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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 computationWed, 17 Nov 2010 09:52:04 +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/17/t1289987417avulgj1t1i3fegz.htm/, Retrieved Wed, 24 Apr 2024 21:11:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=96569, Retrieved Wed, 24 Apr 2024 21:11:22 +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] [mini-tutorial cor...] [2010-11-12 09:39:22] [3074aa973ede76ac75d398946b01602f]
-    D  [Pearson Correlation] [] [2010-11-12 17:37:29] [b1e5ec7263cdefe98ec76e1a1363de05]
-    D    [Pearson Correlation] [] [2010-11-12 18:50:27] [b1e5ec7263cdefe98ec76e1a1363de05]
-             [Pearson Correlation] [mini turtorial : ...] [2010-11-17 09:52:04] [fea2623c21d84eea50328c29ea7301e7] [Current]
Feedback Forum

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12
8
8
8
9
7
4
11
7
7
12
10
10
8
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12
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5
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20
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11
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4
7
11
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8
5
4
8
10
6
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13
9
10
20
5
11
6
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9
10
9
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7
6
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16
Dataseries Y:
Download CSV
Histogram 
24
25
17
18
18
16
20
16
18
17
23
30
23
18
15
12
21
15
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31
27
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28
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31

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'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=96569&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=96569&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=96569&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'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean8.2264150943396221.5849056603774
Biased Variance7.2820695383885132.5446778212887
Biased Standard Deviation2.698530996373495.70479428387113
Covariance4.81609744447098
Correlation0.310876453554704
Determination0.0966441693747498
T-Test4.09834230525445
p-value (2 sided)6.65330421218968e-05
p-value (1 sided)3.32665210609484e-05
Degrees of Freedom157
Number of Observations159

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 8.22641509433962 & 21.5849056603774 \tabularnewline
Biased Variance & 7.28206953838851 & 32.5446778212887 \tabularnewline
Biased Standard Deviation & 2.69853099637349 & 5.70479428387113 \tabularnewline
Covariance & 4.81609744447098 \tabularnewline
Correlation & 0.310876453554704 \tabularnewline
Determination & 0.0966441693747498 \tabularnewline
T-Test & 4.09834230525445 \tabularnewline
p-value (2 sided) & 6.65330421218968e-05 \tabularnewline
p-value (1 sided) & 3.32665210609484e-05 \tabularnewline
Degrees of Freedom & 157 \tabularnewline
Number of Observations & 159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=96569&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]8.22641509433962[/C][C]21.5849056603774[/C][/ROW]
[ROW][C]Biased Variance[/C][C]7.28206953838851[/C][C]32.5446778212887[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.69853099637349[/C][C]5.70479428387113[/C][/ROW]
[ROW][C]Covariance[/C][C]4.81609744447098[/C][/ROW]
[ROW][C]Correlation[/C][C]0.310876453554704[/C][/ROW]
[ROW][C]Determination[/C][C]0.0966441693747498[/C][/ROW]
[ROW][C]T-Test[/C][C]4.09834230525445[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]6.65330421218968e-05[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]3.32665210609484e-05[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]157[/C][/ROW]
[ROW][C]Number of Observations[/C][C]159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=96569&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=96569&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
Mean8.2264150943396221.5849056603774
Biased Variance7.2820695383885132.5446778212887
Biased Standard Deviation2.698530996373495.70479428387113
Covariance4.81609744447098
Correlation0.310876453554704
Determination0.0966441693747498
T-Test4.09834230525445
p-value (2 sided)6.65330421218968e-05
p-value (1 sided)3.32665210609484e-05
Degrees of Freedom157
Number of Observations159


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')