Posts about Statistics

Full and Fractional Factorial Test Design

An Essential Primer on Full and Fractional Factorial Test Design

Since full factorial gathers additional data, it reveals all possible interactions, but as seen by the numbers above, there is a trade-off. More data equals more information but more data also equals a longer test duration. The minimum data requirements for full factorial are very high since you are showing every experiment.

Even if you are using full factorial to get the same amount of information as a fractional factorial test, it will take more time since you need more data to see statistically relevant differences between the many experiments. You might be wondering how fractional factorial can be accurate if interactions are possible?

Random interactions of high relevance are very rare, especially when looking for interactions of more than 2 factors. You really need to design tests where you look for meaningful interactions that are based on true business requirements rather than hoping for a random and low influence interaction between a red button, a hero shot and a headline.

I am a fan of design of experiments as long time readers know (see posts on design of experiments).

Some good resources for more on the topics discussed above: What Can You Find Out From 8 and 16 Experimental Runs? by George Box – Statistics for ExperimentersDesign of Experiments in Advertising.

Related: Google Website Optimizerfactorial experiment articlesUsing Design of ExperimentsMarketers Are Embracing Statistical Design of Experiments

Quality, SPC and Your Career

Lead To Succeed [sigh, ASQ broke the link so I removed it, it sure gets tiring how backwards some organizations till are about using the internet, June 2010] by Stephen S. Prevette:

* Succeed as a quality professional by branding yourself and providing a service or product your manager and organization deem worth paying for.
* Lead your manager “your customers” by providing the data they need in a form they can understand.

This is a great article on how to apply quality (Deming, Statistical Process Control, Six Sigma, Lean Manufacturing) ideas and move forward professionally; even when those ideas are not always shared by the organization.
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Box on Quality

Bill Hunter and George Box

Dr. George Box is not as well known in the general management community as his ideas merit (in my biased opinion – photo of Bill Hunter and George Box). He is well know in the statistics field as one of the leading statistical minds. Box on Quality is an excellent book that gathers his essays from his 65th to 80th year. The book has just been issued in paperback (which helps as the hardback was pricey).

While some of the essays are aimed at a reader with an advanced understanding of statistics, many of the articles are aimed at any manager attempting to apply Quality Management principles (SPC, Deming, process improvement, six sigma, etc.). An except from the book provides a table of contents and an introduction.

Some of the articles from the book are available online. I encourage you to take a look at several of the articles and then go ahead and add this book to your prized management resources, if you find them worthwhile.

Statistics for Experimenters – Second Edition

Buy Statistics for Experimenters

The classic Statistics for Experimenters has been updated by George Box and Stu Hunter, two of the three original authors. Bill Hunter, who was my father, and the other author, died in 1986. Order online: Statistics for Experimenters: Design, Innovation, and Discovery , 2nd Edition by George E. P. Box, J. Stuart Hunter, William G. Hunter.
I happen to agree with those who call this book a classic, however, I am obviously biased.

Google Scholar citations for the first edition of Statistics for Experimenters.
Citations in Cite Seer to the first edition.

The first edition includes the text of Experiment by Cole Porter. In 1978 finding a recording of this song was next to impossible. Now Experiment can be heard on the De-Lovely soundtrack.

Text from the publisher on the 2nd Edition:
Rewritten and updated, this new edition of Statistics for Experimenters adopts the same approaches as the landmark First Edition by teaching with examples, readily understood graphics, and the appropriate use of computers. Catalyzing innovation, problem solving, and discovery, the Second Edition provides experimenters with the scientific and statistical tools needed to maximize the knowledge gained from research data, illustrating how these tools may best be utilized during all stages of the investigative process. The authors’ practical approach starts with a problem that needs to be solved and then examines the appropriate statistical methods of design and analysis.
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Control Charts in Health Care

This post is an edited version of a message I sent to the Deming Electronic Network.

I find the “control charts in health care” thread quite interesting.

From Mike Woolbert’s post
> I have read many comments about the 8 minute ambulance trip.
> This doesn’t seem to be a system measure, but a result measure.

It seems to me the 8 minute (90% of the time) measure is an attempt at a process measure (in a sense, you can see it as a result measure, but it is also a measure that will have an impact on overall results and as such can be used a process indicator). For it to be a process measure rather than than a process target however, it should actual be a measure of what has happened not a statement that we want to have 90% arrive within 8 minutes.

Jonathan Siegel’s comments on this topic were excellent.

The control chart was developed to aid in process improvement. A control chart helps monitor the process (to aid in putting in place counter-measures, when needed, and for identification of special causes). The control chart can be used to see if the process is in control and what the expected results from the system are.
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Management Improvement History

Originally posted to the Deming Electronic Network, 22 Sep 1999, in reponse to this message

I would like to say that I think it is good that we have disagreements on the DEN. I think it is a strength of the DEN, not a weakness. However, I think we sometimes get to personal with no real purpose. One example of this, for me, is: “Well, I guess we knew different Demings. Mine was a teacher named Dr. W. Edwards Deming.” I doubt this statement is meant to be taken literally, and if it is not I do not see what it adds to the discussion. I point this out not because I think this is some bad act that should be punished but that I think we need to continue to develop a sense of how we wish to express our disagreements and I think that we should try to do so more constructively.

For the past 60 years we’ve been looking for the magic bullet that will improve the quality of our products, services and lives. In the 1940s, we applied statistics through sampling, SPC and design of experiments to improve our products. In the 1950s, we used quality cost and total quality control to bring about quality improvement. In the 1960s, zero defects and MIL-Q-9858A drove the quality improvement process. In the 1970s, quality circles, process qualification and supplier qualification became key quality issues. In the 1980s, employee training in problem solving, team activities and just-in-time inventory were the things to do.”

I find this statement so far from the truth that it would seriously damage any PDSA with this as an accepted assessment of history. I do not believe Deming had such an inaccurate view (of course I may be wrong). I do believe we need to improve our practice of Quality (and to do that we need to understand what happened in the past and why it was not more successful). The idea that Design of Experiments (DoE) was at the core of some Quality Movement to me is not at all accurate. Continue reading

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