Normality test statistics explained
Skewness measures the asymmetry of the distribution. A perfectly symmetric distribution has skewness of 0. Positive skewness indicates a longer right tail; negative skewness indicates a longer left tail.
Excess kurtosis measures the heaviness of the tails relative to a normal distribution. Normal data has excess kurtosis of 0. Positive kurtosis (leptokurtic) means heavier tails; negative kurtosis (platykurtic) means lighter tails.
The Jarque-Bera test combines skewness and kurtosis into a single test statistic that follows a chi-square distribution with 2 degrees of freedom under the null hypothesis of normality.
JB = (n/6)(S² + K²/4)
Jarque-Bera statistic where S is skewness and K is excess kurtosis.