::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 a mean. 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 population variance, and the power (default is 50%).
In addition, the minimum sample size is computed for the case where the population variance is unknown (the specified population variance is used as a starting value in the t-distribution).

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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))) z2 <- z*z z2one <- z1*z1 z24 <- z2 * par4 z24one <- z2one * par4 npop <- array(NA, 200) ppop <- array(NA, 200) for (i in 1:200) { ppop[i] <- i * 100 npop[i] <- ppop[i] * z24 / (z24 + (ppop[i] - 1) * par2*par2) } 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," Population Var. = ") dumtext <- paste(dumtext, par4) mtext(dumtext) grid() dev.off() par2sq <- par2 * par2 num <- par1 * z24 denom <- z24 + (par1 - 1) * par2sq (n <- num/denom) num1 <- par1 * z24one denom1 <- z24one + (par1 - 1) * par2sq (n1 <- num1/denom1) 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,"Population Variance",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") (ni <- z24 / (par2sq)) (ni1 <- z24one / (par2sq)) a<-table.start() a<-table.row.start(a) a<-table.element(a,"Minimum Sample Size (for Infinite Populations)",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,"Population Variance",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,ni) 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,ni1) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab") (z <- abs(qt((1-par3)/2,n-1)) + abs(qt(1-par5,n-1))) (z1 <- abs(qt(1-par3,n1-1)) + abs(qt(1-par5,n1-1))) z2 <- z*z z2one <- z1*z1 z24 <- z2 * par4 z24one <- z2one * par4 par2sq <- par2 * par2 num <- par1 * z24 denom <- z24 + (par1 - 1) * par2sq (n <- num/denom) num1 <- par1 * z24one denom1 <- z24one + (par1 - 1) * par2sq (n1 <- num1/denom1) a<-table.start() a<-table.row.start(a) a<-table.element(a,"Minimum Sample Size (Unknown Population Variance)",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,"Population Variance",header=TRUE) a<-table.element(a,"unknown") a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"t(alpha/2) + t(beta)",header=TRUE) a<-table.element(a,z) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"t(alpha) + t(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") (z <- abs(qt((1-par3)/2,ni-1)) + abs(qt(1-par5,ni-1))) (z1 <- abs(qt(1-par3,ni1-1)) + abs(qt(1-par5,ni1-1))) z2 <- z*z z2one <- z1*z1 z24 <- z2 * par4 z24one <- z2one * par4 (ni <- z24 / (par2sq)) (ni1 <- z24one / (par2sq)) a<-table.start() a<-table.row.start(a) a<-table.element(a,"Minimum Sample Size<br />(Infinite Population, Unknown Population Variance)",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,"Population Variance",header=TRUE) a<-table.element(a,"unknown") a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"t(alpha/2) + t(beta)",header=TRUE) a<-table.element(a,z) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"t(alpha) + t(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,ni) 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,ni1) 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 Mean) (v1.0.3) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL http://www.wessa.net/rwasp_samplenorm.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 : wessa.net

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