Sensitivity (Accuracy) of the commonly used test with the assumption of normality

 

More on this in technical papers by Minitab, ref 2.

Minitab Technical Assistance, ref 3, is developed to guide the user on unusual data, normality and sample size check. Minitab assistance is available for limited tests, basic statistical tests.

Test assumptions for basic statistical tests like Z-test, t-test, correlation, variance, normality and outlier test can be found in Ref 4.

Test assumptions for quality and process improvement tests like MSA, Control Charts, Acceptance sampling and capability analysis can be found in Ref 5.

Test assumptions for Statistical modeling tools like ANOVA, Regression, DoE, Predictive analytics, Reliability and Multivariate can be found in Ref 6.

Test assumptions for Predictive Analytics tools like CART, TreeNet, Random Forest and MARS can be found in Ref. 6.

Test assumptions for Multivariate methods like PCA, Factor Analysis, Item Analysis, K-mean Cluster, Discriminant analysis and Correspondence analysis can be found in Ref.6.

Normality assumptions for control charts for individuals data, ref7.

Data should be moderately normal.

Moderate departures from normality do not significantly affect the results of the chart. However, severe departures from normality can increase the number of false out-of-control signals.

If the data are very skewed, you could try a Box-Cox transformation to see if that corrects the nonnormal condition. If your process naturally produces nonnormal data and the transformation is effective, you can use the chart of the transformed data to assess the stability of your process.

Normality assumptions for control charts for subgroup data

Although many control charts for variables data are formally based on the assumption of normality, you can still obtain good results with nonnormal data if you collect data in subgroups. 

The relationship between robustness to nonnormality and sample size is based on the central limit theorem. As long as your subgroups are independent, larger subgroup sizes will tend to result in subgroup means that are more normally distributed. Although the required subgroup size depends on how nonnormal the data are, in practice, any subgroup at all is often adequate.

While transformations are not usually necessary for control charts with subgroups, if the data are very skewed, you may want to consider a Box-Cox transformation.

If you are uncertain about whether the data from your process require transformation, compare control charts with transformed and untransformed data. Then, consider whether the charts give different out-of-control signals and which signals are more useful for describing the process.

Reference

1. Testing for Normality: A Tale of Two Samples by Anderson-Darling (minitab.com)
2. Technical Papers - Minitab
3. The Assistant | Minitab
4. Statistics - Minitab
5. Quality and Process Improvement - Minitab
6. Statistical Modeling - Minitab
7. Normality assumptions for control charts - Minitab
8. Independent t-test in Minitab - Procedure, output and interpretation of the output using a relevant example. (laerd.com)
9. One-sample t-test in Minitab - Procedure, output and interpretation of the output using a relevant example. (laerd.com)
10. One-way ANOVA in Minitab | Procedure, output and interpretation of the output using a relevant example. (laerd.com)
11. Linear regression in Minitab - Procedure, output and interpretation of the output using a relevant example. (laerd.com)