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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 computationMon, 03 Nov 2008 12:14:50 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/03/t1225739742ayisrwpph2jbtsm.htm/, Retrieved Thu, 30 Apr 2026 01:49:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=21021, Retrieved Thu, 30 Apr 2026 01:49:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact418

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Pearson Correlation] [RNR-RCF] [2008-11-03 19:14:50] [00a0a665d7a07edd2e460056b0c0c354] [Current]
-    D    [Pearson Correlation] [RLEZ - RNR] [2008-11-03 19:25:11] [82d201ca7b4e7cd2c6f885d29b5b6937]
-           [Pearson Correlation] [Hypothesis testin...] [2008-11-03 20:19:51] [8d78428855b119373cac369316c08983]
-    D    [Pearson Correlation] [REV-RNR] [2008-11-03 19:32:10] [82d201ca7b4e7cd2c6f885d29b5b6937]
-           [Pearson Correlation] [Hypothesis testin...] [2008-11-03 20:22:11] [8d78428855b119373cac369316c08983]
-         [Pearson Correlation] [Hypothesis testin...] [2008-11-03 20:17:30] [8d78428855b119373cac369316c08983]
Feedback Forum
2008-11-06 21:50:46 [Stéphanie Van Dyck] [reply] 
De redenering is juist, maar het is gemakkelijker om het Kendall Tau correlation plot te gebruiken. Hierbij moet je maar 1 berekening maken en kan je de juiste oplossing op de grafiek of in het schema aflezen.
2008-11-11 11:35:35 [Inge Meelberghs] [reply] 
Zoals Stefanie al zei kan ik beter de Kendall Tau grafiek gebruiken om na te gaan welke variable het beste is om een voorspelling te maken over RNR. In dit geval was dit RCF. Dit konden we afleiden uit de grafiek en de tabel.

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/11/t12264002620rzqbs4mhjx57e9.htm

De tabel geeft ons informatie over de tau en de p-value.
Met tau wordt de correlatiecoëfficient bedoelt. Hier kunnen we zien dat deze het hoogst ligt bij (RNR,RCF), namelijk 0,809.
De p-value geeft de betrouwbaarheid aan. Deze is bij (RNR,RCF) het laagst, namelijk 0,01. Dit is goed want des te lager de p-value, des te groter de betrouwbaarheid.

Hetzelfde kunnen we allemaal afleiden uit de Kendall tau grafiek. Bovenaan zien we de scaterplots met de correlatielijnen. Onderaan zien we de waarden van de P-value, de betrouwbaarheid dus en niét de correlatiecoëfficienten. Ook hier kunnen we dan concluderen dat de scaterplot (RNR,RCF) een mooi positief verloop aanneemt. De waarde van de p-value is zoals eerder al gezegd 0,01 wat duidt op een grote betrouwbaarheid.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4,8	
-4,2	
1,6	
5,2	
9,2	
4,6	
10,6
Dataseries Y:
Download CSV
Histogram 
20,8	
17,1	
22,3	
25,1	
27,7	
24,9	
29,5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21021&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=21021&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21021&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean4.5428571428571423.9142857142857
Biased Variance20.568163265306115.2355102040816
Biased Standard Deviation4.535213695660453.90326916879705
Covariance19.3042857142857
Correlation0.934718181651295
Determination0.873698079109504
T-Test5.88112912470809
p-value (2 sided)0.00201871267116260
p-value (1 sided)0.00100935633558130
Degrees of Freedom5
Number of Observations7

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 4.54285714285714 & 23.9142857142857 \tabularnewline
Biased Variance & 20.5681632653061 & 15.2355102040816 \tabularnewline
Biased Standard Deviation & 4.53521369566045 & 3.90326916879705 \tabularnewline
Covariance & 19.3042857142857 \tabularnewline
Correlation & 0.934718181651295 \tabularnewline
Determination & 0.873698079109504 \tabularnewline
T-Test & 5.88112912470809 \tabularnewline
p-value (2 sided) & 0.00201871267116260 \tabularnewline
p-value (1 sided) & 0.00100935633558130 \tabularnewline
Degrees of Freedom & 5 \tabularnewline
Number of Observations & 7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21021&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]4.54285714285714[/C][C]23.9142857142857[/C][/ROW]
[ROW][C]Biased Variance[/C][C]20.5681632653061[/C][C]15.2355102040816[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.53521369566045[/C][C]3.90326916879705[/C][/ROW]
[ROW][C]Covariance[/C][C]19.3042857142857[/C][/ROW]
[ROW][C]Correlation[/C][C]0.934718181651295[/C][/ROW]
[ROW][C]Determination[/C][C]0.873698079109504[/C][/ROW]
[ROW][C]T-Test[/C][C]5.88112912470809[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00201871267116260[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00100935633558130[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]5[/C][/ROW]
[ROW][C]Number of Observations[/C][C]7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=21021&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21021&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
Mean4.5428571428571423.9142857142857
Biased Variance20.568163265306115.2355102040816
Biased Standard Deviation4.535213695660453.90326916879705
Covariance19.3042857142857
Correlation0.934718181651295
Determination0.873698079109504
T-Test5.88112912470809
p-value (2 sided)0.00201871267116260
p-value (1 sided)0.00100935633558130
Degrees of Freedom5
Number of Observations7


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')