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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 computationFri, 04 Dec 2015 10:29:23 +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/04/t144922498557ohi15utrdh57u.htm/, Retrieved Fri, 01 Nov 2024 00:06:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285053, Retrieved Fri, 01 Nov 2024 00:06:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123

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 -25] [2015-12-04 10:29:23] [b273fd68f4630bf668d6e366c549a45c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20.7
20.7
20.7
18
18
18
16.9
16.9
16.9
24.4
24.4
24.4
15.5
15.5
15.5
18.4
18.4
18.4
16.2
16.2
16.2
20.6
20.6
20.6
19.8
19.8
19.8
21.6
21.6
21.6
22.3
22.3
22.3
23.7
23.7
23.7
22.1
22.1
22.1
26.6
26.6
26.6
23.5
23.5
23.5
19.6
19.6
19.6
20
20
20
20.1
20.1
20.1
16
16
16
18.9
18.9
18.9
Dataseries Y:
Download CSV
Histogram 
21.6
21.6
21.6
19.4
19.4
19.4
15.9
15.9
15.9
21.8
21.8
21.8
17.6
17.6
17.6
19
19
19
16.3
16.3
16.3
22.5
22.5
22.5
23.8
23.8
23.8
24.6
24.6
24.6
22.7
22.7
22.7
25.2
25.2
25.2
26.4
26.4
26.4
26
26
26
23.2
23.2
23.2
22.7
22.7
22.7
24
24
24
20.7
20.7
20.7
23.8
23.8
23.8
27.1
27.1
27.1

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285053&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285053&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285053&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean20.24522.215
Biased Variance8.4524759.865275
Biased Standard Deviation2.907314052523393.14090353242502
Covariance5.71151694915254
Correlation0.615043291337623
Determination0.378278250219416
T-Test5.94048156130503
p-value (2 sided)1.70819242306663e-07
p-value (1 sided)8.54096211533317e-08
95% CI of Correlation[0.427954201410717, 0.751588843129527]
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 20.245 & 22.215 \tabularnewline
Biased Variance & 8.452475 & 9.865275 \tabularnewline
Biased Standard Deviation & 2.90731405252339 & 3.14090353242502 \tabularnewline
Covariance & 5.71151694915254 \tabularnewline
Correlation & 0.615043291337623 \tabularnewline
Determination & 0.378278250219416 \tabularnewline
T-Test & 5.94048156130503 \tabularnewline
p-value (2 sided) & 1.70819242306663e-07 \tabularnewline
p-value (1 sided) & 8.54096211533317e-08 \tabularnewline
95% CI of Correlation & [0.427954201410717, 0.751588843129527] \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285053&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]20.245[/C][C]22.215[/C][/ROW]
[ROW][C]Biased Variance[/C][C]8.452475[/C][C]9.865275[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.90731405252339[/C][C]3.14090353242502[/C][/ROW]
[ROW][C]Covariance[/C][C]5.71151694915254[/C][/ROW]
[ROW][C]Correlation[/C][C]0.615043291337623[/C][/ROW]
[ROW][C]Determination[/C][C]0.378278250219416[/C][/ROW]
[ROW][C]T-Test[/C][C]5.94048156130503[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.70819242306663e-07[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]8.54096211533317e-08[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.427954201410717, 0.751588843129527][/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=285053&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285053&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
Mean20.24522.215
Biased Variance8.4524759.865275
Biased Standard Deviation2.907314052523393.14090353242502
Covariance5.71151694915254
Correlation0.615043291337623
Determination0.378278250219416
T-Test5.94048156130503
p-value (2 sided)1.70819242306663e-07
p-value (1 sided)8.54096211533317e-08
95% CI of Correlation[0.427954201410717, 0.751588843129527]
Degrees of Freedom58
Number of Observations60






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.3352, p-value = 0.5129
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.5388, p-value = 0.1704
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.476, p-value = 0.2307

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.0717, p-value = 0.007574


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.3352, p-value = 0.5129
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.5388, p-value = 0.1704
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.476, p-value = 0.2307

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.0717, p-value = 0.007574

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285053&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.3352, p-value = 0.5129
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.5388, p-value = 0.1704
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.476, p-value = 0.2307

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.0717, p-value = 0.007574

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285053&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285053&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 = 1.3352, p-value = 0.5129
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.5388, p-value = 0.1704
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.476, p-value = 0.2307

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.0717, p-value = 0.007574


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()