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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 13:02:00 -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/t1225742557noaqfnl14pgdpt3.htm/, Retrieved Sun, 19 May 2024 09:38:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=21140, Retrieved Sun, 19 May 2024 09:38:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact168

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [RNR - RNVM] [2008-11-03 19:03:20] [82d201ca7b4e7cd2c6f885d29b5b6937]
F         [Pearson Correlation] [Hypothesis testin...] [2008-11-03 20:02:00] [d6e9f26c3644bfc30f06303d9993b878] [Current]
Feedback Forum
2008-11-05 17:45:50 [Ciska Tanghe] [reply] 
Je geeft een correct antwoord, maar de manier waarop je dit antwoord bekomen hebt, is nogal omslachtig. Een betere methode is Kendall tau Correlation Matrix waar je de vijf reeksen in één grafiek hebt en deze gemakkelijk kan vergelijken.
2008-11-11 13:26:00 [Sanne Kerckhofs] [reply] 
Het antwoord is correct maar het zou veel eenvoudiger kunnen worden opgelost namelijk met het gebruik maken van de Kendall Tau Correlation Matrix. De correcte oplossing zou dan de volgende zijn: http://www.freestatistics.org/blog/date/2008/Nov/03/t1225706212pzh6w9duceiv00s.htm
Hier krijg je dan een overzicht van alle correlaties waaruit je dan kan afleiden dat REV de meest betrouwbare variabele is om een voorspelling te maken over RNR. Hoe kleiner de p-waarde, hoe groter de betrouwbaarheid. De laagste p-waarde geeft dus de hoogste betrouwbaarheid van de correlatie.

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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 
4,2	
2,6	
3	
3,8	
4	
3,5	
4,1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21140&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=21140&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21140&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean4.542857142857143.6
Biased Variance20.56816326530610.311428571428571
Biased Standard Deviation4.535213695660450.55805785670356
Covariance2.61333333333333
Correlation0.885056581705508
Determination0.783325152820238
T-Test4.25159403195624
p-value (2 sided)0.00807948566831929
p-value (1 sided)0.00403974283415964
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 & 3.6 \tabularnewline
Biased Variance & 20.5681632653061 & 0.311428571428571 \tabularnewline
Biased Standard Deviation & 4.53521369566045 & 0.55805785670356 \tabularnewline
Covariance & 2.61333333333333 \tabularnewline
Correlation & 0.885056581705508 \tabularnewline
Determination & 0.783325152820238 \tabularnewline
T-Test & 4.25159403195624 \tabularnewline
p-value (2 sided) & 0.00807948566831929 \tabularnewline
p-value (1 sided) & 0.00403974283415964 \tabularnewline
Degrees of Freedom & 5 \tabularnewline
Number of Observations & 7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=21140&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]3.6[/C][/ROW]
[ROW][C]Biased Variance[/C][C]20.5681632653061[/C][C]0.311428571428571[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.53521369566045[/C][C]0.55805785670356[/C][/ROW]
[ROW][C]Covariance[/C][C]2.61333333333333[/C][/ROW]
[ROW][C]Correlation[/C][C]0.885056581705508[/C][/ROW]
[ROW][C]Determination[/C][C]0.783325152820238[/C][/ROW]
[ROW][C]T-Test[/C][C]4.25159403195624[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00807948566831929[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00403974283415964[/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=21140&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=21140&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
Mean4.542857142857143.6
Biased Variance20.56816326530610.311428571428571
Biased Standard Deviation4.535213695660450.55805785670356
Covariance2.61333333333333
Correlation0.885056581705508
Determination0.783325152820238
T-Test4.25159403195624
p-value (2 sided)0.00807948566831929
p-value (1 sided)0.00403974283415964
Degrees of Freedom5
Number of Observations7


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')