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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, 08 Dec 2009 23:38:46 -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/09/t1260340883zhn2sxqdppgpkep.htm/, Retrieved Mon, 29 Apr 2024 16:06:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64882, Retrieved Mon, 29 Apr 2024 16:06:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Paper: Pearson Co...] [2009-12-09 06:38:46] [762da55b2e2304daaed24a7cc507d14d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
108.8
128.4
121.1
119.5
128.7
108.7
105.5
119.8
111.3
110.6
120.1
97.5
107.7
127.3
117.2
119.8
116.2
111
112.4
130.6
109.1
118.8
123.9
101.6
112.8
128
129.6
125.8
119.5
115.7
113.6
129.7
112
116.8
127
112.1
114.2
121.1
131.6
125
120.4
117.7
117.5
120.6
127.5
112.3
124.5
115.2
104.7
130.9
129.2
113.5
125.6
107.6
107
121.6
110.7
106.3
118.6
104.6
Dataseries Y:
Download CSV
Histogram 
122,2
122,6
122,2
118,8
119
118,2
117,8
116,8
114,6
113,4
113,8
124,2
125,8
125,6
122,4
119
119,4
118,6
118
116
114,8
114,6
114,6
124
125,2
124
117,6
113,2
111,4
112,2
109,8
106,4
105,2
102,2
99,8
111
113
108,4
105,4
102
102,8
103,4
101,6
98,6
98
93,8
95,6
105,6
106,8
103,6
101,2
100,4
103,2
105,6
106,6
107,2
107,4
104,8
107,2
117,4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time8 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 & 8 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64882&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]8 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=64882&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64882&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 time8 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean117.435111.566666666667
Biased Variance68.914608333333371.2322222222222
Biased Standard Deviation8.30148229735718.43991837769905
Covariance-14.9801694915254
Correlation-0.210243992777865
Determination0.0442025364991789
T-Test-1.63777657699991
p-value (2 sided)0.106882927753833
p-value (1 sided)0.0534414638769167
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 117.435 & 111.566666666667 \tabularnewline
Biased Variance & 68.9146083333333 & 71.2322222222222 \tabularnewline
Biased Standard Deviation & 8.3014822973571 & 8.43991837769905 \tabularnewline
Covariance & -14.9801694915254 \tabularnewline
Correlation & -0.210243992777865 \tabularnewline
Determination & 0.0442025364991789 \tabularnewline
T-Test & -1.63777657699991 \tabularnewline
p-value (2 sided) & 0.106882927753833 \tabularnewline
p-value (1 sided) & 0.0534414638769167 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64882&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]117.435[/C][C]111.566666666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]68.9146083333333[/C][C]71.2322222222222[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]8.3014822973571[/C][C]8.43991837769905[/C][/ROW]
[ROW][C]Covariance[/C][C]-14.9801694915254[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.210243992777865[/C][/ROW]
[ROW][C]Determination[/C][C]0.0442025364991789[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.63777657699991[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.106882927753833[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0534414638769167[/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=64882&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64882&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
Mean117.435111.566666666667
Biased Variance68.914608333333371.2322222222222
Biased Standard Deviation8.30148229735718.43991837769905
Covariance-14.9801694915254
Correlation-0.210243992777865
Determination0.0442025364991789
T-Test-1.63777657699991
p-value (2 sided)0.106882927753833
p-value (1 sided)0.0534414638769167
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')