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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 computationMon, 07 Dec 2015 14:18:37 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/07/t14494979637ooc950tm2h8pa8.htm/, Retrieved Thu, 16 May 2024 06:33:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285395, Retrieved Thu, 16 May 2024 06:33:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2015-12-07 14:18:37] [7b81fac622814275349f5d25cf6bd6bd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104
81
101
92
83
101
64
57
108
121
99
109
96
88
91
71
85
93
64
48
96
95
74
91
Dataseries Y:
Download CSV
Histogram 
191
190
220
194
144
192
162
96
265
222
182
203
198
159
196
140
163
177
123
100
227
205
133
190

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285395&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285395&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285395&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean88178
Biased Variance298.4166666666671582.25
Biased Standard Deviation17.274740711995339.7775062063976
Covariance624.347826086957
Correlation0.87075125393086
Determination0.758207746222165
T-Test8.30585331964728
p-value (2 sided)3.14892072417194e-08
p-value (1 sided)1.57446036208597e-08
95% CI of Correlation[0.720401456453861, 0.942934497873222]
Degrees of Freedom22
Number of Observations24

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 88 & 178 \tabularnewline
Biased Variance & 298.416666666667 & 1582.25 \tabularnewline
Biased Standard Deviation & 17.2747407119953 & 39.7775062063976 \tabularnewline
Covariance & 624.347826086957 \tabularnewline
Correlation & 0.87075125393086 \tabularnewline
Determination & 0.758207746222165 \tabularnewline
T-Test & 8.30585331964728 \tabularnewline
p-value (2 sided) & 3.14892072417194e-08 \tabularnewline
p-value (1 sided) & 1.57446036208597e-08 \tabularnewline
95% CI of Correlation & [0.720401456453861, 0.942934497873222] \tabularnewline
Degrees of Freedom & 22 \tabularnewline
Number of Observations & 24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285395&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]88[/C][C]178[/C][/ROW]
[ROW][C]Biased Variance[/C][C]298.416666666667[/C][C]1582.25[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]17.2747407119953[/C][C]39.7775062063976[/C][/ROW]
[ROW][C]Covariance[/C][C]624.347826086957[/C][/ROW]
[ROW][C]Correlation[/C][C]0.87075125393086[/C][/ROW]
[ROW][C]Determination[/C][C]0.758207746222165[/C][/ROW]
[ROW][C]T-Test[/C][C]8.30585331964728[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]3.14892072417194e-08[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.57446036208597e-08[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.720401456453861, 0.942934497873222][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]22[/C][/ROW]
[ROW][C]Number of Observations[/C][C]24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285395&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285395&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
Mean88178
Biased Variance298.4166666666671582.25
Biased Standard Deviation17.274740711995339.7775062063976
Covariance624.347826086957
Correlation0.87075125393086
Determination0.758207746222165
T-Test8.30585331964728
p-value (2 sided)3.14892072417194e-08
p-value (1 sided)1.57446036208597e-08
95% CI of Correlation[0.720401456453861, 0.942934497873222]
Degrees of Freedom22
Number of Observations24






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1472, p-value = 0.5635
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.30003, p-value = 0.8607
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.42842, p-value = 0.2861

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.39673, p-value = 0.3422


\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1472, p-value = 0.5635
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.30003, p-value = 0.8607
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.42842, p-value = 0.2861

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.39673, p-value = 0.3422

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285395&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1472, p-value = 0.5635
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.30003, p-value = 0.8607
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.42842, p-value = 0.2861

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.39673, p-value = 0.3422

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285395&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285395&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1472, p-value = 0.5635
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.30003, p-value = 0.8607
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.42842, p-value = 0.2861

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.39673, p-value = 0.3422


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
library(psychometric)
x <- x[!is.na(y)]
y <- y[!is.na(y)]
y <- y[!is.na(x)]
x <- x[!is.na(x)]
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, sub=main)
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', na.rm = T)
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,'95% CI of Correlation',header=TRUE)
a<-table.element(a,paste('[',CIr(r=cxy, n = lx, level = .95)[1],', ', CIr(r=cxy, n = lx, level = .95)[2],']',sep=''),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')
library(moments)
library(nortest)
jarque.x <- jarque.test(x)
jarque.y <- jarque.test(y)
if(lx>7) {
ad.x <- ad.test(x)
ad.y <- ad.test(y)
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Normality Tests',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.y'),'
',sep=''))
a<-table.row.end(a)
if(lx>7) {
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.y'),'
',sep=''))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
library(car)
bitmap(file='test2.png')
qq.plot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qq.plot(y,main='QQplot of variable y')
dev.off()