We all know what happens when we assume. For example, traditional designed experiments assume that residuals, the differences between the actual and modeled data, follow the normal distribution (as seen in figure 1). These experiments include t tests, analysis of variance (ANOVA), factorial designs, and linear regression. ANOVA is said to be robust to this assumption—that is, it will work even if the normality requirement is not strictly met. However, there are limits even to this.

The results are far more trustworthy, and the test may be better able to detect differences between treatments or levels, if a transformation can make the residuals conform to the normal distribution.

“Assume” is certainly true if we perform a designed experiment and fail to test the residuals for normality. The same applies if we report a process performance index without making sure that the process data follow the assumed distribution. The estimated nonconforming fraction can easily be off by orders of magnitude.

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