Exploratory Data Analysis:
Comparing Distributions

STAT 200 - Chapter 4

Learning Objectives

  • At the end of this lecture, students are expected to be able to:
    • compare distributions using histograms;
    • compare distributions using boxplots;
    • list the advantages and disadvantages of each approach;

Comparing distributions

  • In the previous lecture, we focused our attention on studying the distribution of two categorical variables or a single quantitative variable.

  • In this lecture, we will focus on comparing the distribution of a quantitative variable across two or more groups.

Penguins dataset

Let’s consider the penguins dataset.

species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g sex year
Adelie Torgersen 39.1 18.7 181 3750 male 2007
Adelie Torgersen 39.5 17.4 186 3800 female 2007
Adelie Torgersen 40.3 18.0 195 3250 female 2007
Adelie Torgersen NA NA NA NA NA 2007
Adelie Torgersen 36.7 19.3 193 3450 female 2007
Adelie Torgersen 39.3 20.6 190 3650 male 2007
Adelie Torgersen 38.9 17.8 181 3625 female 2007
Adelie Torgersen 39.2 19.6 195 4675 male 2007
Adelie Torgersen 34.1 18.1 193 3475 NA 2007
Adelie Torgersen 42.0 20.2 190 4250 NA 2007
Adelie Torgersen 37.8 17.1 186 3300 NA 2007
Adelie Torgersen 37.8 17.3 180 3700 NA 2007
Adelie Torgersen 41.1 17.6 182 3200 female 2007
Adelie Torgersen 38.6 21.2 191 3800 male 2007
Adelie Torgersen 34.6 21.1 198 4400 male 2007
Adelie Torgersen 36.6 17.8 185 3700 female 2007
Adelie Torgersen 38.7 19.0 195 3450 female 2007
Adelie Torgersen 42.5 20.7 197 4500 male 2007
Adelie Torgersen 34.4 18.4 184 3325 female 2007
Adelie Torgersen 46.0 21.5 194 4200 male 2007
Adelie Biscoe 37.8 18.3 174 3400 female 2007
Adelie Biscoe 37.7 18.7 180 3600 male 2007
Adelie Biscoe 35.9 19.2 189 3800 female 2007
Adelie Biscoe 38.2 18.1 185 3950 male 2007
Adelie Biscoe 38.8 17.2 180 3800 male 2007
Adelie Biscoe 35.3 18.9 187 3800 female 2007
Adelie Biscoe 40.6 18.6 183 3550 male 2007
Adelie Biscoe 40.5 17.9 187 3200 female 2007
Adelie Biscoe 37.9 18.6 172 3150 female 2007
Adelie Biscoe 40.5 18.9 180 3950 male 2007
Adelie Dream 39.5 16.7 178 3250 female 2007
Adelie Dream 37.2 18.1 178 3900 male 2007
Adelie Dream 39.5 17.8 188 3300 female 2007
Adelie Dream 40.9 18.9 184 3900 male 2007
Adelie Dream 36.4 17.0 195 3325 female 2007
Adelie Dream 39.2 21.1 196 4150 male 2007
Adelie Dream 38.8 20.0 190 3950 male 2007
Adelie Dream 42.2 18.5 180 3550 female 2007
Adelie Dream 37.6 19.3 181 3300 female 2007
Adelie Dream 39.8 19.1 184 4650 male 2007
Adelie Dream 36.5 18.0 182 3150 female 2007
Adelie Dream 40.8 18.4 195 3900 male 2007
Adelie Dream 36.0 18.5 186 3100 female 2007
