mudiff.mblalc.equalvar {SampleSizeMeans}

Bayesian sample size determination for differences in normal means when variances are equal using the Mixed Bayesian/Likelihood Average Length Criterion

Description

The function mudiff.mblalc.equalvar returns the required sample sizes to reach a given posterior credible interval length on average for a fixed coverage probability for the difference between two normal means - using a mixed Bayesian/likelihood approach - when variances are equal.

Usage

mudiff.mblalc.equalvar(len, alpha, beta, level = 0.95)

Arguments

len

The desired average length of the posterior credible interval for the difference between the two unknown means

alpha

First prior parameter of the Gamma density for the common precision (reciprocal of the variance)

beta

Second prior parameter of the Gamma density for the common precision (reciprocal of the variance)

level

The desired fixed coverage probability of the posterior credible interval (e.g., 0.95)

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 precisions of the two normal sampling distributions are unknown but equal, with prior information in the form of a Gamma(alpha, beta) density. The function mudiff.mblalc.equalvar 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 Mixed Bayesian/Likelihood (MBL) approach. MBL approaches use the prior information to derive the predictive distribution of the data, but use only the likelihood function for final inferences. This approach is intended to satisfy investigators who recognize that prior information is important for planning purposes but prefer to base final inferences only on the data.

Value

The required sample sizes (n1, n2) for each group given the inputs to the function.

Note

The sample sizes returned by this function are exact.

Author(s)

Lawrence Joseph [e-mail] 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.mblacc.equalvar, mudiff.mblmodwoc.equalvar, mudiff.mblacc, mudiff.mblalc, mudiff.mblmodwoc, mudiff.mbl.varknown, mudiff.acc.equalvar, mudiff.alc.equalvar, mudiff.modwoc.equalvar, mudiff.acc, mudiff.alc, mudiff.modwoc, mudiff.varknown, mudiff.freq, mu.mblacc, mu.mblalc, mu.mblmodwoc, mu.mbl.varknown, mu.acc, mu.alc, mu.modwoc, mu.varknown, mu.freq

Examples

mudiff.mblalc.equalvar(len=0.2, alpha=2, beta=2)