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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, 05 Dec 2012 10:45:45 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/05/t1354722365c6b6vzc0k057sxe.htm/, Retrieved Fri, 01 Nov 2024 00:05:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=196885, Retrieved Fri, 01 Nov 2024 00:05:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Connected vs Sepa...] [2010-10-04 07:35:56] [b98453cac15ba1066b407e146608df68]
- R     [Pearson Correlation] [Task 7] [2011-10-09 17:47:31] [80bca13c5f9401fbb753952fd2952f4a]
-           [Pearson Correlation] [Pearson correlation] [2012-12-05 15:45:45] [b50c5a50b586467676e2aa32fc920ea8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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32
40
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37
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37
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36
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30
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40
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28
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Dataseries Y:
Download CSV
Histogram 
30
28
31
35
35
37
39
31
38
37
37
35
37
42
28
37
36
37
33
40
30
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32
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27
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36
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32
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39
31
33
46
38
24
28
35
39
37
38
38
32
36
28
38
28
37
28
40
34
33
32
30
33
37
39
42
36
35
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36
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32
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37
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42
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39
37
36
31
32
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21
32
36
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28
42
36
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30
18
37
28
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44
26
34
37
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29
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Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196885&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196885&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196885&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean36.248484848484835.0454545454545
Biased Variance19.962497704315920.3039944903581
Biased Standard Deviation4.467941103496764.5059953939566
Covariance10.6208897485493
Correlation0.52595026181494
Determination0.276623677903204
T-Test11.1995211160927
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom328
Number of Observations330

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 36.2484848484848 & 35.0454545454545 \tabularnewline
Biased Variance & 19.9624977043159 & 20.3039944903581 \tabularnewline
Biased Standard Deviation & 4.46794110349676 & 4.5059953939566 \tabularnewline
Covariance & 10.6208897485493 \tabularnewline
Correlation & 0.52595026181494 \tabularnewline
Determination & 0.276623677903204 \tabularnewline
T-Test & 11.1995211160927 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 328 \tabularnewline
Number of Observations & 330 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196885&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]36.2484848484848[/C][C]35.0454545454545[/C][/ROW]
[ROW][C]Biased Variance[/C][C]19.9624977043159[/C][C]20.3039944903581[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.46794110349676[/C][C]4.5059953939566[/C][/ROW]
[ROW][C]Covariance[/C][C]10.6208897485493[/C][/ROW]
[ROW][C]Correlation[/C][C]0.52595026181494[/C][/ROW]
[ROW][C]Determination[/C][C]0.276623677903204[/C][/ROW]
[ROW][C]T-Test[/C][C]11.1995211160927[/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]328[/C][/ROW]
[ROW][C]Number of Observations[/C][C]330[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196885&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196885&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
Mean36.248484848484835.0454545454545
Biased Variance19.962497704315920.3039944903581
Biased Standard Deviation4.467941103496764.5059953939566
Covariance10.6208897485493
Correlation0.52595026181494
Determination0.276623677903204
T-Test11.1995211160927
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom328
Number of Observations330


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')