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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 computationSun, 07 Dec 2008 08:01:28 -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/2008/Dec/07/t1228662319byosfu8uxxfx220.htm/, Retrieved Wed, 22 May 2024 15:03:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30046, Retrieved Wed, 22 May 2024 15:03:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Back to Back Histogram] [Btb histogram bou...] [2008-12-05 15:29:56] [aa5573c1db401b164e448aef050955a1]
- RMPD  [Pearson Correlation] [Pearson Correlati...] [2008-12-07 14:51:11] [aa5573c1db401b164e448aef050955a1]
-    D      [Pearson Correlation] [Pearson Correlati...] [2008-12-07 15:01:28] [8a1195ff8db4df756ce44b463a631c76] [Current]
-    D        [Pearson Correlation] [Pearson Correlati...] [2008-12-07 15:09:27] [aa5573c1db401b164e448aef050955a1]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
82.7
88.9
105.9
100.8
94
105
58.5
87.6
113.1
112.5
89.6
74.5
82.7
90.1
109.4
96
89.2
109.1
49.1
92.9
107.7
103.5
91.1
79.8
71.9
82.9
90.1
100.7
90.7
108.8
44.1
93.6
107.4
96.5
93.6
76.5
76.7
84
103.3
88.5
99
105.9
44.7
94
107.1
104.8
102.5
77.7
85.2
91.3
106.5
92.4
97.5
107
51.1
98.6
102.2
114.3
99.4
72.5
92.3
99.4
85.9
109.4
97.6
Dataseries Y:
Download CSV
Histogram 
89.3
87.5
106.7
102.5
109.2
123.7
83.1
97
119.1
125.1
113.6
122.4
92.8
97.2
115.6
111.3
114.6
137.5
83.7
106
123.4
126.5
120
141.6
90.5
96.5
113.5
120.1
123.9
144.4
90.8
114.2
138.1
135
131.3
144.6
101.7
108.7
135.3
124.3
138.3
158.2
93.5
124.8
154.4
152.8
148.9
170.3
124.8
134.4
154
147.9
168.1
175.7
116.7
140.8
164.2
173.8
167.8
166.6
135.1
158.1
151.8
168.7
166.9

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'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30046&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30046&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30046&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean91.7123076923077127.983076923077
Biased Variance259.981694674556643.928790532544
Biased Standard Deviation16.123947862560125.3757520190544
Covariance206.733649038462
Correlation0.49749358034927
Determination0.247499862488736
T-Test4.55202316925818
p-value (2 sided)2.48489615863878e-05
p-value (1 sided)1.24244807931939e-05
Degrees of Freedom63
Number of Observations65

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 91.7123076923077 & 127.983076923077 \tabularnewline
Biased Variance & 259.981694674556 & 643.928790532544 \tabularnewline
Biased Standard Deviation & 16.1239478625601 & 25.3757520190544 \tabularnewline
Covariance & 206.733649038462 \tabularnewline
Correlation & 0.49749358034927 \tabularnewline
Determination & 0.247499862488736 \tabularnewline
T-Test & 4.55202316925818 \tabularnewline
p-value (2 sided) & 2.48489615863878e-05 \tabularnewline
p-value (1 sided) & 1.24244807931939e-05 \tabularnewline
Degrees of Freedom & 63 \tabularnewline
Number of Observations & 65 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30046&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]91.7123076923077[/C][C]127.983076923077[/C][/ROW]
[ROW][C]Biased Variance[/C][C]259.981694674556[/C][C]643.928790532544[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]16.1239478625601[/C][C]25.3757520190544[/C][/ROW]
[ROW][C]Covariance[/C][C]206.733649038462[/C][/ROW]
[ROW][C]Correlation[/C][C]0.49749358034927[/C][/ROW]
[ROW][C]Determination[/C][C]0.247499862488736[/C][/ROW]
[ROW][C]T-Test[/C][C]4.55202316925818[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.48489615863878e-05[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.24244807931939e-05[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]63[/C][/ROW]
[ROW][C]Number of Observations[/C][C]65[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30046&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30046&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
Mean91.7123076923077127.983076923077
Biased Variance259.981694674556643.928790532544
Biased Standard Deviation16.123947862560125.3757520190544
Covariance206.733649038462
Correlation0.49749358034927
Determination0.247499862488736
T-Test4.55202316925818
p-value (2 sided)2.48489615863878e-05
p-value (1 sided)1.24244807931939e-05
Degrees of Freedom63
Number of Observations65


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')