Shapiro-Wilk Test: A Guide

## Introduction The Shapiro-Wilk test is a statistical hypothesis test used to determine whether a sample comes from a normally distributed population. It is widely used in various fields, including statistics, machine learning, and data analysis. ## Description The Shapiro-Wilk test statistic is denoted as W and is calculated based on the ordered values of the sample data. If the sample is normally distributed, the W statistic will be close to 1. Conversely, non-normal distributions will result in a W statistic significantly less than 1. ## Applications The Shapiro-Wilk test finds applications in: * **Checking for normality:** Assessing whether data meets the assumption of normality before performing statistical analyses. * **Outlier detection:** Identifying data points that deviate significantly from the normal distribution. * **Model selection:** Comparing different models that assume different distributions for the data. ## Software Implementations The Shapiro-Wilk test can be performed using various statistical software packages, including: * **Excel:** Use the "Shapiro_Wilk" function. * **SPSS:** Navigate to "Analyze" > "Nonparametric Tests" > "Legacy Dialogs" > "One-Sample Tests" > "Shapiro-Wilk." * **SAS:** Use the "shapiro_wilk" procedure. * **MATLAB:** Employ the "shapirotest" function from the "stats" package. * **Minitab:** Select "Stat" > "Basic Statistics" > "Shapiro-Wilk Test." * **R:** Utilize the "shapiro.test" function from the "stats" package. ## Limitations Like all statistical tests, the Shapiro-Wilk test has limitations. It is sensitive to sample size, with larger samples providing more reliable results. Additionally, the test assumes that the sample data is independent and identically distributed.