Adelie Dream 44.1 19.7 196 4400 male 2007
Adelie Dream 37.0 16.9 185 3000 female 2007
Adelie Dream 39.6 18.8 190 4600 male 2007
Adelie Dream 41.1 19.0 182 3425 male 2007
Adelie Dream 37.5 18.9 179 2975 NA 2007
Adelie Dream 36.0 17.9 190 3450 female 2007
Adelie Dream 42.3 21.2 191 4150 male 2007
Adelie Biscoe 39.6 17.7 186 3500 female 2008
Adelie Biscoe 40.1 18.9 188 4300 male 2008
Adelie Biscoe 35.0 17.9 190 3450 female 2008
Adelie Biscoe 42.0 19.5 200 4050 male 2008
Adelie Biscoe 34.5 18.1 187 2900 female 2008
Adelie Biscoe 41.4 18.6 191 3700 male 2008
Adelie Biscoe 39.0 17.5 186 3550 female 2008
Adelie Biscoe 40.6 18.8 193 3800 male 2008
Adelie Biscoe 36.5 16.6 181 2850 female 2008
Adelie Biscoe 37.6 19.1 194 3750 male 2008
Adelie Biscoe 35.7 16.9 185 3150 female 2008
Adelie Biscoe 41.3 21.1 195 4400 male 2008
Adelie Biscoe 37.6 17.0 185 3600 female 2008
Adelie Biscoe 41.1 18.2 192 4050 male 2008
Adelie Biscoe 36.4 17.1 184 2850 female 2008
Adelie Biscoe 41.6 18.0 192 3950 male 2008
Adelie Biscoe 35.5 16.2 195 3350 female 2008
Adelie Biscoe 41.1 19.1 188 4100 male 2008
Adelie Torgersen 35.9 16.6 190 3050 female 2008
Adelie Torgersen 41.8 19.4 198 4450 male 2008
Adelie Torgersen 33.5 19.0 190 3600 female 2008
Adelie Torgersen 39.7 18.4 190 3900 male 2008
Adelie Torgersen 39.6 17.2 196 3550 female 2008
Adelie Torgersen 45.8 18.9 197 4150 male 2008
Adelie Torgersen 35.5 17.5 190 3700 female 2008
Adelie Torgersen 42.8 18.5 195 4250 male 2008
Adelie Torgersen 40.9 16.8 191 3700 female 2008
Adelie Torgersen 37.2 19.4 184 3900 male 2008
Adelie Torgersen 36.2 16.1 187 3550 female 2008
Adelie Torgersen 42.1 19.1 195 4000 male 2008
Adelie Torgersen 34.6 17.2 189 3200 female 2008
Adelie Torgersen 42.9 17.6 196 4700 male 2008
Adelie Torgersen 36.7 18.8 187 3800 female 2008
Adelie Torgersen 35.1 19.4 193 4200 male 2008
Adelie Dream 37.3 17.8 191 3350 female 2008
Adelie Dream 41.3 20.3 194 3550 male 2008
Adelie Dream 36.3 19.5 190 3800 male 2008
Adelie Dream 36.9 18.6 189 3500 female 2008
Adelie Dream 38.3 19.2 189 3950 male 2008
Adelie Dream 38.9 18.8 190 3600 female 2008
Adelie Dream 35.7 18.0 202 3550 female 2008
Adelie Dream 41.1 18.1 205 4300 male 2008
Adelie Dream 34.0 17.1 185 3400 female 2008
Adelie Dream 39.6 18.1 186 4450 male 2008
Adelie Dream 36.2 17.3 187 3300 female 2008
Adelie Dream 40.8 18.9 208 4300 male 2008
Adelie Dream 38.1 18.6 190 3700 female 2008
Adelie Dream 40.3 18.5 196 4350 male 2008
Adelie Dream 33.1 16.1 178 2900 female 2008
Adelie Dream 43.2 18.5 192 4100 male 2008
Adelie Biscoe 35.0 17.9 192 3725 female 2009
Adelie Biscoe 41.0 20.0 203 4725 male 2009
Adelie Biscoe 37.7 16.0 183 3075 female 2009
Adelie Biscoe 37.8 20.0 190 4250 male 2009
