ShapiroWilktestillä

Shapiro-Wilk test, also known as Shapiro-Wilk W test, is a statistical test used to determine whether a sample comes from a normally distributed population. It is one of the most powerful tests for normality and is widely used in various fields, including statistics, data analysis, and quality control. The test was developed by Samuel Sanford Shapiro and Martin Wilk in 1965.

The Shapiro-Wilk test is based on the comparison of the sample data with the expected values from a normal distribution. It calculates a test statistic, W, which ranges from 0 to 1. A value of 1 indicates a perfect normal distribution, while a value closer to 0 suggests a departure from normality. The test also provides a p-value, which helps in determining the significance of the result. If the p-value is less than a chosen significance level (commonly 0.05), the null hypothesis of normality is rejected.

The Shapiro-Wilk test is particularly useful when the sample size is small, as it is more sensitive to deviations from normality compared to other tests like the Kolmogorov-Smirnov test. However, it is less effective for larger sample sizes, where other tests like the Anderson-Darling test may be more appropriate.

In summary, the Shapiro-Wilk test is a robust and widely used method for assessing the normality of a dataset. Its ability to detect deviations from normality, even in small samples, makes it a valuable tool in statistical analysis.