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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 computationWed, 11 Nov 2009 09:38:33 -0700
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/Nov/11/t1257957565rgompqmcyin9voc.htm/, Retrieved Thu, 25 Apr 2024 17:37:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=55765, Retrieved Thu, 25 Apr 2024 17:37:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Icons vs. Inprod ...] [2009-11-11 16:38:33] [41dcf2419e4beff0486cef71832b5d35] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
23
19
18
19
19
22
23
20
14
14
14
15
11
17
16
20
24
23
20
21
19
23
23
23
23
27
26
17
24
26
24
27
27
26
24
23
23
24
17
21
19
22
22
18
16
14
12
14
16
8
3
0
5
1
1
3
6
7
8
14
Dataseries Y:
Download CSV
Histogram 
25,7
24,7
24,2
23,6
24,4
22,5
19,4
18,1
18,1
20,7
19,1
18,3
16,9
17,9
20,2
21,2
23,8
24
26,6
25,3
27,6
24,7
26,6
24,4
24,6
26
24,8
24
22,7
23
24,1
24
22,7
22,6
23,1
24,4
23
22
21,3
21,5
21,3
23,2
21,8
23,3
21
22,4
20,4
19,9
21,3
18,9
15,6
12,5
7,8
5,5
4
3,3
3,7
3,1
5
6,3

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=55765&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=55765&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=55765&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean17.466666666666719.8683333333333
Biased Variance51.615555555555642.6101638888889
Biased Standard Deviation7.184396673037736.52764612160378
Covariance38.925197740113
Correlation0.816177622465578
Determination0.666145911413564
T-Test10.7577223320174
p-value (2 sided)1.99840144432528e-15
p-value (1 sided)9.9920072216264e-16
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 17.4666666666667 & 19.8683333333333 \tabularnewline
Biased Variance & 51.6155555555556 & 42.6101638888889 \tabularnewline
Biased Standard Deviation & 7.18439667303773 & 6.52764612160378 \tabularnewline
Covariance & 38.925197740113 \tabularnewline
Correlation & 0.816177622465578 \tabularnewline
Determination & 0.666145911413564 \tabularnewline
T-Test & 10.7577223320174 \tabularnewline
p-value (2 sided) & 1.99840144432528e-15 \tabularnewline
p-value (1 sided) & 9.9920072216264e-16 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=55765&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]17.4666666666667[/C][C]19.8683333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]51.6155555555556[/C][C]42.6101638888889[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]7.18439667303773[/C][C]6.52764612160378[/C][/ROW]
[ROW][C]Covariance[/C][C]38.925197740113[/C][/ROW]
[ROW][C]Correlation[/C][C]0.816177622465578[/C][/ROW]
[ROW][C]Determination[/C][C]0.666145911413564[/C][/ROW]
[ROW][C]T-Test[/C][C]10.7577223320174[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.99840144432528e-15[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]9.9920072216264e-16[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=55765&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=55765&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
Mean17.466666666666719.8683333333333
Biased Variance51.615555555555642.6101638888889
Biased Standard Deviation7.184396673037736.52764612160378
Covariance38.925197740113
Correlation0.816177622465578
Determination0.666145911413564
T-Test10.7577223320174
p-value (2 sided)1.99840144432528e-15
p-value (1 sided)9.9920072216264e-16
Degrees of Freedom58
Number of Observations60


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')