Adelie Biscoe 37.9 18.6 193 2925 female 2009
Adelie Biscoe 39.7 18.9 184 3550 male 2009
Adelie Biscoe 38.6 17.2 199 3750 female 2009
Adelie Biscoe 38.2 20.0 190 3900 male 2009
Adelie Biscoe 38.1 17.0 181 3175 female 2009
Adelie Biscoe 43.2 19.0 197 4775 male 2009
Adelie Biscoe 38.1 16.5 198 3825 female 2009
Adelie Biscoe 45.6 20.3 191 4600 male 2009
Adelie Biscoe 39.7 17.7 193 3200 female 2009
Adelie Biscoe 42.2 19.5 197 4275 male 2009
Adelie Biscoe 39.6 20.7 191 3900 female 2009
Adelie Biscoe 42.7 18.3 196 4075 male 2009
Adelie Torgersen 38.6 17.0 188 2900 female 2009
Adelie Torgersen 37.3 20.5 199 3775 male 2009
Adelie Torgersen 35.7 17.0 189 3350 female 2009
Adelie Torgersen 41.1 18.6 189 3325 male 2009
Adelie Torgersen 36.2 17.2 187 3150 female 2009
Adelie Torgersen 37.7 19.8 198 3500 male 2009
Adelie Torgersen 40.2 17.0 176 3450 female 2009
Adelie Torgersen 41.4 18.5 202 3875 male 2009
Adelie Torgersen 35.2 15.9 186 3050 female 2009
Adelie Torgersen 40.6 19.0 199 4000 male 2009
Adelie Torgersen 38.8 17.6 191 3275 female 2009
Adelie Torgersen 41.5 18.3 195 4300 male 2009
Adelie Torgersen 39.0 17.1 191 3050 female 2009
Adelie Torgersen 44.1 18.0 210 4000 male 2009
Adelie Torgersen 38.5 17.9 190 3325 female 2009
Adelie Torgersen 43.1 19.2 197 3500 male 2009
Adelie Dream 36.8 18.5 193 3500 female 2009
Adelie Dream 37.5 18.5 199 4475 male 2009
Adelie Dream 38.1 17.6 187 3425 female 2009
Adelie Dream 41.1 17.5 190 3900 male 2009
Adelie Dream 35.6 17.5 191 3175 female 2009
Adelie Dream 40.2 20.1 200 3975 male 2009
Adelie Dream 37.0 16.5 185 3400 female 2009
Adelie Dream 39.7 17.9 193 4250 male 2009
Adelie Dream 40.2 17.1 193 3400 female 2009
Adelie Dream 40.6 17.2 187 3475 male 2009
Adelie Dream 32.1 15.5 188 3050 female 2009
Adelie Dream 40.7 17.0 190 3725 male 2009
Adelie Dream 37.3 16.8 192 3000 female 2009
Adelie Dream 39.0 18.7 185 3650 male 2009
Adelie Dream 39.2 18.6 190 4250 male 2009
Adelie Dream 36.6 18.4 184 3475 female 2009
Adelie Dream 36.0 17.8 195 3450 female 2009
Adelie Dream 37.8 18.1 193 3750 male 2009
Adelie Dream 36.0 17.1 187 3700 female 2009
Adelie Dream 41.5 18.5 201 4000 male 2009
Gentoo Biscoe 46.1 13.2 211 4500 female 2007
Gentoo Biscoe 50.0 16.3 230 5700 male 2007
Gentoo Biscoe 48.7 14.1 210 4450 female 2007
Gentoo Biscoe 50.0 15.2 218 5700 male 2007
Gentoo Biscoe 47.6 14.5 215 5400 male 2007
Gentoo Biscoe 46.5 13.5 210 4550 female 2007
Gentoo Biscoe 45.4 14.6 211 4800 female 2007
Gentoo Biscoe 46.7 15.3 219 5200 male 2007
Gentoo Biscoe 43.3 13.4 209 4400 female 2007
Gentoo Biscoe 46.8 15.4 215 5150 male 2007
Gentoo Biscoe 40.9 13.7 214 4650 female 2007
Gentoo Biscoe 49.0 16.1 216 5550 male 2007
