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Knowledge Base/Normality Test: Does Your Data Qualify for Those Formulas?
6 Sigma7 min read

Normality Test: Does Your Data Qualify for Those Formulas?

You measured 30 parts, calculated Cpk, and confidently submitted the report, only to be asked by the QA manager if a normality test was performed. This is crucial because Cpk, t-test, and ANOVA all rely on the fundamental assumption that the data follows a normal distribution.

Scenario

You measured 30 parts, calculated the average and standard deviation, then computed Cpk, and confidently submitted the report. The QA manager returned, asking, "Did you perform a normality test?" You replied, "What?"

Plain Language Explanation

Cpk, t-test, ANOVA, regression analysis—these tools all share a common underlying assumption:

Your data conforms to a normal distribution (bell curve).

If the data is not normal, the results calculated using these formulas will be unreliable.

Normality Test Tools:

  • Anderson-Darling Test: Most commonly used in manufacturing, sensitive to the central portion of the distribution
  • Shapiro-Wilk Test: Effective for small samples (n < 50)
  • Histogram + Normal Probability Plot: Visual judgment, quick screening

P-value > 0.05 = Fail to reject the normality assumption = Can use normality-related statistical tools

Practical Considerations

What to do if the data is not normal:

  1. First, find the cause: Is there an error in the data? Was data from two different processes mixed in?
  2. Box-Cox Transformation: Mathematically transform skewed data into near-normal.
  3. Switch to non-parametric methods: For Cpk, use a "non-normal process capability index"; for ANOVA, use Kruskal-Wallis.

In which cases is data typically not normal:

  • Yield % (when close to 0 or 100)
  • Time-based data (waiting time, time between failures)
  • Count data (number of defects)

How InsightFab Does It

After uploading data, InsightFab automatically performs a normality test first. If it does not pass, it automatically switches to analysis methods suitable for non-normal data and states in the report, "This data is skewed, Cpk has been calculated using a non-normal correction method."

Key Takeaway

"Cpk calculated using the wrong formula is more dangerous than not calculating it at all—because you think you know the answer."

Want to try it yourself?

Every tool mentioned in this article is available on InsightFab — just upload a CSV to analyze.

Go to Tools

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