# ::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('