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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationTue, 12 Aug 2008 18:04:54 -0600
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/Aug/13/t1218586112gso12ev9v0xrn9q.htm/, Retrieved Tue, 14 May 2024 00:25:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14530, Retrieved Tue, 14 May 2024 00:25:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact243

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [looked appearance] [2008-08-13 00:04:54] [57b70cf7dac5655af4bf79fd35e84c41] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0
4
8
12
16
20
Dataseries Y:
Download CSV
Histogram 
9.9
9
8.7
8.4
7.7
7.2

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14530&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14530&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14530&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean108.48333333333333
Biased Variance46.66666666666670.764722222222222
Biased Standard Deviation6.831300510639730.874483974822994
Covariance-7.08
Correlation-0.98763566791978
Determination0.975424212547351
T-Test-12.6000723936144
p-value (2 sided)0.000228369952493694
p-value (1 sided)0.000114184976246847
Degrees of Freedom4
Number of Observations6

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 10 & 8.48333333333333 \tabularnewline
Biased Variance & 46.6666666666667 & 0.764722222222222 \tabularnewline
Biased Standard Deviation & 6.83130051063973 & 0.874483974822994 \tabularnewline
Covariance & -7.08 \tabularnewline
Correlation & -0.98763566791978 \tabularnewline
Determination & 0.975424212547351 \tabularnewline
T-Test & -12.6000723936144 \tabularnewline
p-value (2 sided) & 0.000228369952493694 \tabularnewline
p-value (1 sided) & 0.000114184976246847 \tabularnewline
Degrees of Freedom & 4 \tabularnewline
Number of Observations & 6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14530&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]10[/C][C]8.48333333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]46.6666666666667[/C][C]0.764722222222222[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]6.83130051063973[/C][C]0.874483974822994[/C][/ROW]
[ROW][C]Covariance[/C][C]-7.08[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.98763566791978[/C][/ROW]
[ROW][C]Determination[/C][C]0.975424212547351[/C][/ROW]
[ROW][C]T-Test[/C][C]-12.6000723936144[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000228369952493694[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000114184976246847[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]4[/C][/ROW]
[ROW][C]Number of Observations[/C][C]6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14530&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14530&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
Mean108.48333333333333
Biased Variance46.66666666666670.764722222222222
Biased Standard Deviation6.831300510639730.874483974822994
Covariance-7.08
Correlation-0.98763566791978
Determination0.975424212547351
T-Test-12.6000723936144
p-value (2 sided)0.000228369952493694
p-value (1 sided)0.000114184976246847
Degrees of Freedom4
Number of Observations6


Figures (Output of Computation)

Input Parameters & R Code

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