The Analysis of Experimental Data

Minimizing the complexity improves communication

Mon, 01/06/2014 - 12:26

You have spent good money obtaining your experimental results, and now the time has come to communicate those results to those who need to take action. This column will describe how to cut through the complexities of your analysis and communicate the results quickly and easily.

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You have 30 seconds to make your point before your boss’s eyes glaze over, and the easiest way to beat this 30-second rule is to use a graph. In thinking about how to beat the 30-second rule Ellis Ott decided to combine the graphic power of the average and range chart with the sensitivity of the analysis of variance (ANOVA). The result was the analysis of means (ANOM). The original version in 1967 used approximate critical values to compute the ANOM decision limits. Over the years several investigators have worked on sharpening up and extending these decision limits. The tables given here are excerpted from the results of the latest such revision carried out during the past two years. However, before we get to the ANOM, we shall begin with the traditional ANOVA.

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Comments

Submitted by Dave Y on Fri, 01/10/2014 - 09:32

If it were me having the test results presented to me, I would want to see a simple line graph with reflectivity on the y axis, temperature and the x axis, and a line for each concentration.  In one view of the chart I could understand.  All that needs to be communicated would be there.

Hi Dave,

Maybe I'm missing something, but isn't Fig. 3 just the chart you're describing, but without decision limits?

Without decisions limits, how would you determine if the differences were real?

Without the ANOME charts, how would you determine the size of the main effects?

My questions are out of genuine curiosity. If you have a better faster easier way to determine these things, I would love to learn them and put them to use.

Thanks for your time, Shrikant Kalegaonkar (LinkedIn: http://www.linkedin.com/in/shrikale/, Twitter: @shrikale)

Submitted by shrikale on Fri, 01/10/2014 - 10:57

Hello Dr. Wheeler,

Your post provided a slightly different approach to the example in "Understanding Industrial Experimentation". It's a cleaner way to determine the decision limits using Table A & the average R. Also, your point made in Fig 6. was much clearer. So, thank you for that.

I did have a question with respect to the range chart and the way the range limit is determined. I used the control chart factor D4 to scale the average R to get the upper limit. For n = 3, D4 = 2.574. However, in your post you use 2.519. Can you help me understand the difference?

One other question: Is it possible for a difference to show up in the ANOVA and not in the ANOM? Is one approach more sensitive or less robust than the other?

To all others:

Dr. Wheeler's book on industrial experimentation is outstanding. I cannot recommend it enough. It helped me learn experimentation methods and put them to use quickly. It's obvious he spent a lot of time trying to view the material from the student's perspective. You should use this book before diving into the classics like "Statistics for Experimenters".

All the best, Shrikant Kalegaonkar (LinkedIn: http://www.linkedin.com/in/shrikale/, Twitter: @shrikale)

Submitted by DenisG on Tue, 03/12/2019 - 10:08

Hi Dr Wheeler,

Interesting article. There is a fourth question that could/should be answered from this data. That is the process optimisation question. For example, if we require Y as an output value for reflectivity, what would be the optimal X input values for both concentration and temperature?  This is easily answered by statistical software, where the mathematical relationship can be determined.

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