epiR (version 0.9-82)

epi.stratasize: Sample size under under stratified random sampling

Description

Estimates the required sample size under under stratified random sampling.

Usage

epi.stratasize(strata.n, strata.mean, strata.var, strata.Py, epsilon.r, 
   method = "mean", conf.level = 0.95)

Arguments

strata.n

vector, defining the size of each strata.

strata.mean

vector, representing the expected means in each strata. Only used when method = "mean", "total" or "pps".

strata.var

vector, representing the expected variance in each strata. Only used when method = "mean", "total" or "pps".

strata.Py

vector, representing the expected proportions in each strata. Only used when method = "proportion".

epsilon.r

the maximum relative difference between our estimate and the unknown population value.

method

a character string indicating the method to be used. Options are mean, total, proportion, or pps.

conf.level

scalar, defining the level of confidence in the computed result.

Value

A list containing the following:

strata.sample

the estimated sample size for each strata.

strata.total

the estimated total size.

strata.stats

mean the mean across all strata, sigma.bx the among-strata variance, sigma.wx the within-strata variance, and sigma.x the among-strata variance plus the within-strata variance, rel.var the within-strata variance divided by the square of the mean, and gamma the ratio of among-strata variance to within-strata variance.

References

Levy PS, Lemeshow S (1999). Sampling of Populations Methods and Applications. Wiley Series in Probability and Statistics, London, pp. 175 - 179.

Examples

## EXAMPLE 1:
## Hospital episodes (Levy and Lemeshow 1999, page 176 -- 178)
## We plan to take a sample of the members of a health maintenance 
## organisation (HMO) for purposes of estimating the average number
## of hospital episodes per person per year. The sample will be selected
## from membership lists according to age (under 45 years, 45 -- 64 years, 
## 65 years and over). The number of members in each strata are 600, 500,
## and 400 (respectively). Previous data estimates the mean number of 
## hospital episodes per year for each strata as 0.164, 0.166, and 0.236
## (respectively). The variance of these estimates are 0.245, 0.296, and 
## 0.436 (respectively). How many from each strata should be sampled to be
## 95% that the sample estimate of hospital episodes is within 20% of the 
## true value?

strata.n <- c(600, 500, 400)
strata.mean <- c(0.164, 0.166, 0.236)
strata.var <- c(0.245, 0.296, 0.436)
epi.stratasize(strata.n, strata.mean, strata.var, strata.Py, 
   epsilon.r = 0.20, method = "mean", conf.level = 0.95)

## The number allocated to the under 45 years, 45 -- 64 years, and 65 years 
## and over stratums should be 223, 186, and 149 (a total of 558). These 
## results differ from the worked example provided in Levy and Lemeshow where 
## certainty is set to approximately 99%.

## EXAMPLE 2:
## Dairies are to be sampled to determine the proportion of herd managers 
## using foot bathes. Herds are stratified according to size (small, medium, 
## and large). The number of herds in each strata are 1500, 2500, and 4000
## (respectively). A review of the literature indicates that use of foot bathes
## on farms is in the order of 0.50, with the probability of usage increasing
## as herds get larger. How many dairies should be sampled?

strata.n <- c(1500, 2500, 4000)
strata.Py <- c(0.50, 0.60, 0.70)
epi.stratasize(strata.n, strata.mean, strata.var, strata.Py, 
   epsilon.r = 0.20, method = "proportion", conf.level = 0.95)

## A total of 54 herds should be sampled: 10 small, 17 medium, and 27 large.