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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationMon, 29 Apr 2019 16:31:22 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2019/Apr/29/t1556548321gu1gglpziuljnhy.htm/, Retrieved Sun, 12 May 2024 11:24:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=318793, Retrieved Sun, 12 May 2024 11:24:07 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [RE: Módulo 1] [2019-04-29 14:31:22] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19
22
28
30
31
4.0

35
17
11
4.0
33
3.0
2.0

2.0
17
3.0
13
5.0

3.0
3.0
4.0
4.0
1.0
3.0
8.0
2.0
6.0
4.0
19
13

17
19
15
6.0
16
29
4.0
3.0
2.0
1.0
Dataseries Y:
Download CSV
Histogram 
40.922
51.823
33.110
35.906
17.521
9.080

58.998
49.400
10.632
10.444
40.269
6.829
14.127

8.437
21.980
3.220
8.740
3.486

10.720
4.363
4.575
2.973
3.610
10.936
9.066
3.448
9.960
3.253
30.813
36.039

33.238
22.672
31.995
20.249
33.861
32.410
2.856
3.679
1.663
0.756

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318793&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [ROW]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=318793&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318793&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean11.52518.451475
Biased Variance104.749375255.102757449375
Biased Standard Deviation10.234714211935815.9719365591457
Covariance138.230667307692
Correlation0.824471644030149
Determination0.679753491809777
T-Test8.98101290310614
p-value (2 sided)6.19782444864616e-11
p-value (1 sided)3.09891222432308e-11
95% CI of Correlation[0.690236051653447, 0.903845729358411]
Degrees of Freedom38
Number of Observations40

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 11.525 & 18.451475 \tabularnewline
Biased Variance & 104.749375 & 255.102757449375 \tabularnewline
Biased Standard Deviation & 10.2347142119358 & 15.9719365591457 \tabularnewline
Covariance & 138.230667307692 \tabularnewline
Correlation & 0.824471644030149 \tabularnewline
Determination & 0.679753491809777 \tabularnewline
T-Test & 8.98101290310614 \tabularnewline
p-value (2 sided) & 6.19782444864616e-11 \tabularnewline
p-value (1 sided) & 3.09891222432308e-11 \tabularnewline
95% CI of Correlation & [0.690236051653447, 0.903845729358411] \tabularnewline
Degrees of Freedom & 38 \tabularnewline
Number of Observations & 40 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318793&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]11.525[/C][C]18.451475[/C][/ROW]
[ROW][C]Biased Variance[/C][C]104.749375[/C][C]255.102757449375[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]10.2347142119358[/C][C]15.9719365591457[/C][/ROW]
[ROW][C]Covariance[/C][C]138.230667307692[/C][/ROW]
[ROW][C]Correlation[/C][C]0.824471644030149[/C][/ROW]
[ROW][C]Determination[/C][C]0.679753491809777[/C][/ROW]
[ROW][C]T-Test[/C][C]8.98101290310614[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]6.19782444864616e-11[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]3.09891222432308e-11[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.690236051653447, 0.903845729358411][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]38[/C][/ROW]
[ROW][C]Number of Observations[/C][C]40[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=318793&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318793&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
Mean11.52518.451475
Biased Variance104.749375255.102757449375
Biased Standard Deviation10.234714211935815.9719365591457
Covariance138.230667307692
Correlation0.824471644030149
Determination0.679753491809777
T-Test8.98101290310614
p-value (2 sided)6.19782444864616e-11
p-value (1 sided)3.09891222432308e-11
95% CI of Correlation[0.690236051653447, 0.903845729358411]
Degrees of Freedom38
Number of Observations40






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.3526, p-value = 0.06882
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.7792, p-value = 0.09167
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.3542, p-value = 4.506e-06

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.9807, p-value = 3.845e-05


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.3526, p-value = 0.06882
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.7792, p-value = 0.09167
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.3542, p-value = 4.506e-06

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.9807, p-value = 3.845e-05

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318793&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.3526, p-value = 0.06882
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.7792, p-value = 0.09167
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.3542, p-value = 4.506e-06

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.9807, p-value = 3.845e-05

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=318793&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318793&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 = 5.3526, p-value = 0.06882
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.7792, p-value = 0.09167
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.3542, p-value = 4.506e-06

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.9807, p-value = 3.845e-05


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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Variance',header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Standard Deviation',header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Covariance',header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Correlation',header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Determination',header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-Test',header=TRUE)
a<-table.element(a,as.matrix(corxy$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')
qqPlot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qqPlot(y,main='QQplot of variable y')
dev.off()