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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationMon, 28 Dec 2009 10:52:35 -0700
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/Dec/28/t1262022832i7wbxsiuve5ttip.htm/, Retrieved Sun, 05 May 2024 19:53:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71026, Retrieved Sun, 05 May 2024 19:53:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Back to Back hist...] [2008-12-17 13:53:25] [7458e879e85b911182071700fff19fbd]
-   P   [Pearson Correlation] [Pearson Correlati...] [2008-12-22 18:34:33] [7458e879e85b911182071700fff19fbd]
- RMPD      [Pearson Correlation] [] [2009-12-28 17:52:35] [2cb08c489280d8b0442b27107dd2bcd8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
40.22
44.23
45.85
53.38
53.26
51.8
55.3
57.81
63.96
63.77
59.15
56.12
57.42
63.52
61.71
63.01
68.18
72.03
69.75
74.41
74.33
64.24
60.03
59.44
62.5
55.04
58.34
61.92
67.65
67.68
70.3
75.26
71.44
76.36
81.71
92.6
90.6
92.23
94.09
102.79
109.65
124.05
132.69
135.81
116.07
101.42
75.73
55.48
43.8
45.29
44.01
47.48
51.07
57.84
69.04
65.61
72.87
68.41
73.25
77.43
Dataseries Y:
Download CSV
Histogram 
2921.44
2981.85
3080.58
3106.22
3119.31
3061.26
3097.31
3161.69
3257.16
3277.01
3295.32
3363.99
3494.17
3667.03
3813.06
3917.96
3895.51
3801.06
3570.12
3701.61
3862.27
3970.1
4138.52
4199.75
4290.89
4443.91
4502.64
4356.98
4591.27
4696.96
4621.4
4562.84
4202.52
4296.49
4435.23
4105.18
4116.68
3844.49
3720.98
3674.4
3857.62
3801.06
3504.37
3032.6
3047.03
2962.34
2197.82
2014.45
1862.83
1905.41
1810.99
1670.07
1864.44
2052.02
2029.6
2070.83
2293.41
2443.27
2513.17
2466.92

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71026&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71026&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71026&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'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean70.34053360.29016666667
Biased Variance455.795238083333724186.166011639
Biased Standard Deviation21.3493615380726850.991284333535
Covariance4612.73502194915
Correlation0.249660171573752
Determination0.0623302012702354
T-Test1.96353341935619
p-value (2 sided)0.0543842995318347
p-value (1 sided)0.0271921497659173
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 70.3405 & 3360.29016666667 \tabularnewline
Biased Variance & 455.795238083333 & 724186.166011639 \tabularnewline
Biased Standard Deviation & 21.3493615380726 & 850.991284333535 \tabularnewline
Covariance & 4612.73502194915 \tabularnewline
Correlation & 0.249660171573752 \tabularnewline
Determination & 0.0623302012702354 \tabularnewline
T-Test & 1.96353341935619 \tabularnewline
p-value (2 sided) & 0.0543842995318347 \tabularnewline
p-value (1 sided) & 0.0271921497659173 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71026&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]70.3405[/C][C]3360.29016666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]455.795238083333[/C][C]724186.166011639[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]21.3493615380726[/C][C]850.991284333535[/C][/ROW]
[ROW][C]Covariance[/C][C]4612.73502194915[/C][/ROW]
[ROW][C]Correlation[/C][C]0.249660171573752[/C][/ROW]
[ROW][C]Determination[/C][C]0.0623302012702354[/C][/ROW]
[ROW][C]T-Test[/C][C]1.96353341935619[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0543842995318347[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0271921497659173[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71026&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71026&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
Mean70.34053360.29016666667
Biased Variance455.795238083333724186.166011639
Biased Standard Deviation21.3493615380726850.991284333535
Covariance4612.73502194915
Correlation0.249660171573752
Determination0.0623302012702354
T-Test1.96353341935619
p-value (2 sided)0.0543842995318347
p-value (1 sided)0.0271921497659173
Degrees of Freedom58
Number of Observations60


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')