# ::Free Statistics and Forecasting Software::

v1.2.1

### :: Pearson Correlation - 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 the following Pearson Correlation output: Scatter Plot, Pearson Product Moment Correlation, Covariance, Determination, and the Correlation T-Test. The Jarque-Bera and Anderson-Darling Normality Tests are applied to both variales. If non-normality is detected one should use a rank correlation instead (for instance the Kendall Rank Correlation). In both tests a rejection of the null hypothesis implies a deviation from normality. Accepting the null hypothesis does not necessarily imply normality.

Enter (or paste) your data delimited by hard returns.

 Send output to: Browser Blue - Charts White Browser Black/White CSV Data X (click to load default data) 20 40 30 50 60 Data Y: 80 60 10 20 30 Chart options Width: Height: Title: Label y-axis: Label x-axis:

 Source code of R module library(psychometric) x <- x[!is.na(y)] y <- y[!is.na(y)] y <- y[!is.na(x)] x <- x[!is.na(x)] bitmap(file="test1.png") histx <- hist(x, plot=FALSE) histy <- hist(y, plot=FALSE) maxcounts <- max(c(histx\$counts, histx\$counts)) xrange <- c(min(x),max(x)) yrange <- c(min(y),max(y)) nf <- layout(matrix(c(2,0,1,3),2,2,byrow=TRUE), c(3,1), c(1,3), TRUE) par(mar=c(4,4,1,1)) plot(x, y, xlim=xrange, ylim=yrange, xlab=xlab, ylab=ylab, sub=main) par(mar=c(0,4,1,1)) barplot(histx\$counts, axes=FALSE, ylim=c(0, maxcounts), space=0) par(mar=c(4,0,1,1)) barplot(histy\$counts, axes=FALSE, xlim=c(0, maxcounts), space=0, horiz=TRUE) dev.off() lx = length(x) makebiased = (lx-1)/lx varx = var(x)*makebiased vary = var(y)*makebiased corxy <- cor.test(x,y,method="pearson", na.rm = T) cxy <- as.matrix(corxy\$estimate)[1,1] load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Pearson Product Moment Correlation - Ungrouped Data",3,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Statistic",1,TRUE) a<-table.element(a,"Variable X",1,TRUE) a<-table.element(a,"Variable Y",1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Mean",header=TRUE) a<-table.element(a,mean(x)) a<-table.element(a,mean(y)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Biased Variance",header=TRUE) a<-table.element(a,varx) a<-table.element(a,vary) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Biased Standard Deviation",header=TRUE) a<-table.element(a,sqrt(varx)) a<-table.element(a,sqrt(vary)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Covariance",header=TRUE) a<-table.element(a,cov(x,y),2) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Correlation",header=TRUE) a<-table.element(a,cxy,2) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Determination",header=TRUE) a<-table.element(a,cxy*cxy,2) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"T-Test",header=TRUE) a<-table.element(a,as.matrix(corxy\$statistic)[1,1],2) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"p-value (2 sided)",header=TRUE) a<-table.element(a,(p2 <- as.matrix(corxy\$p.value)[1,1]),2) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"p-value (1 sided)",header=TRUE) a<-table.element(a,p2/2,2) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"95% CI of Correlation",header=TRUE) a<-table.element(a,paste("[",CIr(r=cxy, n = lx, level = .95)[1],", ", CIr(r=cxy, n = lx, level = .95)[2],"]",sep=""),2) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Degrees of Freedom",header=TRUE) a<-table.element(a,lx-2,2) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Number of Observations",header=TRUE) a<-table.element(a,lx,2) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab") library(moments) library(nortest) jarque.x <- jarque.test(x) jarque.y <- jarque.test(y) if(lx>7) { ad.x <- ad.test(x) ad.y <- ad.test(y) } a<-table.start() a<-table.row.start(a) a<-table.element(a,'Normality Tests',1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,paste('
',RC.texteval('jarque.x'),'
',sep='')) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,paste('
',RC.texteval('jarque.y'),'
',sep='')) a<-table.row.end(a) if(lx>7) { a<-table.row.start(a) a<-table.element(a,paste('
',RC.texteval('ad.x'),'
',sep='')) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,paste('
',RC.texteval('ad.y'),'
',sep='')) a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable1.tab") library(car) bitmap(file="test2.png") qqPlot(x,main="QQplot of variable x") dev.off() bitmap(file="test3.png") qqPlot(y,main="QQplot of variable y") dev.off()
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 Cite this software as: Wessa P., (2017), Pearson Correlation (v1.0.13) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL https://www.wessa.net/rwasp_correlation.wasp/ The R code is based on : Borghers, E, and P. Wessa, Statistics - Econometrics - Forecasting, Office for Research Development and Education, http://www.xycoon.com/
 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
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