Accessing Model Accuracy and Goodness-of-Fit Tests for Normality

In addition to the Summary, there are four sections in this chapter. Section 3.1 defines bias and variance and introduces the concept of bias–variance tradeoff. Section 3.2 defines accuracy and precision from three perspectives: (1) scientific methods, (2) International Organization for Standardization (ISO) methods, and (3) statistical and machine learning methods, and describes the relationship between accuracy and precision. Section 3.3 introduces three approaches for goodness-of-fit tests for normality – graphical methods, descriptive methods (focusing on the skewness and kurtosis tests), and statistical testing methods – which include six most commonly used tests: (1) chi-square test, (2) Kolmogorov-Smirnov test, (3) Anderson-Darling test, (4) Shapiro-Wilk test, (5) Lilliefors test, and (6) D&s;Agostino-Pearson test. Section 3.4 provides some remarks on goodness-of-fit tests for normality. Briefly, sample sizes matter in the power of tests. In general, the Shapiro-Wilk and Anderson-Darling tests are the two most powerful normality tests. The D’Agostino-Pearson test is a powerful and informative omnibus test for normality for skewed and/or kurtic distributions. In practice, the Lilliefors test is more often used than the Kolmogorov-Smirnov test because the Lilliefors test does not need to specify the mean and variance.