Sample Size Calculation for Proportion Estimation

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
P	expected proportion of events with domain between values 0 and 1. Default is P=0.5.
N	positive integer for population size. Default is N=Inf, which means that calculations are carried out without finite population correction.
level	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

See also

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