Non-Normal and Non-Transformable Data

What do you do with data that is non-normal and non-transformable data? Read and learn how this quick and simple Minitab resource helps you do just that! 

Non-Normal and Non-Transformable Data

The following text was from the PDF article that is available through the link below.

Now to get back to the original question, how do you get an “S” shaped probability plot; Three cases came to mind that make an “S” shape with shorter tails than a normal and one with longer tails. Each of these cases will fail to be made normal using a transformation. These are examples where you would have to use your process knowledge to find a cause for the non-normality.

Each of the example distributions used in this article are shown below with their descriptive statistics using Minitab. Skewness and the kurtosis are the key points in this article. The first four were non-transformable with an “S” shaped probability plot. These have low skewness values, but have non-zero kurtosis values. Notice that the sign of the kurtosis value relates to the direction of the “S”. Shorter tails have the (-) kurtosis values. The last tow data sets show higher skewness values. A positive skew means it is skewed to the higher values. The kurtosis in these two is quite high because there is one really long tail. Notice that the magnitude of each value are the same, which is because the flipped data was created from the lognormal data using the following
equation: (30-lognormal).

For the complete no-normal and non-transformable data article text, download the PDF using the link below.

Predictive Analytics Reporting (A Related Situation)

The article references non-normal and non-transformable data; however, sometimes process output data over time is from a situation that is log-normal by nature.  For example:

  • The flatness of a part that is bounded by zero and can only have positive values.
  • The time it takes to execute a task that is bounded by zero and can only have positive values.

A 30,000-foot-level report-out addresses this issue, which is illustrated in the plot below, where specification limits were 0.5 – 7.0:


Non-Normal And Non-Transformable Data


In this 30,000-foot-level predictive analytics plot:

  1. Process stability is assessed (from a high-level point of view) using the individuals chart on the left. For this situation, stability is concluded since no point was above or below the upper and lower control limits. Process is then concluded to be predictable.
  2. Process capability is next assessed using a probability plot of the time-series data against a specification of 0.5 to 7.0.  Since the process was concluded to be stable, the data for this plot are considered to be a random sample of the future.
  3. Process capability/performance statement is then recorded at the bottom of the chart.

For reference, the above 30,000-foot-level plot was created from a randomly generated log-normal distribution.  The resulting data set from this random generation, is plotted below:


Non-Normal And Non-Transformable Data -- lognormal histogram


An Integrated Enterprise Excellence (IEE) business management system provides a methodology where 30,000-foot-level reporting can be provided throughout an organization where there is a structured linkage to the processes that created the metrics.  An IEE 5-book set provides the details of implementing the IEE system and its 30,000-foot-level reporting. Automatic updates to the metrics are available through the Enterprise Performance Reporting System (EPRS) software.


Contact Us to set up a time to discuss with Forrest Breyfogle how your organization might gain much from an Integrated Enterprise Excellence (IEE) Business Process Management System and its predictive analytics reporting of process outputs.


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