Gentoo Biscoe 45.5 13.7 214 4650 female 2007
Gentoo Biscoe 48.4 14.6 213 5850 male 2007
Gentoo Biscoe 45.8 14.6 210 4200 female 2007
Gentoo Biscoe 49.3 15.7 217 5850 male 2007
Gentoo Biscoe 42.0 13.5 210 4150 female 2007
Gentoo Biscoe 49.2 15.2 221 6300 male 2007
Gentoo Biscoe 46.2 14.5 209 4800 female 2007
Gentoo Biscoe 48.7 15.1 222 5350 male 2007
Gentoo Biscoe 50.2 14.3 218 5700 male 2007
Gentoo Biscoe 45.1 14.5 215 5000 female 2007
Gentoo Biscoe 46.5 14.5 213 4400 female 2007
Gentoo Biscoe 46.3 15.8 215 5050 male 2007
Gentoo Biscoe 42.9 13.1 215 5000 female 2007
Gentoo Biscoe 46.1 15.1 215 5100 male 2007
Gentoo Biscoe 44.5 14.3 216 4100 NA 2007
Gentoo Biscoe 47.8 15.0 215 5650 male 2007
Gentoo Biscoe 48.2 14.3 210 4600 female 2007
Gentoo Biscoe 50.0 15.3 220 5550 male 2007
Gentoo Biscoe 47.3 15.3 222 5250 male 2007
Gentoo Biscoe 42.8 14.2 209 4700 female 2007
Gentoo Biscoe 45.1 14.5 207 5050 female 2007
Gentoo Biscoe 59.6 17.0 230 6050 male 2007
Gentoo Biscoe 49.1 14.8 220 5150 female 2008
Gentoo Biscoe 48.4 16.3 220 5400 male 2008
Gentoo Biscoe 42.6 13.7 213 4950 female 2008
Gentoo Biscoe 44.4 17.3 219 5250 male 2008
Gentoo Biscoe 44.0 13.6 208 4350 female 2008
Gentoo Biscoe 48.7 15.7 208 5350 male 2008
Gentoo Biscoe 42.7 13.7 208 3950 female 2008
Gentoo Biscoe 49.6 16.0 225 5700 male 2008
Gentoo Biscoe 45.3 13.7 210 4300 female 2008
Gentoo Biscoe 49.6 15.0 216 4750 male 2008
Gentoo Biscoe 50.5 15.9 222 5550 male 2008
Gentoo Biscoe 43.6 13.9 217 4900 female 2008
Gentoo Biscoe 45.5 13.9 210 4200 female 2008
Gentoo Biscoe 50.5 15.9 225 5400 male 2008
Gentoo Biscoe 44.9 13.3 213 5100 female 2008
Gentoo Biscoe 45.2 15.8 215 5300 male 2008
Gentoo Biscoe 46.6 14.2 210 4850 female 2008
Gentoo Biscoe 48.5 14.1 220 5300 male 2008
Gentoo Biscoe 45.1 14.4 210 4400 female 2008
Gentoo Biscoe 50.1 15.0 225 5000 male 2008
Gentoo Biscoe 46.5 14.4 217 4900 female 2008
Gentoo Biscoe 45.0 15.4 220 5050 male 2008
Gentoo Biscoe 43.8 13.9 208 4300 female 2008
Gentoo Biscoe 45.5 15.0 220 5000 male 2008
Gentoo Biscoe 43.2 14.5 208 4450 female 2008
Gentoo Biscoe 50.4 15.3 224 5550 male 2008
Gentoo Biscoe 45.3 13.8 208 4200 female 2008
Gentoo Biscoe 46.2 14.9 221 5300 male 2008
Gentoo Biscoe 45.7 13.9 214 4400 female 2008
Gentoo Biscoe 54.3 15.7 231 5650 male 2008
Gentoo Biscoe 45.8 14.2 219 4700 female 2008
Gentoo Biscoe 49.8 16.8 230 5700 male 2008
Gentoo Biscoe 46.2 14.4 214 4650 NA 2008
Gentoo Biscoe 49.5 16.2 229 5800 male 2008
Gentoo Biscoe 43.5 14.2 220 4700 female 2008
Gentoo Biscoe 50.7 15.0 223 5550 male 2008
Gentoo Biscoe 47.7 15.0 216 4750 female 2008
Gentoo Biscoe 46.4 15.6 221 5000 male 2008
Gentoo Biscoe 48.2 15.6 221 5100 male 2008
