Assessing the Normality of Continuous Data: Shapiro-Wilk Test and Methods

Introduction

In statistical analysis, assessing the normality of continuous data is crucial to ensure the validity of many parametric tests. One widely used method for testing normality is the Shapiro-Wilk test.

Shapiro-Wilk Test

The Shapiro-Wilk test is a non-parametric test that evaluates the null hypothesis that the data follows a normal distribution. The p-value of the test indicates the probability of obtaining the observed sample of data if the null hypothesis is true.

If the p-value is less than a predetermined significance level (usually 0.05), it suggests that the data is not normally distributed. In our case, the p-value of 0.006 indicates that the data is significantly non-normal.

Methods for Assessing Normality

Aside from the Shapiro-Wilk test, there are various other methods available to test the normality of continuous data:

• Kolmogorov-Smirnov Test: Another non-parametric test that compares the empirical distribution of the data to the normal distribution.
• Anderson-Darling Test: A powerful non-parametric test that is sensitive to deviations from normality, especially in the tails.
• Jarque-Bera Test: A parametric test that assesses the skewness and kurtosis of the data to determine if it follows a normal distribution.
• Q-Q Plot: A graphical method that compares the quantiles of the data to the quantiles of a normal distribution.

Conclusion

Assessing the normality of continuous data is an important step in statistical analysis. The Shapiro-Wilk test is a commonly used method, but other methods are also available. By understanding the different methods and their strengths and weaknesses, researchers can choose the most appropriate test for their specific data and research questions.