# ::Free Statistics and Forecasting Software::

v1.2.1

### :: Paired and Unpaired Two Samples Tests about the Mean - Free Statistics Software (Calculator) ::

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 various types of parametric and non-parametric tests for comparing the means of two paired or unpaired samples: classical Paired Two Sample t-Test, classical Unpaired Two Sample t-Test, Welch t-Test, Wilcoxon Signed-Rank Test, and Wilcoxon Rank-Sum Test (Mann-Whitney U Test).

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

 Send output to: Browser Blue - Charts White Browser Black/White CSV Data X (click to load default data) 3 9 5 5 6 6 3 7 2 8 6 5 8 8 5 4 3 3 3 5 4 4 5 9 3 9 5 5 6 6 3 7 2 8 6 5 8 8 5 4 3 3 3 5 4 4 5 9 Names of X columns: A B Column number of first sample Column number of second sample Confidence Alternative two.sidedlessgreater Are observations paired? unpairedpaired Null Hypothesis Chart options Width: Height: Title:

 Source code of R module par1 <- as.numeric(par1) #column number of first sample par2 <- as.numeric(par2) #column number of second sample par3 <- as.numeric(par3) #confidence (= 1 - alpha) if (par5 == 'unpaired') paired <- FALSE else paired <- TRUE par6 <- as.numeric(par6) #H0 z <- t(y) if (par1 == par2) stop("Please, select two different column numbers") if (par1 < 1) stop("Please, select a column number greater than zero for the first sample") if (par2 < 1) stop("Please, select a column number greater than zero for the second sample") if (par1 > length(z[1,])) stop("The column number for the first sample should be smaller") if (par2 > length(z[1,])) stop("The column number for the second sample should be smaller") if (par3 <= 0) stop("The confidence level should be larger than zero") if (par3 >= 1) stop("The confidence level should be smaller than zero") (r.t <- t.test(z[,par1],z[,par2],var.equal=TRUE,alternative=par4,paired=paired,mu=par6,conf.level=par3)) (v.t <- var.test(z[,par1],z[,par2],conf.level=par3)) (r.w <- t.test(z[,par1],z[,par2],var.equal=FALSE,alternative=par4,paired=paired,mu=par6,conf.level=par3)) (w.t <- wilcox.test(z[,par1],z[,par2],alternative=par4,paired=paired,mu=par6,conf.level=par3)) (ks.t <- ks.test(z[,par1],z[,par2],alternative=par4)) m1 <- mean(z[,par1],na.rm=T) m2 <- mean(z[,par2],na.rm=T) mdiff <- m1 - m2 newsam1 <- z[!is.na(z[,par1]),par1] newsam2 <- z[,par2]+mdiff newsam2 <- newsam2[!is.na(newsam2)] (ks1.t <- ks.test(newsam1,newsam2,alternative=par4)) mydf <- data.frame(cbind(z[,par1],z[,par2])) colnames(mydf) <- c("Variable 1","Variable 2") bitmap(file="test1.png") boxplot(mydf, notch=TRUE, ylab="value",main=main) dev.off() bitmap(file="test2.png") qqnorm(z[,par1],main="Normal QQplot - Variable 1") qqline(z[,par1]) dev.off() bitmap(file="test3.png") qqnorm(z[,par2],main="Normal QQplot - Variable 2") qqline(z[,par2]) dev.off() load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,paste("Two Sample t-test (",par5,")",sep=""),2,TRUE) a<-table.row.end(a) if(!paired){ a<-table.row.start(a) a<-table.element(a,"Mean of Sample 1",header=TRUE) a<-table.element(a,r.t\$estimate[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Mean of Sample 2",header=TRUE) a<-table.element(a,r.t\$estimate[[2]]) a<-table.row.end(a) } else { a<-table.row.start(a) a<-table.element(a,"Difference: Mean1 - Mean2",header=TRUE) a<-table.element(a,r.t\$estimate) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,"t-stat",header=TRUE) a<-table.element(a,r.t\$statistic[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"df",header=TRUE) a<-table.element(a,r.t\$parameter[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"p-value",header=TRUE) a<-table.element(a,r.t\$p.value) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"H0 value",header=TRUE) a<-table.element(a,r.t\$null.value[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Alternative",header=TRUE) a<-table.element(a,r.t\$alternative) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"CI Level",header=TRUE) a<-table.element(a,attr(r.t\$conf.int,"conf.level")) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"CI",header=TRUE) a<-table.element(a,paste("[",r.t\$conf.int[1],",",r.t\$conf.int[2],"]",sep="")) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"F-test to compare two variances",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"F-stat",header=TRUE) a<-table.element(a,v.t\$statistic[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"df",header=TRUE) a<-table.element(a,v.t\$parameter[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"p-value",header=TRUE) a<-table.element(a,v.t\$p.value) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"H0 