Help With Statistics: Technical Articles
General Statistics
Modeling and Interpreting Interactions in Multiple Regression
Normal Probability Plots and Tests for Normality
A Modified Path of Steepest Ascent for Split-Plot Experiments
How To Analyze a Split-Plot Experiment
How To Recognize a Split-Plot Experiment
When To Use Fisher's Exact Test
Why We Don't "Accept" the Null Hypothesis
Some Misconceptions about Confidence Intervals
The Two-Sample t-Test and Randomization Test and Dataset
Sample Size Determination for the Test of One Proportion
The Paired T-Test Using Minitab
One Sample T-Test Using Minitab
Quality Statistics
Determining if Your Measurement System is Adequate
Identifying the Distribution of Data is Key to Analysis
Modeling Non-Normal Data Using Statistical Software
Breakthrough Improvement for Your Inspection Process
Avoiding Mean Square Error Bias in Designed Experiments
Non-Traditional MSA with Continuous Data and Dataset
Some Misconceptions about the Normal Distribution
Measurement System Analysis and Destructive Testing
Some Misconceptions about R2
Measurement System Analysis with Attribute Data
Confidence Intervals for Capability Indices & Dataset
On The Use of Indicator Variables in Regression Analysis
Using CUSUM Charts for Small Shifts
Evaluating the Usefulness of Data Using Gage R&R
Capability Analysis Using Minitab
Using Exponentially Weighted Moving Average (EWMA) Charts
Analysis of Variance (ANOVA) Using Minitab
To improve a process, you need reliable data. Is your measurement system providing data you can depend on? Find out with Minitab’s Gage R&R Study and Gage Run Chart. Michelle Paret, Quality Magazine, March 2008 top
Knowing the distribution of your data is essential to choosing the right statistical method. Learn how Minitab’s Individual Distribution Identification can help you quickly determine the distribution of your data so you can make this critical choice. Asia Pacific Engineer, December 2007 top
Using a supplier of tantalum as an example, this article discusses how to demonstrate process stability and capability for quality characteristics that do not follow the normal distribution. Louis Johnson, R&D Magazine, August 2007, Vol. 49, No. 8 top
This article presents “The Six Step Method for Inspection Improvement” – a process to increase the accuracy of pass/fail decisions made when visually evaluating manufactured parts for defects. The process is illustrated by a case study from Hitchiner Manufacturing Company, Inc., a manufacturer of precision metal parts who successfully implemented this method. Louis Johnson, Six Sigma Forum - American Society for Quality, May 2007 top
A method of constructing interactions in multiple regression models is described which produces interaction variables that are uncorrelated with their component variables and with any lower-order interaction variables. The method is, in essence, a partial Gram-Schmidt orthogonalization that makes use of standard regression procedures, requiring neither special programming nor the use of special-purpose programs before proceeding with the analysis. top
Normal probability plots are often used as an informal means of assessing the non-normality of a set of data. One problem confronting persons inexperienced with probability plots is that considerable practice is necessary before one can learn to judge them with any degree of confidence. Some objective measure of the straightness of a probability plot would be helpful, especially for students just beginning their statistical education. top
This article investigates the path of steepest ascent used in response surface designs within a split-plot structure. It presents three methods for calculating the coordinates along the path. Scott M. Kowalski, Connie M. Borror, and Douglas C. Montgomery, Journal of Quality Technology, January 2005, Vol. 37, No. 1 top
This article describes how to correctly set up and analyze a split-plot experiment using a real-life example. Also discussed is how the two different estimates of experimental error required in split-plot designs are calculated and used to determine which factors are significant. Kevin J. Potcner and Scott M. Kowalski, Quality Progress, December 2004 top
This article discusses the causes and consequences of bias in the mean square error (MSE) term and provides suggestions for detecting and correcting MSE bias. James A. Colton, Scientific Computing & Instrumentation, April 2004 top
This article addresses the relationship between standard (manufacturing) measurement system analyses, and those encountered in the Service Quality/Transactional arena. Keith M. Bower, Six Sigma Forum - American Society for Quality, December 2003 top
This article describes split-plot experiments, commonly used with hard-to-change factors, as compared to completely randomized experiments. Three real-life examples are presented that describe when and how split-plot experiments can be used. The article also shows how the analysis of split-plot designs differs from completely randomized designs. Scott M. Kowalski and Kevin J. Potcner, Quality Progress, November 2003 top
