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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, 15 Dec 2015 13:24:27 +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/15/t1450186146lttrdesn2493t3e.htm/, Retrieved Sat, 25 May 2024 00:20:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286485, Retrieved Sat, 25 May 2024 00:20:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76

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...] [2015-12-15 13:24:27] [722e07e565c67c42d7d1b696fdc83dd3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
93.08
94.56
94.94
96.42
98.79
97.46
98.16
98.68
99.66
99.98
Dataseries Y:
Download CSV
Histogram 
119
117
113
111
106
108
103
112
100
96

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286485&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286485&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286485&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean97.173108.5
Biased Variance4.91404148.65
Biased Standard Deviation2.21676363196446.97495519698872
Covariance-15.2983333333333
Correlation-0.890483381194612
Determination0.792960652183789
T-Test-5.53534082689072
p-value (2 sided)0.000550363501897455
p-value (1 sided)0.000275181750948728
95% CI of Correlation[-0.974009861396126, -0.59376351254175]
Degrees of Freedom8
Number of Observations10

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 97.173 & 108.5 \tabularnewline
Biased Variance & 4.914041 & 48.65 \tabularnewline
Biased Standard Deviation & 2.2167636319644 & 6.97495519698872 \tabularnewline
Covariance & -15.2983333333333 \tabularnewline
Correlation & -0.890483381194612 \tabularnewline
Determination & 0.792960652183789 \tabularnewline
T-Test & -5.53534082689072 \tabularnewline
p-value (2 sided) & 0.000550363501897455 \tabularnewline
p-value (1 sided) & 0.000275181750948728 \tabularnewline
95% CI of Correlation & [-0.974009861396126, -0.59376351254175] \tabularnewline
Degrees of Freedom & 8 \tabularnewline
Number of Observations & 10 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286485&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]97.173[/C][C]108.5[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4.914041[/C][C]48.65[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.2167636319644[/C][C]6.97495519698872[/C][/ROW]
[ROW][C]Covariance[/C][C]-15.2983333333333[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.890483381194612[/C][/ROW]
[ROW][C]Determination[/C][C]0.792960652183789[/C][/ROW]
[ROW][C]T-Test[/C][C]-5.53534082689072[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000550363501897455[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000275181750948728[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.974009861396126, -0.59376351254175][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]8[/C][/ROW]
[ROW][C]Number of Observations[/C][C]10[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286485&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286485&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
Mean97.173108.5
Biased Variance4.91404148.65
Biased Standard Deviation2.21676363196446.97495519698872
Covariance-15.2983333333333
Correlation-0.890483381194612
Determination0.792960652183789
T-Test-5.53534082689072
p-value (2 sided)0.000550363501897455
p-value (1 sided)0.000275181750948728
95% CI of Correlation[-0.974009861396126, -0.59376351254175]
Degrees of Freedom8
Number of Observations10






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.85558, p-value = 0.6519
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.47385, p-value = 0.7891
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.31168, p-value = 0.4929

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.14276, p-value = 0.9541


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.85558, p-value = 0.6519
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.47385, p-value = 0.7891
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.31168, p-value = 0.4929

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.14276, p-value = 0.9541

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286485&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.85558, p-value = 0.6519
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.47385, p-value = 0.7891
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.31168, p-value = 0.4929

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.14276, p-value = 0.9541

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286485&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286485&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 = 0.85558, p-value = 0.6519
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.47385, p-value = 0.7891
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.31168, p-value = 0.4929

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.14276, p-value = 0.9541


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()