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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, 19 Oct 2008 14:46:02 -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/Oct/19/t1224449248yvdkyzym448hzix.htm/, Retrieved Sun, 19 May 2024 14:12:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17103, Retrieved Sun, 19 May 2024 14:12:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Het aantal werklo...] [2008-10-10 14:34:09] [5e74953d94072114d25d7276793b561e]
-   PD  [Univariate Data Series] [(verbeterde reeks...] [2008-10-14 19:02:31] [5e74953d94072114d25d7276793b561e]
- RMPD      [Pearson Correlation] [correlatie tussen...] [2008-10-19 20:46:02] [5925747fb2a6bb4cfcd8015825ee5e92] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
28
30
32
31
32
34
32
35
29
33
33
34
32
27
26
22
22
23
23
19
15
5
1
11
18
20
21
19
20
19
18
16
16
16
15
11
10
6
1
8
10
9
6
8
14
4
13
13
16
18
16
15
13
19
15
17
17
13
12
13
13
16
17
14
8
8
8
9
5
11
10
14
18
17
14
15
13
17
17
17
17
21
20
11
18
20
18
21
21
20
18
17
17
18
11
15
13
16
16
12
10
8
6
8
Dataseries Y:
Download CSV
Histogram 
7.5
7.2
6.9
6.7
6.4
6.3
6.8
7.3
7.1
7.1
6.8
6.5
6.3
6.1
6.1
6.3
6.3
6
6.2
6.4
6.8
7.5
7.5
7.6
7.6
7.4
7.3
7.1
6.9
6.8
7.5
7.6
7.8
8
8.1
8.2
8.3
8.2
8
7.9
7.6
7.6
8.2
8.3
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.5
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.6
8.2
8.1
8
8.6
8.7
8.8
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.1
8.2
8.1
8.1
7.9
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.6
6.2
6.2
6.8
6.9

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=17103&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=17103&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17103&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
Mean16.70192307692317.64326923076923
Biased Variance57.88230399408280.66014700443787
Biased Standard Deviation7.608042060483290.812494310403384
Covariance-2.91610343539955
Correlation-0.467211556544129
Determination0.218286638568388
T-Test-5.33691019413565
p-value (2 sided)5.73617122230499e-07
p-value (1 sided)2.86808561115250e-07
Degrees of Freedom102
Number of Observations104

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 16.7019230769231 & 7.64326923076923 \tabularnewline
Biased Variance & 57.8823039940828 & 0.66014700443787 \tabularnewline
Biased Standard Deviation & 7.60804206048329 & 0.812494310403384 \tabularnewline
Covariance & -2.91610343539955 \tabularnewline
Correlation & -0.467211556544129 \tabularnewline
Determination & 0.218286638568388 \tabularnewline
T-Test & -5.33691019413565 \tabularnewline
p-value (2 sided) & 5.73617122230499e-07 \tabularnewline
p-value (1 sided) & 2.86808561115250e-07 \tabularnewline
Degrees of Freedom & 102 \tabularnewline
Number of Observations & 104 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17103&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]16.7019230769231[/C][C]7.64326923076923[/C][/ROW]
[ROW][C]Biased Variance[/C][C]57.8823039940828[/C][C]0.66014700443787[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]7.60804206048329[/C][C]0.812494310403384[/C][/ROW]
[ROW][C]Covariance[/C][C]-2.91610343539955[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.467211556544129[/C][/ROW]
[ROW][C]Determination[/C][C]0.218286638568388[/C][/ROW]
[ROW][C]T-Test[/C][C]-5.33691019413565[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]5.73617122230499e-07[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.86808561115250e-07[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]102[/C][/ROW]
[ROW][C]Number of Observations[/C][C]104[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17103&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17103&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
Mean16.70192307692317.64326923076923
Biased Variance57.88230399408280.66014700443787
Biased Standard Deviation7.608042060483290.812494310403384
Covariance-2.91610343539955
Correlation-0.467211556544129
Determination0.218286638568388
T-Test-5.33691019413565
p-value (2 sided)5.73617122230499e-07
p-value (1 sided)2.86808561115250e-07
Degrees of Freedom102
Number of Observations104


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')