Gentoo Biscoe 46.5 14.8 217 5200 female 2008
Gentoo Biscoe 46.4 15.0 216 4700 female 2008
Gentoo Biscoe 48.6 16.0 230 5800 male 2008
Gentoo Biscoe 47.5 14.2 209 4600 female 2008
Gentoo Biscoe 51.1 16.3 220 6000 male 2008
Gentoo Biscoe 45.2 13.8 215 4750 female 2008
Gentoo Biscoe 45.2 16.4 223 5950 male 2008
Gentoo Biscoe 49.1 14.5 212 4625 female 2009
Gentoo Biscoe 52.5 15.6 221 5450 male 2009
Gentoo Biscoe 47.4 14.6 212 4725 female 2009
Gentoo Biscoe 50.0 15.9 224 5350 male 2009
Gentoo Biscoe 44.9 13.8 212 4750 female 2009
Gentoo Biscoe 50.8 17.3 228 5600 male 2009
Gentoo Biscoe 43.4 14.4 218 4600 female 2009
Gentoo Biscoe 51.3 14.2 218 5300 male 2009
Gentoo Biscoe 47.5 14.0 212 4875 female 2009
Gentoo Biscoe 52.1 17.0 230 5550 male 2009
Gentoo Biscoe 47.5 15.0 218 4950 female 2009
Gentoo Biscoe 52.2 17.1 228 5400 male 2009
Gentoo Biscoe 45.5 14.5 212 4750 female 2009
Gentoo Biscoe 49.5 16.1 224 5650 male 2009
Gentoo Biscoe 44.5 14.7 214 4850 female 2009
Gentoo Biscoe 50.8 15.7 226 5200 male 2009
Gentoo Biscoe 49.4 15.8 216 4925 male 2009
Gentoo Biscoe 46.9 14.6 222 4875 female 2009
Gentoo Biscoe 48.4 14.4 203 4625 female 2009
Gentoo Biscoe 51.1 16.5 225 5250 male 2009
Gentoo Biscoe 48.5 15.0 219 4850 female 2009
Gentoo Biscoe 55.9 17.0 228 5600 male 2009
Gentoo Biscoe 47.2 15.5 215 4975 female 2009
Gentoo Biscoe 49.1 15.0 228 5500 male 2009
Gentoo Biscoe 47.3 13.8 216 4725 NA 2009
Gentoo Biscoe 46.8 16.1 215 5500 male 2009
Gentoo Biscoe 41.7 14.7 210 4700 female 2009
Gentoo Biscoe 53.4 15.8 219 5500 male 2009
Gentoo Biscoe 43.3 14.0 208 4575 female 2009
Gentoo Biscoe 48.1 15.1 209 5500 male 2009
Gentoo Biscoe 50.5 15.2 216 5000 female 2009
Gentoo Biscoe 49.8 15.9 229 5950 male 2009
Gentoo Biscoe 43.5 15.2 213 4650 female 2009
Gentoo Biscoe 51.5 16.3 230 5500 male 2009
Gentoo Biscoe 46.2 14.1 217 4375 female 2009
Gentoo Biscoe 55.1 16.0 230 5850 male 2009
Gentoo Biscoe 44.5 15.7 217 4875 NA 2009
Gentoo Biscoe 48.8 16.2 222 6000 male 2009
Gentoo Biscoe 47.2 13.7 214 4925 female 2009
Gentoo Biscoe NA NA NA NA NA 2009
Gentoo Biscoe 46.8 14.3 215 4850 female 2009
Gentoo Biscoe 50.4 15.7 222 5750 male 2009
Gentoo Biscoe 45.2 14.8 212 5200 female 2009
Gentoo Biscoe 49.9 16.1 213 5400 male 2009
Chinstrap Dream 46.5 17.9 192 3500 female 2007
Chinstrap Dream 50.0 19.5 196 3900 male 2007
Chinstrap Dream 51.3 19.2 193 3650 male 2007
Chinstrap Dream 45.4 18.7 188 3525 female 2007
Chinstrap Dream 52.7 19.8 197 3725 male 2007
Chinstrap Dream 45.2 17.8 198 3950 female 2007
Chinstrap Dream 46.1 18.2 178 3250 female 2007
Chinstrap Dream 51.3 18.2 197 3750 male 2007
Chinstrap Dream 46.0 18.9 195 4150 female 2007
Chinstrap Dream 51.3 19.9 198 3700 male 2007
