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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 computationFri, 17 Dec 2010 11:37:48 +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/17/t1292585759wsem7xjjy1lh0fb.htm/, Retrieved Tue, 07 May 2024 01:34:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111395, Retrieved Tue, 07 May 2024 01:34:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Pearson Correlation] [Screen dimensions] [2010-09-25 10:10:17] [b98453cac15ba1066b407e146608df68]
F   PD  [Pearson Correlation] [Workshop 1; Task ...] [2010-10-04 20:13:29] [8ffb4cfa64b4677df0d2c448735a40bb]
-   PD    [Pearson Correlation] [Paper; Scatterplo...] [2010-12-16 14:53:33] [8ffb4cfa64b4677df0d2c448735a40bb]
-    D      [Pearson Correlation] [Paper; Scatterplo...] [2010-12-16 15:18:23] [8ffb4cfa64b4677df0d2c448735a40bb]
-    D          [Pearson Correlation] [Paper; Scatterplo...] [2010-12-17 11:37:48] [50e0b5177c9c80b42996aa89930b928a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15.38
15.03
15.21
15.20
14.60
13.79
14.54
14.31
13.93
14.82
14.46
14.85
14.95
14.43
14.84
14.39
15.70
15.34
13.98
14.75
14.81
14.67
15.03
14.34
12.54
11.37
12.58
13.06
12.50
11.11
12.39
12.34
11.54
10.22
8.50
9.06
9.28
7.24
7.58
7.81
8.54
9.27
10.11
9.21
10.71
10.85
11.77
11.81
Dataseries Y:
Download CSV
Histogram 
31.27
35.83
37.12
36.77
35.17
37.25
33.77
30.59
33.59
37.24
34.81
34.94
34.47
30.48
30.94
30.60
28.42
25.89
26.32
27.18
25.85
26.32
23.07
20.19
18.65
17.74
17.26
16.01
17.94
15.53
14.49
15.35
14.67
12.95
8.81
9.33
9.31
9.03
10.96
14.26
14.20
13.70
17.46
18.73
20.37
18.72
21.60
22.75

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111395&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]3 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=111395&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111395&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean12.5987523.2895833333333
Biased Variance6.1390901041666780.9309498263889
Biased Standard Deviation2.477718729833288.99616306134948
Covariance19.2573909574468
Correlation0.84595009873331
Determination0.715631569546896
T-Test10.7592740803221
p-value (2 sided)3.77475828372553e-14
p-value (1 sided)1.88737914186277e-14
Degrees of Freedom46
Number of Observations48

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 12.59875 & 23.2895833333333 \tabularnewline
Biased Variance & 6.13909010416667 & 80.9309498263889 \tabularnewline
Biased Standard Deviation & 2.47771872983328 & 8.99616306134948 \tabularnewline
Covariance & 19.2573909574468 \tabularnewline
Correlation & 0.84595009873331 \tabularnewline
Determination & 0.715631569546896 \tabularnewline
T-Test & 10.7592740803221 \tabularnewline
p-value (2 sided) & 3.77475828372553e-14 \tabularnewline
p-value (1 sided) & 1.88737914186277e-14 \tabularnewline
Degrees of Freedom & 46 \tabularnewline
Number of Observations & 48 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111395&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]12.59875[/C][C]23.2895833333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]6.13909010416667[/C][C]80.9309498263889[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.47771872983328[/C][C]8.99616306134948[/C][/ROW]
[ROW][C]Covariance[/C][C]19.2573909574468[/C][/ROW]
[ROW][C]Correlation[/C][C]0.84595009873331[/C][/ROW]
[ROW][C]Determination[/C][C]0.715631569546896[/C][/ROW]
[ROW][C]T-Test[/C][C]10.7592740803221[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]3.77475828372553e-14[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.88737914186277e-14[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]46[/C][/ROW]
[ROW][C]Number of Observations[/C][C]48[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111395&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111395&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
Mean12.5987523.2895833333333
Biased Variance6.1390901041666780.9309498263889
Biased Standard Deviation2.477718729833288.99616306134948
Covariance19.2573909574468
Correlation0.84595009873331
Determination0.715631569546896
T-Test10.7592740803221
p-value (2 sided)3.77475828372553e-14
p-value (1 sided)1.88737914186277e-14
Degrees of Freedom46
Number of Observations48


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')