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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 computationSat, 18 Apr 2009 19:08:29 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Apr/19/t1240103529yjuy5aneet17fa3.htm/, Retrieved Sat, 11 May 2024 18:55:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39243, Retrieved Sat, 11 May 2024 18:55:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact291

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [test3bb] [2009-04-19 01:08:29] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
66
50
86
86
61
80
80
80
70
64
79
84
80
65
75
60
40
73
59
95
84
62
35
98
40
84
59
70
66
41
54
53
75
73
79
80
50
50
80
96
72
77
90
60
65
92
55
70
38
59
70
70
80
70
79
50
73
55
66
66
63
70
80
79
68
50
37
84
77
63
48
61
41
70
80
50
91
88
75
63
84
64
68
72
70
79
66
63
77
64
84
59
93
45
78
94
54
59
55
70
61
69
37
84
55
37
39
64
80
61
77
82
91
64
80
48
59
50
99
Dataseries Y:
Download CSV
Histogram 
50
33
13
84
46
85
28
81
63
27
84
83
6
7
62
10
50
60
28
28
2
73
71
80
82
27
5
25
54
30
10
24
55
50
77
27
22
74
63
65
33
76
97
76
42
90
28
43
21
96
87
53
81
78
43
15
83
80
79
44
92
45
81
69
23
48
8
86
61
72
87
46
75
31
83
55
79
81
79
77
71
77
90
7
54
83
43
105
61
50
45
34
118
11
20
78
7
95
39
32
74
99
93
97
16
53
38
40
71
84
94
7
83
17
88
6
27
6
48

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39243&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39243&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39243&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'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean6854.8571428571429
Biased Variance230.504201680672841.78631452581
Biased Standard Deviation15.18236482504229.0135539795767
Covariance124.796610169492
Correlation0.280929587315165
Determination0.0789214330290689
T-Test3.16622718779208
p-value (2 sided)0.00196941277557117
p-value (1 sided)0.000984706387785583
Degrees of Freedom117
Number of Observations119

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 68 & 54.8571428571429 \tabularnewline
Biased Variance & 230.504201680672 & 841.78631452581 \tabularnewline
Biased Standard Deviation & 15.182364825042 & 29.0135539795767 \tabularnewline
Covariance & 124.796610169492 \tabularnewline
Correlation & 0.280929587315165 \tabularnewline
Determination & 0.0789214330290689 \tabularnewline
T-Test & 3.16622718779208 \tabularnewline
p-value (2 sided) & 0.00196941277557117 \tabularnewline
p-value (1 sided) & 0.000984706387785583 \tabularnewline
Degrees of Freedom & 117 \tabularnewline
Number of Observations & 119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39243&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]68[/C][C]54.8571428571429[/C][/ROW]
[ROW][C]Biased Variance[/C][C]230.504201680672[/C][C]841.78631452581[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]15.182364825042[/C][C]29.0135539795767[/C][/ROW]
[ROW][C]Covariance[/C][C]124.796610169492[/C][/ROW]
[ROW][C]Correlation[/C][C]0.280929587315165[/C][/ROW]
[ROW][C]Determination[/C][C]0.0789214330290689[/C][/ROW]
[ROW][C]T-Test[/C][C]3.16622718779208[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00196941277557117[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000984706387785583[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]117[/C][/ROW]
[ROW][C]Number of Observations[/C][C]119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39243&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39243&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
Mean6854.8571428571429
Biased Variance230.504201680672841.78631452581
Biased Standard Deviation15.18236482504229.0135539795767
Covariance124.796610169492
Correlation0.280929587315165
Determination0.0789214330290689
T-Test3.16622718779208
p-value (2 sided)0.00196941277557117
p-value (1 sided)0.000984706387785583
Degrees of Freedom117
Number of Observations119


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')