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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 computationTue, 27 Oct 2009 05:43:22 -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/27/t1256643839jb7n5v4fuud2fhr.htm/, Retrieved Tue, 07 May 2024 21:38:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50898, Retrieved Tue, 07 May 2024 21:38:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSHW WS 4 - Deel 2 - Vraag 3
Estimated Impact131

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]
- RMPD  [Bivariate Explorative Data Analysis] [WS 4 - Deel 2 - V...] [2009-10-26 08:33:16] [b103a1dc147def8132c7f643ad8c8f84]
- RM D      [Pearson Correlation] [WS 4 - Deel 2 - V...] [2009-10-27 11:43:22] [a45cc820faa25ce30779915639528ec2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.740840024
2.714694744
2.459588842
2.791165108
2.815408719
2.708050201
2.701361213
2.681021529
2.727852828
2.884800713
2.797281335
2.734367509
2.884800713
2.766319109
2.63188884
2.879198457
2.884800713
2.856470206
2.815408719
2.772588722
2.809402695
2.949688335
2.879198457
2.844909384
2.923161581
2.791165108
2.714694744
2.954910279
2.87356464
2.949688335
2.890371758
2.862200881
2.879198457
3.04927304
2.844909384
2.965273066
2.985681938
2.867898902
2.785011242
2.970414466
2.990719732
2.995732274
2.850706502
2.939161922
2.923161581
3.063390922
2.923161581
2.985681938
3.034952987
2.975529566
2.87356464
2.985681938
3.100092289
3.0301337
2.884800713
3.039749159
3.054001182
3.063390922
3.135494216
3.058707073
3.173878459
3.109060959
2.90690106
3.126760536
3.104586678
2.879198457
2.797281335
2.772588722
2.797281335
2.87356464
2.809402695
2.785011242
2.90690106
Dataseries Y:
Download CSV
Histogram 
14.2
13.5
11.9
14.6
15.6
14.1
14.9
14.2
14.6
17.2
15.4
14.3
17.5
14.5
14.4
16.6
16.7
16.6
16.9
15.7
16.4
18.4
16.9
16.5
18.3
15.1
15.7
18.1
16.8
18.9
19
18.1
17.8
21.5
17.1
18.7
19
16.4
16.9
18.6
19.3
19.4
17.6
18.6
18.1
20.4
18.1
19.6
19.9
19.2
17.8
19.2
22
21.1
19.5
22.2
20.9
22.2
23.5
21.5
24.3
22.8
20.3
23.7
23.3
19.6
18
17.3
16.8
18.2
16.5
16
18.4

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=50898&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=50898&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50898&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
Mean2.8902569445342517.9849315068493
Biased Variance0.01735718412780877.03114280352787
Biased Standard Deviation0.1317466664770262.65163021621188
Covariance0.333515745462329
Correlation0.941615033632456
Determination0.88663887156265
T-Test23.5651646168721
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom71
Number of Observations73

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2.89025694453425 & 17.9849315068493 \tabularnewline
Biased Variance & 0.0173571841278087 & 7.03114280352787 \tabularnewline
Biased Standard Deviation & 0.131746666477026 & 2.65163021621188 \tabularnewline
Covariance & 0.333515745462329 \tabularnewline
Correlation & 0.941615033632456 \tabularnewline
Determination & 0.88663887156265 \tabularnewline
T-Test & 23.5651646168721 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 71 \tabularnewline
Number of Observations & 73 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50898&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]2.89025694453425[/C][C]17.9849315068493[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.0173571841278087[/C][C]7.03114280352787[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.131746666477026[/C][C]2.65163021621188[/C][/ROW]
[ROW][C]Covariance[/C][C]0.333515745462329[/C][/ROW]
[ROW][C]Correlation[/C][C]0.941615033632456[/C][/ROW]
[ROW][C]Determination[/C][C]0.88663887156265[/C][/ROW]
[ROW][C]T-Test[/C][C]23.5651646168721[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]71[/C][/ROW]
[ROW][C]Number of Observations[/C][C]73[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50898&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50898&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
Mean2.8902569445342517.9849315068493
Biased Variance0.01735718412780877.03114280352787
Biased Standard Deviation0.1317466664770262.65163021621188
Covariance0.333515745462329
Correlation0.941615033632456
Determination0.88663887156265
T-Test23.5651646168721
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom71
Number of Observations73


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0 ; par2 = 36 ;
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')