Introduction

Shapiro-Wilk Test

Introduction

The Shapiro-Wilk test is a statistical test that is used to determine whether or not a given dataset follows a normal distribution. The test is based on the assumption that the data is normally distributed and produces a p-value that indicates the probability of the data being non-normal. A p-value of less than 0.05 is considered to be statistically significant and indicates that the data is not normally distributed.

Applications

The Shapiro-Wilk test is used in a variety of applications, including: * Data analysis and validation * Hypothesis testing * Statistical modeling The test can be used to determine if a dataset is suitable for use in a particular statistical analysis or model. For example, many statistical models assume that the data is normally distributed. If the Shapiro-Wilk test indicates that the data is not normally distributed, then the model may not be appropriate.

Limitations

The Shapiro-Wilk test has some limitations, including: * It is not as powerful as some other tests of normality, such as the Kolmogorov-Smirnov test. * It is sensitive to outliers, which can affect the p-value. * It is not a suitable test for datasets that are very small or very large. Despite its limitations, the Shapiro-Wilk test is a widely used and useful test for determining whether or not a dataset is normally distributed.