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# power calculation for counts

Hi,

I have three groups that I compare with a different count as outcome.

I would like to calculate the power for this comparison.

I was thinking of proc glmpower and using Poisson as link function.

However this is not supported.

Is there a macro written and available for use that would be able to support my question?

Thanks, Katrien

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‎08-09-2012 08:06 AM
Posts: 2,655

## Re: power calculation for counts

That is one of the assumptions behind the link function--that it normalizes the data.  For years before good maximum likelihood algorithms existed, data were transformed to meet normality assumptions.  Actually, the preferred transformation for count data was a square root transformation (Sokal and Rohlf, Biometry, 1969).  However, since you indicate that you will probably be analyzing the data using one of SAS's generalized linear model procedures (dist=poisson), and the Poisson distribution defaults to a log link, I suggested transforming using the log.  Warning: If you have zeroes in your dependent variable, you probably ought to transform as log(y + 1). You may want to do some data exploration to check the assumption of having a Poisson distribution (e.g. are the mean and variance approximately equal?, are the data over-represented with zeroes?).  You could find yourself wanting to use a negative binomial distribution (variance>mean) or a zero-inflated Poisson or negative binomial.

An alternative to the log transform would be to use the square root transformation prior to GLMPOWER, and analyze with  LINK=POWER(0.5).

Good luck.

Steve Denham

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Posts: 2,655

## Re: power calculation for counts

You could try transforming your data prior to using glmpower.  Since the analysis for the Poisson defaults to a log link, that seems like a logical first choice.

Steve Denham

New Contributor
Posts: 3

## Re: power calculation for counts

Hi Steve,

Suppose I log transform the data, do you then suggest that I could treat my data as if normal?

Then proc glmpower would work.

Katrien

Solution
‎08-09-2012 08:06 AM
Posts: 2,655

## Re: power calculation for counts

That is one of the assumptions behind the link function--that it normalizes the data.  For years before good maximum likelihood algorithms existed, data were transformed to meet normality assumptions.  Actually, the preferred transformation for count data was a square root transformation (Sokal and Rohlf, Biometry, 1969).  However, since you indicate that you will probably be analyzing the data using one of SAS's generalized linear model procedures (dist=poisson), and the Poisson distribution defaults to a log link, I suggested transforming using the log.  Warning: If you have zeroes in your dependent variable, you probably ought to transform as log(y + 1). You may want to do some data exploration to check the assumption of having a Poisson distribution (e.g. are the mean and variance approximately equal?, are the data over-represented with zeroes?).  You could find yourself wanting to use a negative binomial distribution (variance>mean) or a zero-inflated Poisson or negative binomial.

An alternative to the log transform would be to use the square root transformation prior to GLMPOWER, and analyze with  LINK=POWER(0.5).

Good luck.

Steve Denham

New Contributor
Posts: 3

## Re: power calculation for counts

Thanks a lot Steve. I will proceed as you suggest.

Nice day, Katrien

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