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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 computationSun, 21 Dec 2008 09:59:50 -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/2008/Dec/21/t12298788301o2qclzbswsylre.htm/, Retrieved Fri, 17 May 2024 20:20:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35688, Retrieved Fri, 17 May 2024 20:20:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Case Paper] [2007-12-14 14:05:18] [80dc8bee9e9ee44ea58af3349c835ac7]
-    D    [Pearson Correlation] [Paper: Pearson Co...] [2008-12-21 16:59:50] [3a23ee8a65a3056dd39b310a09ef5fc1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
143.5
127.1
137.3
132.5
132.7
138.6
129.2
128.7
135.7
134.4
145.0
151.1
136.3
133.2
128.8
136.3
131.3
128.6
139.3
120.8
126.7
128.6
137.5
140.8
132.3
130.5
117.1
131.4
129.4
119.2
133.6
113.2
122.1
130.9
131.7
126.7
132.3
124.8
111.1
131.3
118.6
119.4
124.0
108.7
115.9
130.5
125.4
126.0
130.4
119.3
117.4
127.9
112.5
115.1
124.3
107.6
110.7
117.9
115.2
130.4
Dataseries Y:
Download CSV
Histogram 
95.0
61.5
88.5
93.3
89.2
101.3
97.0
102.2
100.3
78.2
105.9
119.9
108.0
77.0
93.1
109.5
100.4
99.0
113.9
102.1
101.6
84.0
110.7
111.6
110.7
73.1
87.5
109.6
99.3
92.1
109.3
94.5
91.4
82.9
103.3
96.0
104.8
65.8
78.7
100.3
85.0
94.5
97.9
91.9
87.2
84.4
99.2
105.4
110.9
69.8
86.8
106.7
88.8
96.9
108.1
93.7
94.8
79.8
95.6
107.9

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'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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35688&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35688&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35688&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'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean127.31333333333395.4633333333333
Biased Variance86.2554888888889150.006655555556
Biased Standard Deviation9.2873833176459812.2477204228197
Covariance48.2565988700565
Correlation0.41716593358523
Determination0.174027416144036
T-Test3.49574718593133
p-value (2 sided)0.000913296578279432
p-value (1 sided)0.000456648289139716
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 127.313333333333 & 95.4633333333333 \tabularnewline
Biased Variance & 86.2554888888889 & 150.006655555556 \tabularnewline
Biased Standard Deviation & 9.28738331764598 & 12.2477204228197 \tabularnewline
Covariance & 48.2565988700565 \tabularnewline
Correlation & 0.41716593358523 \tabularnewline
Determination & 0.174027416144036 \tabularnewline
T-Test & 3.49574718593133 \tabularnewline
p-value (2 sided) & 0.000913296578279432 \tabularnewline
p-value (1 sided) & 0.000456648289139716 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35688&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]127.313333333333[/C][C]95.4633333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]86.2554888888889[/C][C]150.006655555556[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]9.28738331764598[/C][C]12.2477204228197[/C][/ROW]
[ROW][C]Covariance[/C][C]48.2565988700565[/C][/ROW]
[ROW][C]Correlation[/C][C]0.41716593358523[/C][/ROW]
[ROW][C]Determination[/C][C]0.174027416144036[/C][/ROW]
[ROW][C]T-Test[/C][C]3.49574718593133[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000913296578279432[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000456648289139716[/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=35688&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35688&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
Mean127.31333333333395.4633333333333
Biased Variance86.2554888888889150.006655555556
Biased Standard Deviation9.2873833176459812.2477204228197
Covariance48.2565988700565
Correlation0.41716593358523
Determination0.174027416144036
T-Test3.49574718593133
p-value (2 sided)0.000913296578279432
p-value (1 sided)0.000456648289139716
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')