Kurtosis measures how long the tails of a distribution are. Values near 0 indicate a normal distribution; negative values indicate thin tails, while positive values indicate fat tails. section 17.4.1
Use kurtosis during exploratory data analysis to judge distribution shape:
- Read kurtosis beside skewness in continuous-variable summaries; together, they indicate whether a distribution resembles a normal distribution. section 17.4.1
- Treat values close to zero as consistent with normality, and values farther from zero as evidence of thinner or fatter tails. section 17.4.3
- Compare the statistic with QQ plots and density plots rather than interpreting it in isolation. section 17.4.3
NBA odds data
A tableone summary reports kurtosis for variables such as ptsR, openspreadR, and closespreadH. SmartEDA extends the check with density plots and QQ plots, showing values near zero for normally distributed openspreadH and more distant values for non-normal diff_margin_closespreadH. section 17.4.1 section 17.4.3
options(scipen = 999) summary(tableOne) ## ## ### Summary of continuous variables ### ## ## strata: Overall ## n miss p.miss mean sd median p25 p75 min max skew kurt ## ptsR 1230 0 0 110 12 110 101 118 68 168 0.1 0.2 ## openspreadR 1230 0 0 2 6 3 -2 8 -16 18 -0.2 -0.6 ## opentotal 1230 0 0 222 9 222 216 228 196 243 -0.2 -0.4 ## closespreadR 1230 0 0 3 7 4 -2 8 -17 18 -0.2 -0.7 ## closetotal 1230 0 0 222 9 222 216 228 194 244 -0.1 -0.3 ## ptsH 1230 0 0 113 13 112 104 121 77 161 0.2 0.1 ## openspreadH 1230 0 0 -2 6 -3 -8 2 -18 16 0.2 -0.6 ## closespreadH 1230 0 0 -3 7 -4 -8 2 -18 17 0.2 -0.7 ## ## ====================================================================== ## ## ### Summary of categorical variables ### ## ## strata: Overall ## var n miss p.miss level freq percent cum.percent ## teamR 1230 0 0.0 Atlanta 41 3.3 3.3 ## Boston 41 3.3 6.7 ## Brooklyn 41 3.3 10.0 ## Toronto 41 3.3 93.3 ## Utah 41 3.3 96.7 ## Washington 41 3.3 100.0 ## ## venueR 1230 0 0.0 R 1230 100.0 100.0 ## ## teamH 1230 0 0.0 Atlanta 41 3.3 3.3 ## Boston 41 3.3 6.7 ## Brooklyn 41 3.3 10.0 ## Toronto 41 3.3 93.3 ## Utah 41 3.3 96.7 ## Washington 41 3.3 100.0 ## ## venueH 1230 0 0.0 H 1230 100.0 100.0 ## ## month2 1230 0 0.0 1 110 8.9 8.9 ## 2 219 17.8 26.7 ## 3 219 17.8 44.6 ## 4 221 18.0 62.5 ## 5 158 12.8 75.4 ## 6 224 18.2 93.6 ## 7 79 6.4 100.0 ##
Inspect the continuous-variable summary, including sample size, mean, spread, skewness, and kurtosis for NBA odds variables. section 17.4.1
