The normal probability plot is a graphical technique to identify substantive departures from normality. This is due to the central limit theorem. As with skewness, a general guideline is that kurtosis within ±1 of the normal distribution’s kurtosis indicates sufficient normality. A symmetric distribution such as a normal distribution has a skewness of 0, and a distribution that is skewed to the left, e.g., when the mean is less than the median, has a negative skewness. 1. Dealing with Skewness and Kurtosis Many classical statistical tests and intervals depend on normality assumptions. 1(2). Skewness – Skewness measures the degree and direction of asymmetry. In Stata, you can test normality by either graphical or numerical methods. Request for Confidence Intervals for Proportions ," Stata Technical Bulletin , StataCorp LP, vol. The latter involve computing the Shapiro-Wilk, Shapiro-Francia, and Skewness/Kurtosis tests. 1(2). So observing substantial skewness in some sample data suggests that the normality assumption is violated. Such violations of normality are no problem for large sample sizes-say N > 20 or 25 or so. Combining skewness and kurtosis is still a useful test of normality provided that the limiting variance accounts for the serial correlation in the data. In this case, most tests are robust against such violations. Determining if skewness and kurtosis are significantly non-normal. Similarly, what does a normal probability plot tell us? The tests are applied to 21 macroeconomic time series. The normal distribution has skewness = 0. For this data set, the skewness is 1.08 and the kurtosis is 4.46, which indicates moderate skewness and kurtosis. Conducting normality test in STATA. The former include drawing a stem-and-leaf plot, scatterplot, box-plot, histogram, probability-probability (P-P) plot, and quantile-quantile (Q-Q) plot. Significant skewness and kurtosis clearly indicate that data are not normal. A normal distribution has skewness and excess kurtosis of 0, so if your distribution is close to those values then it is probably close to normal. I carried out sktest of normality and results are as follows Skewness/Kurtosis tests for Normality joint -----Variable Obs Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 pm 16,059 0.0000 0.0000 . Choose 'Distributional plots and tests' Select 'Skewness and kurtosis normality tests'. . One application is testing for normality: many statistics inferences require that a distribution be normal or nearly normal. of 0.0010 for skewness, 0.0442 for kurtosis, and 0.0024 for the joint univariate test. "Tests for Departure from Normality," Stata Technical Bulletin, StataCorp LP, vol. Conclusion There is certainly much more we could say about parametric tests, skewness, and kurtosis, but I think that we’ve covered enough material for an introductory article. 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