Chinstrap Dream 46.6 17.8 193 3800 female 2007
Chinstrap Dream 51.7 20.3 194 3775 male 2007
Chinstrap Dream 47.0 17.3 185 3700 female 2007
Chinstrap Dream 52.0 18.1 201 4050 male 2007
Chinstrap Dream 45.9 17.1 190 3575 female 2007
Chinstrap Dream 50.5 19.6 201 4050 male 2007
Chinstrap Dream 50.3 20.0 197 3300 male 2007
Chinstrap Dream 58.0 17.8 181 3700 female 2007
Chinstrap Dream 46.4 18.6 190 3450 female 2007
Chinstrap Dream 49.2 18.2 195 4400 male 2007
Chinstrap Dream 42.4 17.3 181 3600 female 2007
Chinstrap Dream 48.5 17.5 191 3400 male 2007
Chinstrap Dream 43.2 16.6 187 2900 female 2007
Chinstrap Dream 50.6 19.4 193 3800 male 2007
Chinstrap Dream 46.7 17.9 195 3300 female 2007
Chinstrap Dream 52.0 19.0 197 4150 male 2007
Chinstrap Dream 50.5 18.4 200 3400 female 2008
Chinstrap Dream 49.5 19.0 200 3800 male 2008
Chinstrap Dream 46.4 17.8 191 3700 female 2008
Chinstrap Dream 52.8 20.0 205 4550 male 2008
Chinstrap Dream 40.9 16.6 187 3200 female 2008
Chinstrap Dream 54.2 20.8 201 4300 male 2008
Chinstrap Dream 42.5 16.7 187 3350 female 2008
Chinstrap Dream 51.0 18.8 203 4100 male 2008
Chinstrap Dream 49.7 18.6 195 3600 male 2008
Chinstrap Dream 47.5 16.8 199 3900 female 2008
Chinstrap Dream 47.6 18.3 195 3850 female 2008
Chinstrap Dream 52.0 20.7 210 4800 male 2008
Chinstrap Dream 46.9 16.6 192 2700 female 2008
Chinstrap Dream 53.5 19.9 205 4500 male 2008
Chinstrap Dream 49.0 19.5 210 3950 male 2008
Chinstrap Dream 46.2 17.5 187 3650 female 2008
Chinstrap Dream 50.9 19.1 196 3550 male 2008
Chinstrap Dream 45.5 17.0 196 3500 female 2008
Chinstrap Dream 50.9 17.9 196 3675 female 2009
Chinstrap Dream 50.8 18.5 201 4450 male 2009
Chinstrap Dream 50.1 17.9 190 3400 female 2009
Chinstrap Dream 49.0 19.6 212 4300 male 2009
Chinstrap Dream 51.5 18.7 187 3250 male 2009
Chinstrap Dream 49.8 17.3 198 3675 female 2009
Chinstrap Dream 48.1 16.4 199 3325 female 2009
Chinstrap Dream 51.4 19.0 201 3950 male 2009
Chinstrap Dream 45.7 17.3 193 3600 female 2009
Chinstrap Dream 50.7 19.7 203 4050 male 2009
Chinstrap Dream 42.5 17.3 187 3350 female 2009
Chinstrap Dream 52.2 18.8 197 3450 male 2009
Chinstrap Dream 45.2 16.6 191 3250 female 2009
Chinstrap Dream 49.3 19.9 203 4050 male 2009
Chinstrap Dream 50.2 18.8 202 3800 male 2009
Chinstrap Dream 45.6 19.4 194 3525 female 2009
Chinstrap Dream 51.9 19.5 206 3950 male 2009
Chinstrap Dream 46.8 16.5 189 3650 female 2009
Chinstrap Dream 45.7 17.0 195 3650 female 2009
Chinstrap Dream 55.8 19.8 207 4000 male 2009
Chinstrap Dream 43.5 18.1 202 3400 female 2009
Chinstrap Dream 49.6 18.2 193 3775 male 2009
Chinstrap Dream 50.8 19.0 210 4100 male 2009
Chinstrap Dream 50.2 18.7 198 3775 female 2009

