The function sample.size.prop returns the sample size needed for proportion estimation either with or without consideration of finite population correction.

sample.size.prop(e, P = 0.5, N = Inf, level = 0.95)

## Arguments

e positive number specifying the precision which is half width of confidence interval expected proportion of events with domain between values 0 and 1. Default is P=0.5. positive integer for population size. Default is N=Inf, which means that calculations are carried out without finite population correction. coverage probability for confidence intervals. Default is level=0.95.

## Details

For meaningful calculation, precision e should be chosen smaller than 0.5, because the domain of P is between values 0 and 1. Furthermore, precision e should be smaller than proportion P, respectively (1-P).

## Value

The function sample.size.prop returns a value, which is a list consisting of the components

call

is a list of call components e precision, P expected proportion, N population size, and level coverage probability for confidence intervals

n

estimate of sample size

## References

Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.

## Author

Juliane Manitz

Sprop, sample.size.mean

## Examples

## 1) examples with different precisions
# precision 1% for election forecast of SPD in 2005
sample.size.prop(e=0.01, P=0.5, N=Inf)
#>
#> sample.size.prop object: Sample size for proportion estimate
#> Without finite population correction: N=Inf, precision e=0.01 and expected proportion P=0.5
#>
#> Sample size needed: 9604
#> data(election)
sample.size.prop(e=0.01, P=mean(election$SPD_02), N=Inf) #> #> sample.size.prop object: Sample size for proportion estimate #> Without finite population correction: N=Inf, precision e=0.01 and expected proportion P=0.3861 #> #> Sample size needed: 9106 #> # precision 5% for questionnaire sample.size.prop(e=0.05, P=0.5, N=300) #> #> sample.size.prop object: Sample size for proportion estimate #> With finite population correction: N=300, precision e=0.05 and expected proportion P=0.5 #> #> Sample size needed: 169 #> sample.size.prop(e=0.05, P=0.5, N=Inf) #> #> sample.size.prop object: Sample size for proportion estimate #> Without finite population correction: N=Inf, precision e=0.05 and expected proportion P=0.5 #> #> Sample size needed: 385 #> # precision 10% sample.size.prop(e=0.1, P=0.5, N=300) #> #> sample.size.prop object: Sample size for proportion estimate #> With finite population correction: N=300, precision e=0.1 and expected proportion P=0.5 #> #> Sample size needed: 73 #> sample.size.prop(e=0.1, P=0.5, N=1000) #> #> sample.size.prop object: Sample size for proportion estimate #> With finite population correction: N=1000, precision e=0.1 and expected proportion P=0.5 #> #> Sample size needed: 88 #> ## 2) tables in the book # table 2.2 P_vector <- c(0.2, 0.3, 0.4, 0.5) N_vector <- c(10, 100, 1000, 10000) results <- matrix(NA, ncol=4, nrow=4) for (i in 1:length(P_vector)){ for (j in 1:length(N_vector)){ x <- try(sample.size.prop(e=0.1, P=P_vector[i], N=N_vector[j])) if (class(x)=='try-error') {results[i,j] <- NA} else {results[i,j] <- x$n}
}
}
dimnames(results) <- list(paste('P=',P_vector, sep=''), paste('N=',N_vector, sep=''))
results
#>       N=10 N=100 N=1000 N=10000
#> P=0.2    9    39     58      62
#> P=0.3    9    45     75      81
#> P=0.4   10    48     85      92
#> P=0.5   10    49     88      96# table 2.3
P_vector <- c(0.5, 0.1)
e_vector <- c(0.1, 0.05, 0.03, 0.02, 0.01)
results <- matrix(NA, ncol=2, nrow=5)
for (i in 1:length(e_vector)){
for (j in 1:length(P_vector)){
x <- try(sample.size.prop(e=e_vector[i], P=P_vector[j], N=Inf))
if (class(x)=='try-error') {results[i,j] <- NA}
else {results[i,j] <- x\$n}
}
}
dimnames(results) <- list(paste('e=',e_vector, sep=''), paste('P=',P_vector, sep=''))
results
#>        P=0.5 P=0.1
#> e=0.1     97    35
#> e=0.05   385   139
#> e=0.03  1068   385
#> e=0.02  2401   865
#> e=0.01  9604  3458