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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationFri, 08 Oct 2010 13:44:47 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/08/t1286545514sj0ej7g3ekern0f.htm/, Retrieved Thu, 02 May 2024 05:29:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=82008, Retrieved Thu, 02 May 2024 05:29:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Connected vs Sepa...] [2010-10-04 07:35:56] [b98453cac15ba1066b407e146608df68]
F         [Pearson Correlation] [Connected vs Sepa...] [2010-10-08 13:44:47] [18ef3d986e8801a4b28404e69e5bf56b] [Current]
Feedback Forum
2010-10-16 10:03:11 [1951de723fd2749e12bc2f1a75bd3e74] [reply] 
Je interpreteert zowel de Scatter Plot als de Bivariate Kernel Density Plot correct. Je zegt dat je duidelijker op de scatter plot kan afleiden of beide indexen in relatie staan met elkaar. Ik wil er op wijzen dat je bij de Kernel Density Plot hoogtelijnen (isodensity curves) hebt die makkeljk de gelijke frequenties/dichtheid aangeven. Ook zijn de kleuren een handig hulpmiddel om de hotspot van de plot te vinden. Ook kan je de correlatie snel waarnemen. Wanneer de puntenwolk op de lijn ligt, is er een hoge correlatie van 1. Hoe dichter de correlatie bij 0 ligt, hoe verder de puntenwolk verwijderd ligt van de lijn. (hier is de correlatie 0,52)

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Dataseries Y:
Download CSV
Histogram 
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Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 0 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=82008&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=82008&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=82008&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean36.248484848484835.0454545454545
Biased Variance19.962497704315920.3039944903581
Biased Standard Deviation4.467941103496764.5059953939566
Covariance10.6208897485493
Correlation0.52595026181494
Determination0.276623677903204
T-Test11.1995211160927
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom328
Number of Observations330

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 36.2484848484848 & 35.0454545454545 \tabularnewline
Biased Variance & 19.9624977043159 & 20.3039944903581 \tabularnewline
Biased Standard Deviation & 4.46794110349676 & 4.5059953939566 \tabularnewline
Covariance & 10.6208897485493 \tabularnewline
Correlation & 0.52595026181494 \tabularnewline
Determination & 0.276623677903204 \tabularnewline
T-Test & 11.1995211160927 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 328 \tabularnewline
Number of Observations & 330 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=82008&T=1

[TABLE]
[ROW][C]Pearson Product Moment Correlation - Ungrouped Data[/C][/ROW]
[ROW][C]Statistic[/C][C]Variable X[/C][C]Variable Y[/C][/ROW]
[ROW][C]Mean[/C][C]36.2484848484848[/C][C]35.0454545454545[/C][/ROW]
[ROW][C]Biased Variance[/C][C]19.9624977043159[/C][C]20.3039944903581[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.46794110349676[/C][C]4.5059953939566[/C][/ROW]
[ROW][C]Covariance[/C][C]10.6208897485493[/C][/ROW]
[ROW][C]Correlation[/C][C]0.52595026181494[/C][/ROW]
[ROW][C]Determination[/C][C]0.276623677903204[/C][/ROW]
[ROW][C]T-Test[/C][C]11.1995211160927[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]328[/C][/ROW]
[ROW][C]Number of Observations[/C][C]330[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=82008&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=82008&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean36.248484848484835.0454545454545
Biased Variance19.962497704315920.3039944903581
Biased Standard Deviation4.467941103496764.5059953939566
Covariance10.6208897485493
Correlation0.52595026181494
Determination0.276623677903204
T-Test11.1995211160927
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom328
Number of Observations330


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
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)
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')
cxy <- as.matrix(corxy$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm','Mean',''),header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased.htm','Biased Variance',''),header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased1.htm','Biased Standard Deviation',''),header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('covariance.htm','Covariance',''),header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('pearson_correlation.htm','Correlation',''),header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('coeff_of_determination.htm','Determination',''),header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ttest_statistic.htm','T-Test',''),header=TRUE)
a<-table.element(a,as.matrix(corxy$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,'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')