KANDA DATA

In statistical analysis of research results, normality testing is often treated as an analytical step that is almost always conducted before proceeding to further analysis. Many researchers, students, and data practitioners believe that without a normality test, statistical analysis results become less scientific.

However, the question is: does data normality testing really have to be performed in every statistical analysis? Or are there certain conditions where this test is actually not that necessary?

In this article, Kanda Data briefly yet comprehensively discusses what a normality test is, its purpose, and when normality testing should—and should not—be conducted.

Definition of Normality Testing

A normality test is a statistical procedure used to determine whether data or residuals follow a normal distribution. The normal distribution itself is a theoretical distribution in the shape of a bell curve that is symmetrical, where the mean, median, and mode are located at the same point.

There are several approaches that can be used to detect data normality. We can use graphical methods as well as statistical tests to determine whether the data or residuals are normally distributed.

Some commonly used normality tests include the Shapiro–Wilk test, Kolmogorov–Smirnov test, Lilliefors test, and Jarque–Bera test. In addition to these statistical tests, data normality is also often evaluated visually using histograms, Q–Q plots, or P–P plots.

Purpose of Data Normality Testing

The main purpose of normality testing is not merely to fulfill one step in the analysis process, but to ensure that certain statistical assumptions are satisfied. Many parametric statistical methods, such as the t-test, ANOVA, and OLS linear regression, assume that the error terms (residuals) are normally distributed, rather than the raw data themselves.

By understanding the distribution pattern of the data or residuals, researchers can:

(a) determine whether parametric methods are appropriate to use;

(b) choose nonparametric alternatives if the required assumptions are not met; and

(c) interpret the analysis results more cautiously and in accordance with scientific principles.

When Should We Perform a Normality Test?

After understanding the definition and purpose of normality testing, the next question is when we should conduct it. Normality testing should be performed under the following conditions:

(a) when using parametric statistical methods, especially with small sample sizes, where the normality assumption becomes more critical;

(b) in inferential statistical analyses such as hypothesis testing that are sensitive to assumption violations;

(c) when focusing on residual analysis, where in OLS linear regression, it is the residuals—not the X or Y variables separately—that should be tested for normality; and

(d) when the sample size is relatively small, as violations of normality can significantly affect the validity of statistical tests.

When Do We Not Need to Perform a Normality Test?

On the other hand, there are several conditions in which normality testing is not mandatory or even less relevant:

(a) large sample sizes, where the Central Limit Theorem explains that the sampling distribution of the mean will approach normality even if the original data are not normally distributed;

(b) the use of nonparametric methods, such as Mann–Whitney, Wilcoxon, Kruskal–Wallis, or Spearman, which do not require normal distribution assumptions; and

(c) models that are robust to non-normality, as many modern models and robust statistical approaches are not highly sensitive to violations of the normality assumption.

Conclusion

Data normality testing is not an absolute requirement in every statistical analysis. What is far more important is understanding the objective of the analysis, the methods used, the sample size, and the underlying assumptions of the statistical model.

That concludes the article that Kanda Data can present on this occasion. Hopefully, it is useful and adds insight for those who need it. Stay tuned for the next article update from Kanda Data.