value",header=TRUE) a<-table.element(a,v.t\$null.value[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Alternative",header=TRUE) a<-table.element(a,v.t\$alternative) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"CI Level",header=TRUE) a<-table.element(a,attr(v.t\$conf.int,"conf.level")) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"CI",header=TRUE) a<-table.element(a,paste("[",v.t\$conf.int[1],",",v.t\$conf.int[2],"]",sep="")) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,paste("Welch Two Sample t-test (",par5,")",sep=""),2,TRUE) a<-table.row.end(a) if(!paired){ a<-table.row.start(a) a<-table.element(a,"Mean of Sample 1",header=TRUE) a<-table.element(a,r.w\$estimate[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Mean of Sample 2",header=TRUE) a<-table.element(a,r.w\$estimate[[2]]) a<-table.row.end(a) } else { a<-table.row.start(a) a<-table.element(a,"Difference: Mean1 - Mean2",header=TRUE) a<-table.element(a,r.w\$estimate) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,"t-stat",header=TRUE) a<-table.element(a,r.w\$statistic[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"df",header=TRUE) a<-table.element(a,r.w\$parameter[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"p-value",header=TRUE) a<-table.element(a,r.w\$p.value) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"H0 value",header=TRUE) a<-table.element(a,r.w\$null.value[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Alternative",header=TRUE) a<-table.element(a,r.w\$alternative) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"CI Level",header=TRUE) a<-table.element(a,attr(r.w\$conf.int,"conf.level")) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"CI",header=TRUE) a<-table.element(a,paste("[",r.w\$conf.int[1],",",r.w\$conf.int[2],"]",sep="")) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable1.tab") a<-table.start() a<-table.row.start(a) myWlabel <- "Wilcoxon Signed-Rank Test" if (par5=="unpaired") myWlabel = "Wilcoxon Rank-Sum Test (Mannâ€“Whitney U test)" a<-table.element(a,paste(myWlabel," with continuity correction (",par5,")",sep=""),2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"W",header=TRUE) a<-table.element(a,w.t\$statistic[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"p-value",header=TRUE) a<-table.element(a,w.t\$p.value) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"H0 value",header=TRUE) a<-table.element(a,w.t\$null.value[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Alternative",header=TRUE) a<-table.element(a,w.t\$alternative) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Kolmogorov-Smirnov Test to compare Distributions of two Samples",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"KS Statistic",header=TRUE) a<-table.element(a,ks.t\$statistic[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"p-value",header=TRUE) a<-table.element(a,ks.t\$p.value) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"KS Statistic",header=TRUE) a<-table.element(a,ks1.t\$statistic[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"p-value",header=TRUE) a<-table.element(a,ks1.t\$p.value) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable2.tab")
 Top | Output | Charts | References

 Cite this software as: Wessa P. (2016), Paired and Unpaired Two Samples Tests about the Mean (v1.0.7) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL http://www.wessa.net/rwasp_twosampletests_mean.wasp/ The R code is based on : Dalgaard P., Introductory Statistics with R,2nd ed., 2008, XVI, 364 p., ISBN: 978-0-387-79053-4
 Top | Output | Charts | References
 To cite Wessa.net in publications use:Wessa, P. (2023), Free Statistics Software, Office for Research Development and Education, version 1.2.1, URL https://www.wessa.net/ © All rights reserved. Academic license for non-commercial use only. The free use of the scientific content, services, and applications in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission. Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. We make no warranties or representations as to the accuracy or completeness of such information (or software), and it assumes no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site. Software Version : 1.2.1Algorithms & Software : Patrick Wessa, PhDServer : www.wessa.net
 © Wessa.Net 2002-2023