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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, 16 Dec 2014 11:50:25 +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/16/t1418730636zxf0vgu9r85xhbq.htm/, Retrieved Thu, 16 May 2024 21:44:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=269370, Retrieved Thu, 16 May 2024 21:44:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact55

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Pearson Correlation] [Screen dimensions] [2010-09-25 10:10:17] [b98453cac15ba1066b407e146608df68]
- RM D    [Pearson Correlation] [] [2014-12-16 11:50:25] [6c0da333d5967ad7c023c95d07a1face] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
58
51
57
30
46
51
56
58
44
14
53
42
49
44
62
30
46
50
54
48
55
35
55
41
59
54
55
45
51
47
42
53
53
41
55
55
46
63
43
65
59
39
44
60
57
67
52
52
69
46
46
53
40
70
54
77
45
60
47
50
66
60
41
53
34
51
69
60
45
58
39
51
52
49
63
44
51
52
60
53
53
52
31
51
65
51
49
61
58
62
54
52
72
50
65
53
56
63
62
66
50
45
58
52
53
68
59
58
52
45
58
70
69
71
46
58
39
46
64
67
44
54
41
68
63
57
61
39
69
64
38
59
51
59
51
65
47
50
57
21
47
51
37
67
43
58
51
40
41
58
64
64
58
50
59
55
59
58
41
56
63
77
60
58
64
46
62
60
50
46
44
58
56
43
54
54
56
65
66
62
58
67
25
56
53
56
59
46
49
56
76
33
49
53
58
72
51
42
69
51
54
52
59
51
67
64
58
53
Dataseries Y:
Download CSV
Histogram 
22
17
23
23
28
29
21
24
20
7
19
28
18
26
21
19
20
23
24
16
19
24
21
16
16
21
28
16
23
26
29
18
19
19
16
16
16
18
22
14
20
15
22
24
16
19
24
19
15
11
15
17
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21
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17
20
15
21
16
18
25
21
21
16
20
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28
27
22
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27
17
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15
22
13
21
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22
19
15
20
17
21
23
20
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22
24
24
18
27
19
20
15
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27
20
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13
21
23
26
24
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18
21
23
16
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20
25
22
20
25
27
20
18
26
26
24
27
16
15
25
27
18
16
18
23
21
21
14
24
18
16
25
22
13
20
17
23
22
23
22
23
10
18
25
26
14
23
22
23
19
14
26
24
21
17
16
15
11
19
21
20
16
19
16
11
22
20
26
26
20
24
20
15
23
25
27
23
20
25
24
22
27
20
17
22
26
19
19
24
22
16
22
23
19
20
16
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20
15
22
26

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 0 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269370&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269370&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269370&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 time0 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean53.576923076923120.4423076923077
Biased Variance100.74408284023716.6505177514793
Biased Standard Deviation10.03713519089174.0805045952038
Covariance0.274990709773318
Correlation0.00668192178113343
Determination4.46480786891854e-05
T-Test0.0959057604067634
p-value (2 sided)0.923688652546367
p-value (1 sided)0.461844326273183
Degrees of Freedom206
Number of Observations208

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 53.5769230769231 & 20.4423076923077 \tabularnewline
Biased Variance & 100.744082840237 & 16.6505177514793 \tabularnewline
Biased Standard Deviation & 10.0371351908917 & 4.0805045952038 \tabularnewline
Covariance & 0.274990709773318 \tabularnewline
Correlation & 0.00668192178113343 \tabularnewline
Determination & 4.46480786891854e-05 \tabularnewline
T-Test & 0.0959057604067634 \tabularnewline
p-value (2 sided) & 0.923688652546367 \tabularnewline
p-value (1 sided) & 0.461844326273183 \tabularnewline
Degrees of Freedom & 206 \tabularnewline
Number of Observations & 208 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269370&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]53.5769230769231[/C][C]20.4423076923077[/C][/ROW]
[ROW][C]Biased Variance[/C][C]100.744082840237[/C][C]16.6505177514793[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]10.0371351908917[/C][C]4.0805045952038[/C][/ROW]
[ROW][C]Covariance[/C][C]0.274990709773318[/C][/ROW]
[ROW][C]Correlation[/C][C]0.00668192178113343[/C][/ROW]
[ROW][C]Determination[/C][C]4.46480786891854e-05[/C][/ROW]
[ROW][C]T-Test[/C][C]0.0959057604067634[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.923688652546367[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.461844326273183[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]206[/C][/ROW]
[ROW][C]Number of Observations[/C][C]208[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269370&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269370&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
Mean53.576923076923120.4423076923077
Biased Variance100.74408284023716.6505177514793
Biased Standard Deviation10.03713519089174.0805045952038
Covariance0.274990709773318
Correlation0.00668192178113343
Determination4.46480786891854e-05
T-Test0.0959057604067634
p-value (2 sided)0.923688652546367
p-value (1 sided)0.461844326273183
Degrees of Freedom206
Number of Observations208


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')