Definition

What is the Shapiro-Wilk Test?

Definition

The Shapiro-Wilk test is a statistical test that assesses whether a sample of data comes from a normally distributed population.

Objective

The test aims to determine if the data exhibits characteristics consistent with a normal distribution, which is a bell-shaped curve with specific statistical properties.

How it Works

The Shapiro-Wilk test calculates a statistic, denoted by W, which measures the discrepancy between the sample data and a normal distribution. Smaller values of W indicate a greater deviation from normality.

Significance

If the calculated W value falls below a predefined threshold, the test rejects the null hypothesis of normality, suggesting that the data is not normally distributed. Conversely, if W exceeds the threshold, the test fails to reject the null hypothesis, indicating that the data may reasonably come from a normal distribution.

Applications

The Shapiro-Wilk test is commonly used in various fields to assess the normality of data, including:

* Statistics * Hypothesis testing * Data analysis * Quality control

Conclusion

The Shapiro-Wilk test is a valuable statistical tool that helps researchers and analysts determine whether their data exhibits characteristics consistent with a normal distribution. By understanding the concepts behind this test, researchers can make informed decisions about the validity of their data and the appropriateness of statistical methods that assume normality.