## 141 M 66 175 68 175
## 142 F 52 163 53 160
## 143 F 53 165 55 163
## 144 F 54 176 55 176
## 145 F 64 171 66 171
## 146 F 55 160 55 155
## 147 F 55 165 55 165
## 148 F 59 157 55 158
## 149 F 70 173 67 170
## 150 M 88 184 86 183
## 151 F 57 168 58 165
## 152 F 47 162 47 160
## 153 F 47 150 45 152
## 154 F 55 162 NA NA
## 155 F 48 163 44 160
## 156 M 54 169 58 165
## 157 M 69 172 68 174
## 158 F 59 170 NA NA
## 159 F 58 169 NA NA
## 160 F 57 167 56 165
## 161 F 51 163 50 160
## 162 F 54 161 54 160
## 163 F 53 162 52 158
## 164 F 59 172 58 171
## 165 M 56 163 58 161
## 166 F 59 159 59 155
## 167 F 63 170 62 168
## 168 F 66 166 66 165
## 169 M 96 191 95 188
## 170 F 53 158 50 155
## 171 M 76 169 75 165
## 172 F 54 163 NA NA
## 173 M 61 170 61 170
## 174 M 82 176 NA NA
## 175 M 62 168 64 168
## 176 M 71 178 68 178
## 177 F 60 174 NA NA
## 178 M 66 170 67 165
## 179 M 81 178 82 175
## 180 M 68 174 68 173
## 181 M 80 176 78 175
## 182 F 43 154 NA NA
## 183 M 82 181 NA NA
## 184 F 63 165 59 160
## 185 M 70 173 70 173
## 186 F 56 162 56 160
## 187 F 60 172 55 168
## 188 F 58 169 54 166
## 189 M 76 183 75 180
## 190 F 50 158 49 155
## 191 M 88 185 93 188
## 192 M 89 173 86 173
## 193 F 59 164 59 165
## 194 F 51 156 51 158
## 195 F 62 164 61 161
## 196 M 74 175 71 175
## 197 M 83 180 80 180
## 198 M 81 175 NA NA
## 199 M 90 181 91 178
## 200 M 79 177 81 178str(Davis) # tells the data structure## 'data.frame': 200 obs. of 5 variables:
## $ sex : Factor w/ 2 levels "F","M": 2 1 1 2 1 2 2 2 2 2 ...
## $ weight: int 77 58 53 68 59 76 76 69 71 65 ...
## $ height: int 182 161 161 177 157 170 167 186 178 171 ...
## $ repwt : int 77 51 54 70 59 76 77 73 71 64 ...
## $ repht : int 180 159 158 175 155 165 165 180 175 170 ...How many men and how many women in the sample?
Combining men and women, what are the means and standard deviations for weight, height, reptwt, repht (measured vs self-reported height and weight)?
In these data, weight is in kg (kilograms), height is in cm (centimeters). What is the mean body mass index for the total sample? Note: BMI is computed by kg/meters-squared (divide cm by 100 to yield meters, then square) A BMI below 18.5 is considered underweight. A BMI of 18.5 to 24.9 is considered healthy. A BMI of 25 to 29.9 is considered overweight. A BMI of 30 or higher is considered obese.
Do you spot a problem in the data? What do you think caused it? Fix it.
What is the probability that someone randomly drawn from this sample would be underweight?
What is the probability that someone randomly drawn from a normally distributed population that has this sample’s mean and standard deviation would be underweight?
Discussion question (ask your partner, then we will discuss as a class): How could you decide whether men or women were more accurate in reporting their height? Weight? (Numbers and graphs rather than statistical tests at this point. How would you examine the data and show to people to convince them?)