Skewness And Kurtosis
Two measures of a distribution's shape: skewness describes asymmetry, and kurtosis describes the heaviness of the tails relative to a normal distribution.
Skewness and kurtosis describe how a distribution departs from the symmetric bell shape. Skewness measures asymmetry: positive skew means a long right tail, with the mean pulled above the median, as often happens with income; negative skew means a long left tail. Kurtosis measures tail weight relative to a normal distribution: heavy-tailed distributions produce more extreme values, light-tailed ones fewer. For a normal distribution, both statistics are effectively zero in their commonly reported forms.
In a thesis, skewness and kurtosis are practical normality checks. Report them with your descriptive statistics, alongside histograms, to justify whether parametric tests are appropriate or whether transformations or non-parametric tests are needed. They also guide reporting choices: for clearly skewed variables, the median describes the center more honestly than the mean, a point worth making explicit in your results chapter.
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