| mudiff.alc {SampleSizeMeans} | R Documentation |
Bayesian sample size determination for differences in normal means using the Average Length Criterion
Description
The function mudiff.alc returns the required sample sizes
to reach a desired posterior credible interval length on average for a fixed coverage probability for the difference between two normal means.
Usage
mudiff.alc(len, alpha1, beta1, alpha2, beta2, n01, n02, level = 0.95,
equal = TRUE, m = 10000, mcs = 3)Arguments
len |
The desired average length of the posterior credible interval for the difference between the two unknown means | |||||||||
alpha1 |
First prior parameter of the Gamma density for the precision (reciprocal of the variance) for the first population | |||||||||
beta1 |
Second prior parameter of the Gamma density for the precision (reciprocal of the variance) for the first population | |||||||||
alpha2 |
First prior parameter of the Gamma density for the precision (reciprocal of the variance) for the second population | |||||||||
beta2 |
Second prior parameter of the Gamma density for the precision (reciprocal of the variance) for the second population | |||||||||
n01 |
Prior sample size equivalent for the mean for the first population | |||||||||
n02 |
Prior sample size equivalent for the mean for the second population | |||||||||
level |
The desired fixed coverage probability of the posterior credible interval (e.g., 0.95) | |||||||||
equal |
logical. Whether or not the final group sizes (n1, n2) are forced to be equal:
| |||||||||
m |
The number of points simulated from the preposterior distribution of the data. For each point, the length of the highest posterior density interval of fixed coverage probability level is estimated, in order to approximate the average length. Usually 10000 is sufficient, but one can increase this number at the expense of program running time. | |||||||||
mcs |
The Maximum number of Consecutive Steps allowed in the same direction in the march towards the optimal sample size, before the result for the next upper/lower bound is cross-checked. In our experience, mcs = 3 is a good choice. |
Details
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 precision within each of the two the populations are
unknown, but have prior information in the form of
Gamma(alpha1, beta1) and Gamma(alpha2, beta2) densities, respectively.
Assume that the means are unknown, but have
prior information equivalent to (n01, n02) previous observations, respectively. The function
mudiff.alc returns the required sample sizes to attain the
desired average length len for the posterior credible interval of fixed coverage probability level
for the difference between the two unknown means.
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.
Value
The required sample sizes (n1, n2) for each group given the inputs to the function.
Note
The sample sizes are calculated via Monte Carlo simulations, and therefore may vary from one call to the next.
Author(s)
Lawrence Joseph lawrence.joseph@mcgill.ca and Patrick Bélisle
References
Joseph L, Bélisle P.
Bayesian sample size determination for Normal means and differences between Normal means
The Statistician 1997;46(2):209-226.
See Also
mudiff.acc, mudiff.modwoc, mudiff.acc.equalvar, mudiff.alc.equalvar, mudiff.modwoc.equalvar, mudiff.varknown, mudiff.mblacc, mudiff.mblalc, mudiff.mblmodwoc, mudiff.mblacc.equalvar, mudiff.mblalc.equalvar, mudiff.mblmodwoc.equalvar, mudiff.mbl.varknown, mudiff.freq, mu.acc, mu.alc, mu.modwoc, mu.varknown, mu.mblacc, mu.mblalc, mu.mblmodwoc, mu.mbl.varknown, mu.freq
Examples
mudiff.alc(len=0.2, alpha1=2, beta1=2, alpha2=3, beta2=3, n01=10, n02=25)