This article explores the relationship between Karl Pearson's Chi-Square test and R.A. Fisher's Exact test. A situation when the Chi-Square test may not be appropriate is discussed. Keith M. Bower, ASQ Six Sigma Forum Magazine, August 2003, Vol. 2, No. 4 top
This article discusses a frequently encountered mistake when using hypothesis tests. Keith M. Bower and James A. Colton, Six Sigma Forum - American Society for Quality, July 2003top
This article discusses three misconceptions regarding the use of confidence intervals. Keith M. Bower, Six Sigma Forum - American Society for Quality, July 2003top
In this article, the author investigates situations in which the two-sample t-test may be considered robust to certain assumptions, including normality. Illustrates the randomization test procedure using a hypothetical example. Keith M. Bower, Six Sigma Forum - American Society for Quality, June 2003 top
This article discusses three misconceptions regarding the use of the normal distribution in theory and practice. Keith M. Bower, Six Sigma Forum - American Society for Quality, May 2003top
This article explores the use of a nested design in a measurement system analysis with destructive testing. Includes a discussion of model assumptions and examines results from a practical example. Douglas Gorman and Keith M. Bower, ASQ Six Sigma Forum Magazine, August 2002, Vol. 1, No. 4 top
This article investigates some frequently encountered misconceptions involving the important R2 statistic. The Minitab datasets (MTW files) illustrate concept and support examples from the article. James A. Colton and Keith M. Bower, EXTRAOrdinary Sense (ISSSP Newsletter), August 2002 top
Learn how to use Minitab's Power and Sample Size functionality for the test of one proportion. Keith M. Bower, EXTRAOrdinary Sense (ISSSP Newsletter), February 2002 top
Addresses two statistics for use in a measurement system study involving attribute responses, using Minitab Release 13.31. The important difference between Kappa and Kendall's Coefficient of Concordance is highlighted. Keith M. Bower, KeepingTAB #35 (Minitab Newsletter), February 2002 top
Investigates the use of confidence intervals for two widely used capability indices, namely Cp and Cpk. This paper makes use of a Minitab macro which may be downloaded via Macro Catalog and extends the discussion of his two earlier papers on capability analyses. Keith M. Bower, EXTRAOrdinary Sense (ISSSP Newsletter), August 2001 top
Addresses the use of indicator variables in simple and multiple linear regression analysis. Keith M. Bower, EXTRAOrdinary Sense (ISSSP Newsletter), November 2001 top
In this article, the author investigates the use of the Cumulative Sum (CUSUM) chart, which is a useful tool to detect small changes in a process. This paper makes use of a Minitab macro which may be downloaded from the Macro Catalog. Keith M. Bower, EXTRAOrdinary Sense, May 2001 top
Addresses Gage Repeatability and Reproducibility (Gage R&R) using the functionality in Minitab Release 13.3. After discussing some theory behind the ANOVA output, the associated results from an example are analyzed and conclusions drawn from a practical perspective, referencing several industry-wide guidelines. Keith M. Bower, Asia Pacific Process Engineer, April 2001 top
View the French translation of this article
Addresses the paired t-test procedure, to be used when some dependency exists between two populations. This is illustrated by an experiment involving measurements of tire wear using two distinct methods (hence each tire in the study meets both measurement methods.) Assumptions, results, and the conclusions from this actual study are illustrated using Minitab output. Keith M. Bower, Scientific Computing & Instrumentation, February 2001 top
Capability Analysis Using Minitab
Two-part article: Part 1 (PDF) & Dataset 1 (MTW file) and Part 2 (PDF) & Dataset 2 (MTW file), View the French translation of this article
Part 1 addresses the assumptions and interpretation of capability analyses, including Cp, Cpk as well as "Sigma" values. In this paper, the assumption of Normality is valid for the example under discussion.
Part 2 addresses capability analysis when one is dealing with a process which may not be adequately modeled by a Normal distribution. He discusses data transformations using the Box-Cox technique, as well as the fitting of a Weibull distribution. The paper also includes a methodology for choosing between the two techniques in practice, based on probability plots and the Anderson-Darling statistic. Keith M. Bower, EXTRAOrdinary Sense, January 2001 and March 2001 top
Investigates the Exponentially Weighted Moving Average (EWMA) control chart. After discussing some theory behind the EWMA chart, he provides an example of using this statistical procedure to detect a small process shift. Keith M. Bower, Asia Pacific Process Engineer, October 2000 top
Looks at the assumptions and interpretation of results using the one-sample t-procedure. A case study is used to show the relationship between the P-Value and Confidence Intervals. Keith M. Bower, KeepingTAB #33, October 2000 top
Provides guidelines for performing ANOVA and walks through a detailed example of an analysis using Minitab. Keith M. Bower, Scientific Computing & Instrumentation, February 2000 top