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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 computationSun, 19 Oct 2008 02:55:43 -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/2008/Oct/19/t1224406584v8yrvzljen0a9vi.htm/, Retrieved Tue, 28 May 2024 23:16:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16722, Retrieved Tue, 28 May 2024 23:16:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson Correlati...] [2008-10-19 08:55:43] [fdd69703d301fae09456f660b2f52997] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
64.5
57.9
72.5
82.9
62.7
66.6
70.9
56.3
81.2
67.8
57.2
62.8
51.2
66.5
71.5
67.8
56.9
90.6
64.1
65.7
77.9
84.2
81.7
65.9
76.1
80.1
74.3
86.5
70.9
91.5
93.7
77.5
100.3
85.7
95
73.7
87.6
87.6
92.9
80.7
74
87.7
68.2
117.4
100.1
97.7
101.1
87.6
83.2
85.9
118
87.3
79.5
93.2
99.2
66.6
83.9
100.4
73.5
60.8
Dataseries Y:
Download CSV
Histogram 
53.3
66.9
73.7
71.9
67.9
77.5
82
40.5
76.2
75
64
77.2
63.9
71.4
71.3
50
47.9
55.2
61.8
53.6
60
72.7
63.6
62.1
58.1
68.1
65.5
59.3
65.7
68.3
77.8
49.1
96.9
64.6
67
64.6
84.3
72.6
71.3
52.8
63.9
67.9
74.1
61.7
74.1
83.5
75.6
77.9
69.2
67.8
74.8
69.7
69.9
84.3
81.7
69.3
83.8
96
74.2
70.4

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=16722&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=16722&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16722&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
Mean79.44568.9233333333333
Biased Variance214.590808333333115.519788888889
Biased Standard Deviation14.648918333219510.7480132531035
Covariance69.6945254237288
Correlation0.435276955514546
Determination0.189466028002012
T-Test3.68208712903752
p-value (2 sided)0.0005094208774854
p-value (1 sided)0.0002547104387427
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 79.445 & 68.9233333333333 \tabularnewline
Biased Variance & 214.590808333333 & 115.519788888889 \tabularnewline
Biased Standard Deviation & 14.6489183332195 & 10.7480132531035 \tabularnewline
Covariance & 69.6945254237288 \tabularnewline
Correlation & 0.435276955514546 \tabularnewline
Determination & 0.189466028002012 \tabularnewline
T-Test & 3.68208712903752 \tabularnewline
p-value (2 sided) & 0.0005094208774854 \tabularnewline
p-value (1 sided) & 0.0002547104387427 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16722&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]79.445[/C][C]68.9233333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]214.590808333333[/C][C]115.519788888889[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]14.6489183332195[/C][C]10.7480132531035[/C][/ROW]
[ROW][C]Covariance[/C][C]69.6945254237288[/C][/ROW]
[ROW][C]Correlation[/C][C]0.435276955514546[/C][/ROW]
[ROW][C]Determination[/C][C]0.189466028002012[/C][/ROW]
[ROW][C]T-Test[/C][C]3.68208712903752[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0005094208774854[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0002547104387427[/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=16722&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16722&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
Mean79.44568.9233333333333
Biased Variance214.590808333333115.519788888889
Biased Standard Deviation14.648918333219510.7480132531035
Covariance69.6945254237288
Correlation0.435276955514546
Determination0.189466028002012
T-Test3.68208712903752
p-value (2 sided)0.0005094208774854
p-value (1 sided)0.0002547104387427
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')