Assessment of whether a dataset plausibly originates from a normal distribution is a common task in statistical analysis. Within the R programming environment, several methods exist to evaluate this assumption. These methods include visual inspections, such as histograms and Q-Q plots, and formal statistical tests like the Shapiro-Wilk test, the Kolmogorov-Smirnov test (with modifications for normality), and the Anderson-Darling test. For instance, the Shapiro-Wilk test, implemented using the `shapiro.test()` function, calculates a W statistic to quantify the departure from normality. A p-value associated with this statistic helps determine if the null hypothesis of normality can be rejected at a chosen significance level.
Establishing the distributional properties of data is crucial because many statistical procedures rely on the assumption of normality. Regression analysis, t-tests, and ANOVA, among others, often perform optimally when the underlying data closely approximates a normal distribution. When this assumption is violated, the validity of the statistical inferences drawn from these analyses may be compromised. Historically, the development and application of methods to check for this characteristic have played a significant role in ensuring the reliability and robustness of statistical modeling across diverse fields like medicine, engineering, and finance.
