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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, 17 Dec 2014 23:42:33 +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/2014/Dec/17/t141885978765n465c6yg1qbng.htm/, Retrieved Sun, 19 May 2024 19:17:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270739, Retrieved Sun, 19 May 2024 19:17:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact48

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]
- RM    [Pearson Correlation] [WS 2 task 7] [2014-10-08 20:21:39] [5efa6717cfe6505454df834acc87b53b]
-    D      [Pearson Correlation] [] [2014-12-17 23:42:33] [4621f922aed0297f88122271e88ec2ef] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
86
70
71
108
64
119
97
129
153
78
80
99
68
147
40
57
120
71
84
68
137
79
101
111
189
66
81
63
69
71
64
143
85
86
55
69
120
96
60
95
100
68
57
105
85
103
57
51
69
41
49
50
93
58
54
74
15
69
107
65
58
107
70
53
136
126
95
69
136
58
118
82
50
102
65
90
64
83
70
50
77
37
81
101
79
71
60
55
44
40
56
43
45
32
56
40
34
89
50
56
76
64
74
57
30
62
51
36
Dataseries Y:
Download CSV
Histogram 
18
31
39
46
31
67
35
52
77
37
32
36
38
69
21
26
54
36
42
23
112
35
47
37
109
24
20
22
23
32
30
92
43
55
16
49
71
43
29
56
46
19
23
59
30
61
7
38
32
16
19
22
48
23
26
33
9
24
34
48
18
43
33
28
71
26
67
34
80
29
59
32
47
43
38
29
36
32
35
21
29
12
37
37
47
51
32
21
13
14
-2
20
24
11
23
24
14
52
15
23
35
24
39
29
8
18
24
19

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270739&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270739&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270739&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean76.824074074074135.7962962962963
Biased Variance897.644975994513388.847393689986
Biased Standard Deviation29.960723889694519.7192138202816
Covariance501.001211491866
Correlation0.840150131686561
Determination0.705852243772946
T-Test15.9487651310743
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom106
Number of Observations108

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 76.8240740740741 & 35.7962962962963 \tabularnewline
Biased Variance & 897.644975994513 & 388.847393689986 \tabularnewline
Biased Standard Deviation & 29.9607238896945 & 19.7192138202816 \tabularnewline
Covariance & 501.001211491866 \tabularnewline
Correlation & 0.840150131686561 \tabularnewline
Determination & 0.705852243772946 \tabularnewline
T-Test & 15.9487651310743 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 106 \tabularnewline
Number of Observations & 108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270739&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]76.8240740740741[/C][C]35.7962962962963[/C][/ROW]
[ROW][C]Biased Variance[/C][C]897.644975994513[/C][C]388.847393689986[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]29.9607238896945[/C][C]19.7192138202816[/C][/ROW]
[ROW][C]Covariance[/C][C]501.001211491866[/C][/ROW]
[ROW][C]Correlation[/C][C]0.840150131686561[/C][/ROW]
[ROW][C]Determination[/C][C]0.705852243772946[/C][/ROW]
[ROW][C]T-Test[/C][C]15.9487651310743[/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]106[/C][/ROW]
[ROW][C]Number of Observations[/C][C]108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270739&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270739&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
Mean76.824074074074135.7962962962963
Biased Variance897.644975994513388.847393689986
Biased Standard Deviation29.960723889694519.7192138202816
Covariance501.001211491866
Correlation0.840150131686561
Determination0.705852243772946
T-Test15.9487651310743
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom106
Number of Observations108


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')