Penguins dataset

Figure 1: Penguins species
Figure 2: Bill measurements

Artwork by @allison_horst

Penguins: comparing distributions

  • The Gentoo species seems considerably heavier than the other two species.
  • The Chinstrap and Adelie species seem to have similar body mass distributions;
  • The Chinstrap species seems to have lower variability in body mass.
  • Only the Chinstrap species has outliers (easier to see in the boxplot).

Penguins: comparing distributions

  • It seems that male penguins are slightly heavier than female penguins.

  • The distributions of body mass are bimodal for both male and female penguins.

    • Note that you can’t see that from the boxplots.
    • Can you think of a reason for this?

  • The weight variability is a tiny bit higher for male penguins.

Comparing distributions: Caveats

Compare the histograms and boxplots of the bill length across the sex variable.



What do you notice?

Comparing distributions: Caveats

Comparing distributions: Caveats

  • Let’s add another variable to our analysis: species.

  • Compare the histograms and boxplots of the bill length across the sex and species variable.


What do you notice?

Comparing distributions: Caveats

Comparing distributions: Caveats

  • By grouping all the penguins and comparing the bill length across sex, there’s a huge inflation of variability due to the different species.

  • This hindered our ability to distinguish differences between the sexes.

  • After including the species variable, we could see that male penguins tend to have a larger bill length.

Athletism: comparing distributions

Now, let’s consider the Olympic Games.


Olympic Games happen every four years. We will restrict our attention to Olympic Games after 1950.


In this dataset, we have the time of the athletes in the Final Stage of Sprint events: 100m, 200m, 400m.

Athletism: comparing distributions

This dataset has a total of 797 observations. Below is a sample of 24 rows:

modality sex year name country time
100 m M 2004 Maurice Greene USA 9.87
100 m M 1968 Pablo Montes CUB 10.14
100 m M 2008 Churandy Martina AHO 9.93
100 m M 2008 Michael Frater JAM 9.97
200 m M 1956 Michael Agostini TTO 21.10
200 m M 1972 Lawrence Burton USA 20.37
200 m M 1996 Patrick Stevens BEL 20.27
200 m M 1964 Paul Drayton USA 20.50
400 m M 2000 Danny McFarlane JAM 45.55
400 m M 1972 Horst-Rüdiger Schlöske FRG 45.31
400 m M 1972 Karl Honz FRG 45.68
400 m M 1956 Malcolm Spence RSA 48.30
100 m W 1980 Marlies Göhr GDR 11.07
100 m W 1984 Grace Jackson JAM 11.39
100 m W 1988 Juliet Cuthbert JAM 11.26
100 m W 1996 Marina Trandenkova RUS 11.06
200 m W 1992 Carlette Guidry USA 22.30
200 m W 1996 Marie-Jose Pérec FRA 22.12
200 m W 1992 Galina Malchugina EUN 22.63
200 m W 2016 Elaine Thompson JAM 21.78
400 m W 1984 Ute Thimm FRG 50.37
400 m W 1968 Hermina van der Hoeven NED 53.02
400 m W 1996 Sandie Richards JAM 50.45
400 m W 2016 Libania Grenot ITA 51.25

Athletism: comparing distributions

Compare the distribution of time across sex. What do you notice?

Athletism: comparing distributions

  • In the previous plot, we grouped modalities that are not comparable.

  • By doing so, we are inflating the variability of the distribution so much that we can’t detect differences in times between men and women.

Athletism: comparing distributions

Athletism: comparing distribution

Histograms can, sometimes, help detect these problems by showing the multimodality of the distribution. For example, in this case:

Even though we are comparing only times between men and women, we can see that there’s something else going on here.

References & Attributions

Images Attributions:

Data Attributions:

References

© 2023 Rodolfo Lourenzutti & Eugenia Yu – Material Licensed under CC By-SA 4.0

Horst, Allison Marie, Alison Presmanes Hill, and Kristen B Gorman. 2020. Palmerpenguins: Palmer Archipelago (Antarctica) Penguin Data. https://doi.org/10.5281/zenodo.3960218.