# Shapiro-Wilk, Anderson-Darling and Lilliefors Normality Tutor Run the three workhorse normality tests (Shapiro-Wilk AS R94, Anderson-Darling, Lilliefors) with a Q-Q plot and a Monte-Carlo power comparison. > Canonical page: https://elysiatools.com/en/tools/shapiro-wilk-anderson-darling-lilliefors-normality-tutor - **Category:** Science & Education - **Keywords:** shapiro wilk calculator, normality test online, anderson darling p value, lilliefors test calculator, qq plot normal, test power simulation ## Overview Exact ports of the reference implementations: R’s swilk.c for Shapiro-Wilk, nortest’s ad.test and lillie.test for the other two, validated digit-for-digit against scipy. Includes Blom Q-Q plotting and seeded power simulations across five alternative shapes. ## Inputs - **Numeric sample (comma / space / newline separated)** (textarea): 4.53 5.12 4.87 … or one value per line - **Significance level α** (select) - **Draw the Q-Q plot** (checkbox) - **Power-curve alternative distribution** (select) - **Run the Monte-Carlo power comparison** (checkbox) ## When to use - Checking normality assumptions prior to running parametric analyses such as t-tests, ANOVA, or linear regression. - Evaluating dataset tails, asymmetry, and potential outliers using quantitative tests alongside a Blom Q-Q plot. - Comparing statistical power and detection sensitivity across different non-normal distribution alternatives. ## How it works - Paste numeric observations separated by commas, spaces, or line breaks into the input field. - Select your target significance level (α = 0.01, 0.05, or 0.10) and enable the optional Blom Q-Q plot. - Choose an alternative distribution profile (such as exponential, bimodal, uniform, or Student t3) to run Monte-Carlo power simulations. - Review the resulting HTML report containing test statistics (W, A², D), exact p-values, descriptive metrics, and decision summaries. ## Use cases - Validating experimental assay residuals in laboratory and clinical research datasets. - Demonstrating normality test mechanics and power trade-offs in statistics and data science courses. - Verifying process distribution shapes for statistical quality control in manufacturing workflows. ## Frequently asked questions ### Which normality test is best for general use? Shapiro-Wilk is generally recommended as the most powerful omnibus test, while Anderson-Darling provides superior sensitivity to tail departures. ### How are the p-values and test statistics calculated? Calculations use exact ports of standard R implementations: swilk.c (AS R94) for Shapiro-Wilk, and nortest for Anderson-Darling and Lilliefors, validated against SciPy. ### What formula is used to plot the Q-Q line? The Q-Q plot uses Blom plotting positions to calculate empirical quantiles against theoretical normal quantiles with a robust quartile reference line. ### What does the Monte-Carlo power simulation represent? It simulates empirical rejection rates across various sample sizes to show how effectively each test detects departures from normality for a chosen alternative distribution. ### What data formats are accepted? 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