# propdiff.freq: Frequentist sample size determination for the difference... In SampleSizeProportions: Calculating sample size requirements when estimating the difference between two binomial proportions

## Description

The function `propdiff.freq` returns the required sample sizes to obtain a confidence interval of given length and confidence level for the difference between two binomial proportions.

## Usage

 `1` ```propdiff.freq(len, p1.estimate, p2.estimate, level = 0.95) ```

## Arguments

 `len` The desired total length of the confidence interval for the proportion `p1.estimate` A point estimate for the binomial proportion for the first population `p2.estimate` A point estimate for the binomial proportion for the second population `level` The desired level of the confidence interval (e.g., 0.95)

## Details

Assume that a random sample from each of two populations will be collected in order to estimate the difference between two independent binomial proportions. Assume that the best point estimates for the unknown binomial proportions in the two populations are (p1.estimate, p2.estimate), respectively. The function `propdiff.freq` returns the required sample sizes to attain the desired length len and confidence level level for the confidence interval for the difference between the two unknown proportions from a frequentist point of view, using a normal approximation.

## Value

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

## Author(s)

Lawrence Joseph lawrence.joseph@mcgill.ca, Patrick Belisle and Roxane du Berger

## References

Lemeshow S, Hosmer Jr DW, Klar J, Lwanga SK.
Adequacy of Sample Size in Health Studies. Wiley and Sons, New York, 1990.

Joseph L, du Berger R, and Belisle P.
Bayesian and mixed Bayesian/likelihood criteria for sample size determination
Statistics in Medicine 1997;16(7):769-781.

`propdiff.acc`, `propdiff.modwoc`, `propdiff.woc`, `propdiff.mblacc`, `propdiff.mblalc`, `propdiff.mblmodwoc`, `propdiff.mblwoc`
 `1` ```propdiff.freq(len=0.01, p1.estimate=0.15, p2.estimate=0.20) ```