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LEP
LEP
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Why is there no power estimate for the last category of categorical variables?

In Evaluate Design > Power Analysis, why is there no power estimate for the last category of categorical variables? For example lets lay you have a categorical variable X with three categories.  The resulting power analysis for an experiment will provide a Power for X 1 and X 2 but not X 3.  Why is that and how can I find out what it is?

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Re: Why is there no power estimate for the last category of categorical variables?

JMP uses the effect parameterization for categorical predictors in the linear predictor. That parameterization means for a k-level predictor, only k-1 parameters are estimated. All k parameters must sum to zero, so the first k-1 estimates are free but the last parameter is fixed to be -1 times the sum of the first k-1 parameter estimates.

 

Since there is not estimate, there is no test. If there is no test, then there is no meaning to power.

 

Capture.PNG

 

This simple case with a single categorical factor with 3 levels illustrates your situation and what I explained. Note that JMP also reports the power for the whole term as well as for individual parameters that make up a term. I find this useful because I think in terms of effects, not levels.

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Highlighted

Re: Why is there no power estimate for the last category of categorical variables?

JMP uses the effect parameterization for categorical predictors in the linear predictor. That parameterization means for a k-level predictor, only k-1 parameters are estimated. All k parameters must sum to zero, so the first k-1 estimates are free but the last parameter is fixed to be -1 times the sum of the first k-1 parameter estimates.

 

Since there is not estimate, there is no test. If there is no test, then there is no meaning to power.

 

Capture.PNG

 

This simple case with a single categorical factor with 3 levels illustrates your situation and what I explained. Note that JMP also reports the power for the whole term as well as for individual parameters that make up a term. I find this useful because I think in terms of effects, not levels.

Learn it once, use it forever!
LEP
LEP
Community Trekker

Re: Why is there no power estimate for the last category of categorical variables?

 Thanks Mark, makes sense.

 

For future readers, a good explanation of categorical parameterization (effect coding) that puts Mark's answer in context is here: https://www.jmp.com/en_us/statistics-knowledge-portal/what-is-multiple-regression/mlr-with-categoric...

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