mudiff.modwoc.equalvar calculates conservative sample sizes, in the sense that the desired
posterior credible interval coverage and length for the difference between two normal means
are guaranteed over a given proportion of data sets that can arise according to the prior information, when variances are equal.
The desired total length of the posterior credible interval for the difference between the two unknown means
First prior parameter of the Gamma density for the common precision (reciprocal of the variance)
Second prior parameter of the Gamma density for the common precision (reciprocal of the variance)
Prior sample size equivalent for the mean for the first population
Prior sample size equivalent for the mean for the second population
The desired fixed coverage probability of the posterior credible interval (e.g., 0.95)
The probability that the length of the posterior credible interval of fixed coverage probability level will be at most len
logical. Whether or not the final group sizes (n1, n2) are forced to be equal:
Assume that a sample from each of two populations will be
collected in order to estimate the difference between two independent normal means.
Assume that the precisions of the two normal sampling distributions are
unknown but equal, with prior information in the form of a Gamma(alpha,
beta) density. Assume that the means are unknown, but have
prior information equivalent to (n01, n02) previous observations, respectively.
returns the required sample sizes to attain the desired length len
for the posterior credible interval of fixed coverage probability level
for the difference between the two unknown means.
The Modified Worst Outcome Criterion used is conservative, in the sense that the posterior credible interval
length len is guaranteed over the worst.level proportion of all
possible data sets that can arise according to the prior information, for a fixed coverage probability level.
This function uses a fully Bayesian approach to sample size determination. Therefore, the desired coverages and lengths are only realized if the prior distributions input to the function are used for final inferences. Researchers preferring to use the data only for final inferences are encouraged to use the Mixed Bayesian/Likelihood version of the function.
The required sample sizes (n1, n2) for each group given the inputs to the function.
The sample sizes returned by this function are exact.
It is also correct to state that the coverage probability of the posterior credible interval of fixed length len will be at least level with probability worst.level with the sample sizes returned.
Lawrence Joseph [email protected] and Patrick Belisle
Joseph L, Belisle P.
Bayesian sample size determination for Normal means and differences between Normal means
The Statistician 1997;46(2):209-226.
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