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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 computationMon, 13 Dec 2010 19:34:47 +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/Dec/13/t1292268810b8kbvwpyb0ipo4a.htm/, Retrieved Mon, 06 May 2024 19:04:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109107, Retrieved Mon, 06 May 2024 19:04:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSciene DMA
Estimated Impact124

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Sciene Paper Cros...] [2010-12-13 19:34:47] [f92ba2b01007f169e2985fcc57236bd0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6,3
2,1
9,1
15,8
5,2
10,9
8,3
11
3,2
6,3
6,6
9,5
3,3
11
4,7
10,4
7,4
2,1
17,9
6,1
11,9
13,8
14,3
15,2
10
11,9
6,5
7,5
10,6
7,4
8,4
5,7
4,9
3,2
11
4,9
13,2
9,7
12,8
Dataseries Y:
Download CSV
Histogram 
2
1,8
0,7
3,9
1
3,6
1,4
1,5
0,7
2,1
4,1
1,2
0,5
3,4
1,5
3,4
0,8
0,8
2
1,9
1,3
5,6
3,1
1,8
0,9
1,8
1,9
0,9
2,6
2,4
1,2
0,9
0,5
0,6
2,3
0,5
2,6
0,6
6,6

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=109107&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=109107&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109107&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
Mean8.720512820512821.95897435897436
Biased Variance15.34368178829721.9249835634451
Biased Standard Deviation3.91710119709681.38743776921529
Covariance2.95507422402159
Correlation0.529796492773371
Determination0.280684323754965
T-Test3.79970760814504
p-value (2 sided)0.00052330051124172
p-value (1 sided)0.00026165025562086
Degrees of Freedom37
Number of Observations39

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 8.72051282051282 & 1.95897435897436 \tabularnewline
Biased Variance & 15.3436817882972 & 1.9249835634451 \tabularnewline
Biased Standard Deviation & 3.9171011970968 & 1.38743776921529 \tabularnewline
Covariance & 2.95507422402159 \tabularnewline
Correlation & 0.529796492773371 \tabularnewline
Determination & 0.280684323754965 \tabularnewline
T-Test & 3.79970760814504 \tabularnewline
p-value (2 sided) & 0.00052330051124172 \tabularnewline
p-value (1 sided) & 0.00026165025562086 \tabularnewline
Degrees of Freedom & 37 \tabularnewline
Number of Observations & 39 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109107&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]8.72051282051282[/C][C]1.95897435897436[/C][/ROW]
[ROW][C]Biased Variance[/C][C]15.3436817882972[/C][C]1.9249835634451[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.9171011970968[/C][C]1.38743776921529[/C][/ROW]
[ROW][C]Covariance[/C][C]2.95507422402159[/C][/ROW]
[ROW][C]Correlation[/C][C]0.529796492773371[/C][/ROW]
[ROW][C]Determination[/C][C]0.280684323754965[/C][/ROW]
[ROW][C]T-Test[/C][C]3.79970760814504[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00052330051124172[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00026165025562086[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]37[/C][/ROW]
[ROW][C]Number of Observations[/C][C]39[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109107&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109107&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
Mean8.720512820512821.95897435897436
Biased Variance15.34368178829721.9249835634451
Biased Standard Deviation3.91710119709681.38743776921529
Covariance2.95507422402159
Correlation0.529796492773371
Determination0.280684323754965
T-Test3.79970760814504
p-value (2 sided)0.00052330051124172
p-value (1 sided)0.00026165025562086
Degrees of Freedom37
Number of Observations39


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')