Assessing whether a dataset plausibly originates from a Gaussian distribution is a common statistical task. Several formal methods are available in the R programming environment to evaluate this assumption. These procedures provide a quantitative measure of the compatibility between observed data and the theoretical normal model. For example, one can apply the Shapiro-Wilk test or the Kolmogorov-Smirnov test (with appropriate modifications) to assess normality. These tests yield a p-value, which indicates the probability of observing data as extreme as, or more extreme than, the actual data if it truly were sampled from a Gaussian distribution.
Establishing the normality assumption is crucial for many statistical techniques, as violations can lead to inaccurate inferences. Methods like t-tests and ANOVA rely on the assumption that the underlying data are approximately normally distributed. When this assumption is met, these tests are known to be powerful and efficient. Furthermore, many modeling approaches, such as linear regression, assume that the residuals are normally distributed. Historically, visual inspection of histograms and Q-Q plots were the primary means of evaluating normality. Formal tests offer a more objective, albeit potentially limited, assessment.
