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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, 01 Dec 2015 11:54:57 +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/01/t1448970941aiv8nyu4hw9f3bo.htm/, Retrieved Thu, 16 May 2024 21:33:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284684, Retrieved Thu, 16 May 2024 21:33:01 +0000
QR Codes:

Original text written by user:Eerste test
IsPrivate?No (this computation is public)
User-defined keywordsAnderlecht PC
Estimated Impact124

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [] [2015-09-24 13:12:15] [32b17a345b130fdf5cc88718ed94a974]
-    D    [Pearson Correlation] [Pearson correlati...] [2015-12-01 11:54:57] [7f15ad2b324a02cb27046274e327e025] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.74
0.76
0.75
0.69
0.59
0.71
0.44
0.72
0.7
0.71
0.7
0.57
0.72
0.58
0.63
0.78
0.48
0.58
0.73
0.68
0.66
0.74
0.69
0.63
0.78
0.59
0.69
0.78
0.41
0.68
0.64
0.55
0.81
0.81
0.77
0.77
0.45
0.57
0.69
0.74
0.76
0.83
0.78
0.68
0.57
0.78
0.76
0.67
0.69
0.59
0.77
0.54
0.63
Dataseries Y:
Download CSV
Histogram 
23867
24107
24041
24415
24496
24022
24367
23869
24495
23818
24081
24132
23651
23622
23726
23942
24573
23085
22612
22960
22921
23510
22729
23047
22850
23426
22812
22446
23567
23185
22777
23508
23193
23006
22332
22347
23061
22887
22890
22701
22467
22357
22443
22824
22906
23059
23055
22564
18570
20329
19279
19541
19517

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 Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284684&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284684&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284684&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 Maurice George Kendall' @ kendall.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean0.67471698113207522943.1509433962
Biased Variance0.009866429334282671689355.86400854
Biased Standard Deviation0.09932990151149181299.75223177671
Covariance-11.7766872278665
Correlation-0.0894973216003225
Determination0.00800977057363155
T-Test-0.641713874180446
p-value (2 sided)0.523932837428142
p-value (1 sided)0.261966418714071
95% CI of Correlation[-0.351293151230928, 0.18527848289514]
Degrees of Freedom51
Number of Observations53

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 0.674716981132075 & 22943.1509433962 \tabularnewline
Biased Variance & 0.00986642933428267 & 1689355.86400854 \tabularnewline
Biased Standard Deviation & 0.0993299015114918 & 1299.75223177671 \tabularnewline
Covariance & -11.7766872278665 \tabularnewline
Correlation & -0.0894973216003225 \tabularnewline
Determination & 0.00800977057363155 \tabularnewline
T-Test & -0.641713874180446 \tabularnewline
p-value (2 sided) & 0.523932837428142 \tabularnewline
p-value (1 sided) & 0.261966418714071 \tabularnewline
95% CI of Correlation & [-0.351293151230928, 0.18527848289514] \tabularnewline
Degrees of Freedom & 51 \tabularnewline
Number of Observations & 53 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284684&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]0.674716981132075[/C][C]22943.1509433962[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.00986642933428267[/C][C]1689355.86400854[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.0993299015114918[/C][C]1299.75223177671[/C][/ROW]
[ROW][C]Covariance[/C][C]-11.7766872278665[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.0894973216003225[/C][/ROW]
[ROW][C]Determination[/C][C]0.00800977057363155[/C][/ROW]
[ROW][C]T-Test[/C][C]-0.641713874180446[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.523932837428142[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.261966418714071[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.351293151230928, 0.18527848289514][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]51[/C][/ROW]
[ROW][C]Number of Observations[/C][C]53[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284684&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284684&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
Mean0.67471698113207522943.1509433962
Biased Variance0.009866429334282671689355.86400854
Biased Standard Deviation0.09932990151149181299.75223177671
Covariance-11.7766872278665
Correlation-0.0894973216003225
Determination0.00800977057363155
T-Test-0.641713874180446
p-value (2 sided)0.523932837428142
p-value (1 sided)0.261966418714071
95% CI of Correlation[-0.351293151230928, 0.18527848289514]
Degrees of Freedom51
Number of Observations53






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.5412, p-value = 0.06262
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 46.035, p-value = 1.009e-10
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.0682, p-value = 0.007641

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.2682, p-value = 2.669e-08


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.5412, p-value = 0.06262
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 46.035, p-value = 1.009e-10
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.0682, p-value = 0.007641

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.2682, p-value = 2.669e-08

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284684&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.5412, p-value = 0.06262
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 46.035, p-value = 1.009e-10
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.0682, p-value = 0.007641

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 3.2682, p-value = 2.669e-08

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284684&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284684&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 = 5.5412, p-value = 0.06262
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 46.035, p-value = 1.009e-10
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.0682, p-value = 0.007641

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.2682, p-value = 2.669e-08


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()