::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the minimum sample size that is required to test proportions. The computation takes into account: a margin of error (allowable deviation), the percentage of confidence, the population size (use a large number for infinite populations), the proportion that is tested, and the power (default is 50%).

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Source code of R module

par1 <- as.numeric(par1) par2 <- as.numeric(par2) par3 <- as.numeric(par3) par4 <- as.numeric(par4) par5 <- as.numeric(par5) (z <- abs(qnorm((1-par3)/2)) + abs(qnorm(1-par5))) (z1 <- abs(qnorm(1-par3)) + abs(qnorm(1-par5))) dum <- z*z * par4*(1-par4) dum1 <- z1*z1 * par4*(1-par4) par22 <- par2*par2 npop <- array(NA, 200) ppop <- array(NA, 200) for (i in 1:200) { ppop[i] <- i * 100 npop[i] <- ppop[i] * dum / (dum + (ppop[i]-1)*par22) } bitmap(file="pic1.png") plot(ppop,npop, xlab="population size", ylab="sample size (2 sided test)", main = paste("Minimum Required Sample Size (Confidence =",round(par3*100,2),"%)")) dumtext <- paste("Margin of error = ",par2) dumtext <- paste(dumtext," Response Rate = ") dumtext <- paste(dumtext, par4) mtext(dumtext) grid() dev.off() (n <- par1 * dum / (dum + (par1-1)*par22)) (n1 <- par1 * dum1 / (dum1 + (par1-1)*par22)) load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Minimum Sample Size",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Population Size",header=TRUE) a<-table.element(a,par1) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Margin of Error",header=TRUE) a<-table.element(a,par2) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Confidence",header=TRUE) a<-table.element(a,par3) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Power",header=TRUE) a<-table.element(a,par5) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Response Distribution (Proportion)",header=TRUE) a<-table.element(a,par4) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"z(alpha/2) + z(beta)",header=TRUE) a<-table.element(a,z) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"z(alpha) + z(beta)",header=TRUE) a<-table.element(a,z1) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Minimum Sample Size (2 sided test)",header=TRUE) a<-table.element(a,n) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Minimum Sample Size (1 sided test)",header=TRUE) a<-table.element(a,n1) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab") (n <- dum / par22) (n1 <- dum1 / par22) a<-table.start() a<-table.row.start(a) a<-table.element(a,"Minimum Sample Size (infinite population)",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Population Size",header=TRUE) a<-table.element(a,"infinite") a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Margin of Error",header=TRUE) a<-table.element(a,par2) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Confidence",header=TRUE) a<-table.element(a,par3) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Power",header=TRUE) a<-table.element(a,par5) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Response Distribution (Proportion)",header=TRUE) a<-table.element(a,par4) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"z(alpha/2) + z(beta)",header=TRUE) a<-table.element(a,z) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"z(alpha) + z(beta)",header=TRUE) a<-table.element(a,z1) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Minimum Sample Size (2 sided test)",header=TRUE) a<-table.element(a,n) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Minimum Sample Size (1 sided test)",header=TRUE) a<-table.element(a,n1) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab")

Cite this software as:

Wessa P., (2018), Minimum Sample Size (Testing Proportions) (v1.0.5) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL http://www.wessa.net/rwasp_sample.wasp/

The R code is based on :

NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, 2006-11-12.

To cite Wessa.net in publications use:
Wessa, P. (2024), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL https://www.wessa.net/

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Software Version : 1.2.1
Algorithms & Software : Patrick Wessa, PhD
Server : supernova.wessa.net

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