Generalized power calculations for generalized linear models and more
Abstract. The powercal command can compute any one of the five quantities
involved in power calculations from the other four. These quantities are
power, significance level, detectable difference, sample number, and the
standard deviation (SD) of the influence function, which is equal to the
standard error multiplied by the square root of the sample number.
powercal can take arbitrary expressions (involving constants,
scalars, or variables) as input and calculate the output as a new variable.
The user can therefore plot input variables against output variables, and
this often communicates the tradeoffs involved better than a point
calculation as output by the sampsi command. General formulas are
given for calculating the SD of the influence function when the detectable
difference is a linear combination of link functions of subpopulation means
for an outcome variable distributed according to a generalized linear model
(GLM). This general case includes a very broad range of special cases, where
the parameters to be estimated are differences between subpopulation
proportions, arithmetic means and algebraic means, or ratios between
subpopulation proportions, arithmetic means, geometric means, and odds.
However, powercal is not limited to GLMs and can even be used with
rank methods.
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Roger Newson
View all articles with these keywords:
powercal, power, alpha, significance level, detectable difference, detectable ratio, sample number, standard deviation, influence function, sample design, generalized linear model, proportion, arithmetic mean, algebraic mean, geometric mean, odds
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