A power analysis for a one sample z-test. The function requires \(\alpha\), \(\sigma\), the effect size, the type of test (one tailed or two-tailed), and either power (1 - \(\beta\)) or n (sample size). If n is provided, then power is calculated. Conversely, if one provides power, but not n, then the required n is calculated.
power.z.test(sigma = 1, n = NULL, power = NULL, alpha = 0.05, effect = NULL,
test = c("two.tail", "one.tail"), strict = FALSE)The population standard deviation.
The sample size. Not required if power is specified.
The desired power. Not required if n is specified.
Probability of type I error.
Effect size.
One of two choices: "two.tail" or "one.tail".
Causes the function to use a strict interpretation of power in a two-sided test.
If strict = TRUE then power for a two sided test will include the probability of rejection
in the opposite tail of the true effect. If strict = FALSE (the default) power will be half the value of \(\alpha\) if the true effect size is zero.
Returns a list
The prescribed population variance.
The sample size.
The power.
The type I error probability.
The type of test prescribed.
The effect size.
Bain, L. J., and M. Engelhardt (1992) Introduction to Probability and Mathematical Statistics. Duxbury press. Belmont, CA, USA.
# NOT RUN {
power.z.test(sigma=6,effect=5,power=.9,test="one.tail")
# }
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