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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 computationThu, 22 Dec 2011 10:46:32 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/22/t1324568805apr1085tpdmr1h9.htm/, Retrieved Sat, 18 May 2024 22:01:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159633, Retrieved Sat, 18 May 2024 22:01:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64

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]
- R  D    [Pearson Correlation] [] [2011-12-22 15:46:32] [86c924663d3d275e16f9cde57b3a6185] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14,69
20,15
11,78
21,47
17,54
21,47
18,55
14,33
8,78
17,66
19,64
13,25
16,17
9,66
20,45
24,21
19,65
21,33
14,47
16,22
16,66
19,87
14,55
19,41
20,63
9,12
8,36
19,36
25,78
14,66
27,55
22,63
30,33
22,22
11,99
9,47
10,33
15,36
14,99
17,31
18,94
16,54
18,21
11,74
17,41
9,99
21,14
19,7
14,87
19,65
27,65
13,45
20
13,47
18,54
20
11,47
28,65
24,14
19,87
17,65
13,69
15,47
11,63
10,24
13,54
11
19,74
21,25
29,54
11,41
10,87
8,47
12,69
10,14
18,63
22,54
17,65
16,41
17,65
19,87
21,45
22,65
20,69
23,74
20,96
18,35
17,84
20,54
21,63
27,61
19,47
23,52
25,64
19,33
20,64
18,98
15,67
23,74
22,89
24,66
29,4
19,87
17,55
15,94
21,74
23,51
24,84
18,47
21,01
16,74
27,45
19,54
17,74
21,65
24,74
26,89
23,22
20,16
21,88
Dataseries Y:
Download CSV
Histogram 
27
33,56
47,24
71,23
59,14
40,99
17,54
28,45
39,09
24,69
21,47
39,81
35,66
31,21
30,63
26,11
29,63
44,55
43,9
33,47
55,1
48,13
33,25
25,33
26,98
88,74
36,54
11,78
29,11
32,47
55,17
42,33
22,87
41,36
27,69
20,47
60,03
50,14
30,63
36,99
27,55
18,55
14,33
8,78
40,55
22,63
45,77
41,36
39,44
41,66
66,47
69,48
17,66
19,64
44,47
50,17
21,63
36,12
23,69
54,12
45,16
69,41
41,96
13,25
16,17
9,66
20,45
24,21
33,64
25,44
60,74
71,33
55,21
66,23
19,65
21,33
14,47
16,22
23,56
66,87
54,22
43,98
71,33
55,21
66,23
19,65
21,33
16,66
19,87
14,55
19,41
20,63
60,03
50,14
30,63
36,99
27,55
18,55
14,33
66,47
69,48
17,66
19,64
44,47
50,17
21,63
36,12
23,69
33,25
25,33
26,98
88,74
36,54
11,78
18,55
14,33
8,78
40,55
22,63
45,77

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=159633&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=159633&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159633&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
Mean18.582535.8613333333333
Biased Variance25.6763504166667323.333414888889
Biased Standard Deviation5.0671836770208617.9814742134478
Covariance-1.44998151260504
Correlation-0.0157810624604106
Determination0.000249041932379382
T-Test-0.171447567571479
p-value (2 sided)0.864165520835509
p-value (1 sided)0.432082760417754
Degrees of Freedom118
Number of Observations120

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 18.5825 & 35.8613333333333 \tabularnewline
Biased Variance & 25.6763504166667 & 323.333414888889 \tabularnewline
Biased Standard Deviation & 5.06718367702086 & 17.9814742134478 \tabularnewline
Covariance & -1.44998151260504 \tabularnewline
Correlation & -0.0157810624604106 \tabularnewline
Determination & 0.000249041932379382 \tabularnewline
T-Test & -0.171447567571479 \tabularnewline
p-value (2 sided) & 0.864165520835509 \tabularnewline
p-value (1 sided) & 0.432082760417754 \tabularnewline
Degrees of Freedom & 118 \tabularnewline
Number of Observations & 120 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159633&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]18.5825[/C][C]35.8613333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]25.6763504166667[/C][C]323.333414888889[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]5.06718367702086[/C][C]17.9814742134478[/C][/ROW]
[ROW][C]Covariance[/C][C]-1.44998151260504[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.0157810624604106[/C][/ROW]
[ROW][C]Determination[/C][C]0.000249041932379382[/C][/ROW]
[ROW][C]T-Test[/C][C]-0.171447567571479[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.864165520835509[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.432082760417754[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]118[/C][/ROW]
[ROW][C]Number of Observations[/C][C]120[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159633&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159633&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
Mean18.582535.8613333333333
Biased Variance25.6763504166667323.333414888889
Biased Standard Deviation5.0671836770208617.9814742134478
Covariance-1.44998151260504
Correlation-0.0157810624604106
Determination0.000249041932379382
T-Test-0.171447567571479
p-value (2 sided)0.864165520835509
p-value (1 sided)0.432082760417754
Degrees of Freedom118
Number of Observations120


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')