epiR (version 0.9-22)

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, epsilon, 
   method = "mean", conf.level = 0.95)

Arguments

strata.n

vector, defining the size of each strata.

strata.mean

vector, representing the mean of each strata.

strata.var

vector, representing the variance of each strata.

epsilon

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

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