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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, 28 Oct 2009 11:39:19 -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/2009/Oct/28/t1256751589qy0in1oh950y9h9.htm/, Retrieved Sun, 05 May 2024 22:14:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51640, Retrieved Sun, 05 May 2024 22:14:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
-   PD  [Bivariate Data Series] [] [2009-10-25 17:21:06] [badc6a9acdc45286bea7f74742e15a21]
-   PD    [Bivariate Data Series] [] [2009-10-25 17:43:31] [badc6a9acdc45286bea7f74742e15a21]
-   PD      [Bivariate Data Series] [] [2009-10-28 17:21:09] [badc6a9acdc45286bea7f74742e15a21]
-   PD        [Bivariate Data Series] [] [2009-10-28 17:33:36] [badc6a9acdc45286bea7f74742e15a21]
- RM D          [Bivariate Explorative Data Analysis] [] [2009-10-28 17:35:45] [badc6a9acdc45286bea7f74742e15a21]
- RM                [Pearson Correlation] [] [2009-10-28 17:39:19] [0545e25c765ce26b196961216dc11e13] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4.8841
5.0625
5.0625
6.0025
6.25
6.25
6.9696
7.5625
8.5849
9
10.0489
10.5625
11.4921
12.25
12.25
13.3225
14.0625
14.0625
15.21
16
16
16
16
16
16
16
16
16
16
16
16
17.4724
18.0625
18.0625
15.7609
11.6964
7.5625
5.3361
4
2.7556
1.7161
1.1881
1
1
1
1
Dataseries Y:
Download CSV
Histogram 
1.96
1.44
1
2.89
5.76
4
4.41
4
3.24
7.29
5.29
3.61
4
5.29
7.84
5.76
5.29
7.29
7.29
8.41
9
4.84
5.29
7.84
7.84
7.84
4.84
6.76
7.84
6.25
5.76
5.29
3.61
2.89
4
4.41
2.89
3.24
3.24
3.24
1.69
1.69
1.69
1.44
1.96
4.84
8.41
9.61
12.25
12.96
19.36
16.81
26.01
33.64
34.81
29.16
30.25
23.04
10.24
7.29
4.41
3.61
0.36
0.49
0.04
1
2.89
0.49
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'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=51640&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=51640&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51640&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
Mean8.268155072463777.31028985507246
Biased Variance30.180150339285960.8558260029406
Biased Standard Deviation5.493646360959717.80101442140319
Covariance24.6578274690963
Correlation0.567025840854714
Determination0.321518304196996
T-Test5.63470501191582
p-value (2 sided)3.78259029876205e-07
p-value (1 sided)1.89129514938102e-07
Degrees of Freedom67
Number of Observations69

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 8.26815507246377 & 7.31028985507246 \tabularnewline
Biased Variance & 30.1801503392859 & 60.8558260029406 \tabularnewline
Biased Standard Deviation & 5.49364636095971 & 7.80101442140319 \tabularnewline
Covariance & 24.6578274690963 \tabularnewline
Correlation & 0.567025840854714 \tabularnewline
Determination & 0.321518304196996 \tabularnewline
T-Test & 5.63470501191582 \tabularnewline
p-value (2 sided) & 3.78259029876205e-07 \tabularnewline
p-value (1 sided) & 1.89129514938102e-07 \tabularnewline
Degrees of Freedom & 67 \tabularnewline
Number of Observations & 69 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51640&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]8.26815507246377[/C][C]7.31028985507246[/C][/ROW]
[ROW][C]Biased Variance[/C][C]30.1801503392859[/C][C]60.8558260029406[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]5.49364636095971[/C][C]7.80101442140319[/C][/ROW]
[ROW][C]Covariance[/C][C]24.6578274690963[/C][/ROW]
[ROW][C]Correlation[/C][C]0.567025840854714[/C][/ROW]
[ROW][C]Determination[/C][C]0.321518304196996[/C][/ROW]
[ROW][C]T-Test[/C][C]5.63470501191582[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]3.78259029876205e-07[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.89129514938102e-07[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]67[/C][/ROW]
[ROW][C]Number of Observations[/C][C]69[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51640&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51640&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
Mean8.268155072463777.31028985507246
Biased Variance30.180150339285960.8558260029406
Biased Standard Deviation5.493646360959717.80101442140319
Covariance24.6578274690963
Correlation0.567025840854714
Determination0.321518304196996
T-Test5.63470501191582
p-value (2 sided)3.78259029876205e-07
p-value (1 sided)1.89129514938102e-07
Degrees of Freedom67
Number of Observations69


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')