Sprop: Sampling Proportion Estimation

In samplingbook: Survey Sampling Procedures

Description

The function Sprop estimates the proportion out of samples either with or without consideration of finite population correction. Different methods for calculating confidence intervals for example based on binomial distribution (Agresti and Coull or Clopper-Pearson) or based on hypergeometric distribution are used.

Usage

Sprop(y, m, n = length(y), N = Inf, level = 0.95)

Arguments

y	vector of sample data containing values 0 and 1
m	an optional non-negative integer for number of positive events
n	an optional positive integer for sample size. Default is n=length(y).
N	positive integer for population size. Default is N=Inf, which means calculations are carried out without finite population correction.
level	coverage probability for confidence intervals. Default is level=0.95.

Details

Sprop can be called by usage of a data vector y with the observations 1 for event and 0 for failure. Moreover, it can be called by specifying the number of events m and trials n.

Value

The function Sprop returns a value, which is a list consisting of the components

call	is a list of call components: y sample data, m number of positive events in the sample, n sample size, N population size, level coverage probability for confidence intervals
p	proportion estimate
se	standard error of the proportion estimate
ci	is a list of confidence interval boundaries for proportion. In case of a finite population of size N, it is given approx, the hypergeometric confidence interval with normal distribution approximation, and exact, the exact hypergeometric confidence interval. If the population is very large N=Inf, it is calculated bin, the binomial confidence interval, which is asymptotic, cp the exact confidence interval based on binomial distribution (Clopper-Pearson), and ac, the asymptotic confidence interval based on binomial distribution by Wilson (Agresti and Coull (1998)).
nr	In case of finite population of size N, it is given a list of confidence interval boundaries for number in population with approx, the hypergeometric confidence interval with normal distribution approximation, and exact, the exact hypergeometric confidence interval.

Author(s)

Juliane Manitz

References

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

Agresti, Alan/Coull, Brent A. (1998): Approximate Is Better than 'Exact' for Interval Estimation of Binomial Proportions. The American Statistician, Vol. 52, No. 2 , pp. 119-126.

See Also

Smean, sample.size.prop

Examples

# 1) Survey in company to upgrade office climate
Sprop(m=45, n=100, N=300)
Sprop(m=2, n=100, N=300)

# 2) German opinion poll for 03/07/09 with 
# (http://www.wahlrecht.de/umfragen/politbarometer.htm)
# a) 302 of 1206 respondents who would elect SPD.
# b) 133 of 1206 respondents who would elect the Greens.
Sprop(m=302, n=1206, N=Inf)
Sprop(m=133, n=1206, N=Inf)

# 3) Rare disease of animals (sample size n=500 of N=10.000 animals, one infection)
# for 95% one sided confidence level use level=0.9
Sprop(m=1, n=500, N=10000, level=0.9)

# 4) call with data vector y
y <- c(0,0,1,0,1,0,0,0,1,1,0,0,1)
Sprop(y=y, N=200)
# is the same as
Sprop(m=5, n=13, N=200)

Example output

Loading required package: pps
Loading required package: sampling
Loading required package: survey
Loading required package: grid
Loading required package: Matrix
Loading required package: survival

Attaching package: ‘survival’

The following objects are masked from ‘package:sampling’:

    cluster, strata


Attaching package: ‘survey’

The following object is masked from ‘package:graphics’:

    dotchart


Sprop object: Sample proportion estimate
With finite population correction: N= 300 

Proportion estimate:  0.45 
Standard error:  0.0408 

95% approximate hypergeometric confidence interval: 
 proportion: [0.37,0.53]
 number in population: [111,159]
95% exact hypergeometric confidence interval: 
 proportion: [0.3667,0.5367]
 number in population: [110,161]

Sprop object: Sample proportion estimate
With finite population correction: N= 300 

Proportion estimate:  0.02 
Standard error:  0.0115 

95% approximate hypergeometric confidence interval: 
 proportion: [-0.0025,0.0425]
 number in population: [0,12]
95% exact hypergeometric confidence interval: 
 proportion: [0.0033,0.0633]
 number in population: [1,19]

Sprop object: Sample proportion estimate
Without finite population correction: N= Inf 

Proportion estimate:  0.2504 
Standard error:  0.0125 

95% asymptotic confidence interval:
 proportion: [0.226,0.2749]
95% asymptotic confidence interval with correction by Wilson:
 proportion: [0.2268,0.2756]
95% exact confidence interval by Clopper-Pearson:
 proportion: [0.2262,0.2759]


Sprop object: Sample proportion estimate
Without finite population correction: N= Inf 

Proportion estimate:  0.1103 
Standard error:  0.009 

95% asymptotic confidence interval:
 proportion: [0.0926,0.128]
95% asymptotic confidence interval with correction by Wilson:
 proportion: [0.0938,0.1292]
95% exact confidence interval by Clopper-Pearson:
 proportion: [0.0932,0.1293]


Sprop object: Sample proportion estimate
With finite population correction: N= 10000 

Proportion estimate:  0.002 
Standard error:  0.0019 

90% approximate hypergeometric confidence interval: 
 proportion: [-0.0012,0.0052]
 number in population: [-12,52]
90% exact hypergeometric confidence interval: 
 proportion: [1e-04,0.0093]
 number in population: [1,93]

Sprop object: Sample proportion estimate
With finite population correction: N= 200 

Proportion estimate:  0.3846 
Standard error:  0.1358 

95% approximate hypergeometric confidence interval: 
 proportion: [0.1185,0.6508]
 number in population: [24,130]
95% exact hypergeometric confidence interval: 
 proportion: [0.14,0.68]
 number in population: [28,136]

Sprop object: Sample proportion estimate
With finite population correction: N= 200 

Proportion estimate:  0.3846 
Standard error:  0.1358 

95% approximate hypergeometric confidence interval: 
 proportion: [0.1185,0.6508]
 number in population: [24,130]
95% exact hypergeometric confidence interval: 
 proportion: [0.14,0.68]
 number in population: [28,136]

samplingbook documentation built on April 3, 2021, 1:06 a.m.