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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, 28 Dec 2010 18:02:14 +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/28/t12935592576h156iqf9vff2nm.htm/, Retrieved Sat, 04 May 2024 23:53:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116446, Retrieved Sat, 04 May 2024 23:53:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2010-12-28 18:02:14] [0956ee981dded61b2e7128dae94e5715] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
20.1
21.64
20.95
19.46
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.39
19.94
20.69
20.69
21.64
20.86
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.7
20.67
20.67
20.67
20.67
23.42
30.02
42.03
32.52
29.13
28.57
28.88
27.49
23.75
23.09
23.24
23.52
22.99
23.75
23.05
21.66
20.84
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
20.67
24.44
34.94
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
39.26
41.51
36.41
41.25
58.6
97.81
159.74
161.49
125.32
148.31
193.55
307.5
612.56
459.64
375.91
424
360.66
317.66
368.24
447.95
438.31
382.58
384.93
363.29
344.97
360.91
385.42
385.5
389.09
332.39
295.24
279.91
280.1
272.22
311.33
364.8
410.52
446
606
699
768
950
Dataseries Y:
Download CSV
Histogram 
9.1
9.27
9.59
10.64
12.17
12.81
12.33
11.92
11.92
12.17
12.33
10.39
10.96
11.44
11.36
11.84
11.2
12.17
11.92
11.92
12.73
12.89
15.47
17
14.91
13.62
12.89
12.33
12.33
11.36
10.96
11.36
10.15
9.35
9.59
9.59
9.67
9.19
9.02
8.94
8.38
8.3
8.14
8.3
8.54
9.02
9.27
9.02
9.02
8.38
8.46
7.9
7.17
7.25
7.33
7.41
7.98
7.65
7.41
7.57
7.41
7.49
7.49
8.14
8.38
8.22
8.46
7.98
8.06
8.06
8.54
9.75
12.17
15.23
15.79
15.39
14.34
13.78
13.21
12.65
11.84
11.84
11.6
11.04
10.64
10.39
10.15
9.67
9.67
9.91
9.91
9.91
9.71
9.51
9.32
9.12
9.22
9.22
8.92
8.82
8.82
8.82
8.72
8.34
8.14
8.14
8.04
8.04
8.04
8.14
8.24
8.34
8.53
8.63
8.53
8.72
9.11
8.92
8.82
9.21
9.21
9.4
9.6
9.69
9.74
10.64
12.82
15.06
17.3
20.04
17.9
16.77
17.07
17.1
17.53
17.7
17.37
17.13
17.13
16.7
15.23
13.66
12.96
13.39
13.73
13.86
14.36
14.09
13.89
14.03
14.73
16.3
17.3
17.6
18
19.54
22.34
24.08
23.85
24.08
25.98
26.55
26.75
26.88
26.78
27.18
28.15
28.92
29.16
29.62
29.92
30.26
30.62
31.03
31.56
32.46
33.4
34.8
36.67
38.84
40.51
41.85
44.45
49.33
53.84
56.94
60.61
65.22
72.57
82.38
90.93
96.5
99.6
103.9
107.6
109.6
113.6
118.3
124
130.7
136.2
140.3
144.5
148.2
152.4
156.9
160.5
163
166.6
172.2
177.1
179.9
184
188.9
195.3
201.6
207.34
215.3
214.54

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116446&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116446&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116446&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'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean84.12789954337933.8365296803653
Biased Variance22657.40281841912430.70936603907
Biased Standard Deviation150.52376164054349.3022247575003
Covariance6863.22782432868
Correlation0.920596276748445
Determination0.8474975047631
T-Test34.7264673906534
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom217
Number of Observations219

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 84.127899543379 & 33.8365296803653 \tabularnewline
Biased Variance & 22657.4028184191 & 2430.70936603907 \tabularnewline
Biased Standard Deviation & 150.523761640543 & 49.3022247575003 \tabularnewline
Covariance & 6863.22782432868 \tabularnewline
Correlation & 0.920596276748445 \tabularnewline
Determination & 0.8474975047631 \tabularnewline
T-Test & 34.7264673906534 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 217 \tabularnewline
Number of Observations & 219 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116446&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]84.127899543379[/C][C]33.8365296803653[/C][/ROW]
[ROW][C]Biased Variance[/C][C]22657.4028184191[/C][C]2430.70936603907[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]150.523761640543[/C][C]49.3022247575003[/C][/ROW]
[ROW][C]Covariance[/C][C]6863.22782432868[/C][/ROW]
[ROW][C]Correlation[/C][C]0.920596276748445[/C][/ROW]
[ROW][C]Determination[/C][C]0.8474975047631[/C][/ROW]
[ROW][C]T-Test[/C][C]34.7264673906534[/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]217[/C][/ROW]
[ROW][C]Number of Observations[/C][C]219[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116446&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116446&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
Mean84.12789954337933.8365296803653
Biased Variance22657.40281841912430.70936603907
Biased Standard Deviation150.52376164054349.3022247575003
Covariance6863.22782432868
Correlation0.920596276748445
Determination0.8474975047631
T-Test34.7264673906534
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom217
Number of Observations219


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')