Gnome Power (and Sample Size)

On trusting salespeople and determining GNUs

Fri, 12/09/2011 - 12:09

I was playing around with the power and sample size graphs in Minitab recently, and I noticed something interesting. Power, for the uninitiated, is usually described as the likelihood that you will find a significant effect or difference when one truly exists. But rather than simply describe what I found, I thought I’d invent a completely contrived, obviously fabricated, and wildly unrealistic example to illustrate. (You’re welcome.)

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Meet Bob. Bob works for the company that leads the nation in the production and sale of high-quality garden gnomes. You know the one. The other day, Bob was in his office, admiring the prototypes for the upcoming 2012 North American Gnome Show. He particularly liked the new Ignatius Von Gnomenberger with Fallen Lederhosen (catalog no. 57-MOON-OOPS).

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Comments

Submitted by patnclaire on Mon, 12/12/2011 - 12:15

Will that trade-off application explain about the ubiquitous sample size > 30? What are the tradeoffs? What is the value of Alpha? and Beta? Please advse.

Thanks for your comment PATNCLAIRE. If you have a sample size of 30 or more, you probably have a lot of power. But don't let all that power go to your head, because it is possible to have too much power.

 

For example, suppose our friend Bob became obsessed and tested so many gnomes that he could detect a difference of just 1 GNU with a power of 0.95. The problem is that Bob already indicated that he was not impressed with a difference of 3. So even if a difference of only 1 GNU is statistically significant, it is not practically significant to Bob because it would not cause him to switch suppliers. So in a sense, collecting that much data would not be worth the cost in terms of loss of money, loss of time, or loss of gnomes.  

 

Best,

Greg

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