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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 computationSun, 28 Nov 2010 16:38:06 +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/Nov/28/t1290962205tvtz5nb7f0tcnjl.htm/, Retrieved Thu, 02 May 2024 23:03:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102644, Retrieved Thu, 02 May 2024 23:03:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131

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] [Screen dimensions] [2010-09-25 10:10:17] [b98453cac15ba1066b407e146608df68]
-    D    [Pearson Correlation] [Scatterplot: Popu...] [2010-11-28 16:38:06] [bff44ea937c3f909b1dc9a8bfab919e2] [Current]
-    D      [Pearson Correlation] [Scatterplot: Popu...] [2010-11-28 16:43:40] [26379b86c25fbf0febe6a7a428e65173]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Dataseries Y:
Download CSV
Histogram 
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8
12
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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 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=102644&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=102644&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102644&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
Mean12.044871794871811.6025641025641
Biased Variance8.568499342537811.9061472715319
Biased Standard Deviation2.927199915027643.45052854958945
Covariance5.93407775020678
Correlation0.583743856743056
Determination0.340756890285258
T-Test8.92195203027262
p-value (2 sided)1.33226762955019e-15
p-value (1 sided)6.66133814775094e-16
Degrees of Freedom154
Number of Observations156

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 12.0448717948718 & 11.6025641025641 \tabularnewline
Biased Variance & 8.5684993425378 & 11.9061472715319 \tabularnewline
Biased Standard Deviation & 2.92719991502764 & 3.45052854958945 \tabularnewline
Covariance & 5.93407775020678 \tabularnewline
Correlation & 0.583743856743056 \tabularnewline
Determination & 0.340756890285258 \tabularnewline
T-Test & 8.92195203027262 \tabularnewline
p-value (2 sided) & 1.33226762955019e-15 \tabularnewline
p-value (1 sided) & 6.66133814775094e-16 \tabularnewline
Degrees of Freedom & 154 \tabularnewline
Number of Observations & 156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102644&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]12.0448717948718[/C][C]11.6025641025641[/C][/ROW]
[ROW][C]Biased Variance[/C][C]8.5684993425378[/C][C]11.9061472715319[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.92719991502764[/C][C]3.45052854958945[/C][/ROW]
[ROW][C]Covariance[/C][C]5.93407775020678[/C][/ROW]
[ROW][C]Correlation[/C][C]0.583743856743056[/C][/ROW]
[ROW][C]Determination[/C][C]0.340756890285258[/C][/ROW]
[ROW][C]T-Test[/C][C]8.92195203027262[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.33226762955019e-15[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]6.66133814775094e-16[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]154[/C][/ROW]
[ROW][C]Number of Observations[/C][C]156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102644&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102644&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
Mean12.044871794871811.6025641025641
Biased Variance8.568499342537811.9061472715319
Biased Standard Deviation2.927199915027643.45052854958945
Covariance5.93407775020678
Correlation0.583743856743056
Determination0.340756890285258
T-Test8.92195203027262
p-value (2 sided)1.33226762955019e-15
p-value (1 sided)6.66133814775094e-16
Degrees of Freedom154
Number of Observations156


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')