Purpose
Data transformation is used to transform data that is not normally distributed into data that follows a normal distribution. Thus allows us to calculate basic statistics and valid probabilities related to the population (mean, standard deviation, Z values, probabilities for defects, yield, etc.).
Anatomy
Reference: Juran's Quality Control Handbook
Terminology
A. Mathematical transformations - Prior to using these transformations consult the Application Cookbook.
B. Range of variable studied.
C. Original distribution of the variable.
D. Resulting distribution after applying a mathematical transformation.
Major Considerations
Before using a mathematical transformation apply steps 1 and 2 of the Application Cookbook.
Application Cookbook
If the data is not normally distributed (e.g. fails the normality test in Minitab) conduct the following steps:
1. Examine the data to see if there is a nonstatistical explanation for the unusual distribution pattern. For example, if data is collected from various sources (similar machines or individuals performing the same process) and each one has a different mean or standard deviation, then the combined output of the sources will have an unusual distribution such as a mixture of the individual distributions. In this case, separate analyses could be made for each source (individual, machine, etc.).
2. Analyze the data in terms of averages instead of individual values. Sample averages closely follow a normal distribution even if the population of individual values from which the sample averages came is not normally distributed. If conclusions on a characteristic can be made based on the average value proceed but remember these only apply to the average value and not to the individual values in the population.
3. If steps 1 and 2 do not provide with reliable estimates, use the Weibull distribution. Consult the Application Cookbook of the tool Distribution - Weibull. The resulting straight line can provide estimates of the probabilities for the population.
4. If all above steps fail in providing reliable estimates, use one of the most common mathematical transformations which include:
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