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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 computationThu, 07 Dec 2017 12:01:32 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/07/t15126446367ev14duz7s19uf7.htm/, Retrieved Wed, 15 May 2024 10:21:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308691, Retrieved Wed, 15 May 2024 10:21:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104

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] [2017-12-07 11:01:32] [6ed64e8c4e855e992fbbfd41bce49003] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
64
56
56
63
67
64
64
64
69
60
59
56
63
67
69
58
58
61
62
59
55
65
57
69
59
63
56
63
67
55
55
68
68
68
63
60
64
57
55
59
59
55
64
66
57
69
59
61
60
60
73
61
64
61
62
56
59
68
59
65
Dataseries Y:
Download CSV
Histogram 
1
6
25
20
35
13
2
10
26
5
1
8
7
40
18
2
2
20
24
5
12
15
10
9
9
10
20
10
10
6
17
20
6
20
7
2
26
2
5
10
3
2
35
10
2
5
12
15
6
3
25
9
6
3
3
1
12
20
14
6

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R ServerBig Analytics Cloud Computing Center

\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 time6 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308691&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]6 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308691&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308691&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 time6 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean61.716666666666711.4666666666667
Biased Variance20.369722222222284.7822222222222
Biased Standard Deviation4.513282865301299.20772622433043
Covariance17.3378531073446
Correlation0.410252398918009
Determination0.168307030817981
T-Test3.42597043595097
p-value (2 sided)0.00113173258337826
p-value (1 sided)0.000565866291689129
95% CI of Correlation[0.174506611887196, 0.601515315090988]
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 61.7166666666667 & 11.4666666666667 \tabularnewline
Biased Variance & 20.3697222222222 & 84.7822222222222 \tabularnewline
Biased Standard Deviation & 4.51328286530129 & 9.20772622433043 \tabularnewline
Covariance & 17.3378531073446 \tabularnewline
Correlation & 0.410252398918009 \tabularnewline
Determination & 0.168307030817981 \tabularnewline
T-Test & 3.42597043595097 \tabularnewline
p-value (2 sided) & 0.00113173258337826 \tabularnewline
p-value (1 sided) & 0.000565866291689129 \tabularnewline
95% CI of Correlation & [0.174506611887196, 0.601515315090988] \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308691&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]61.7166666666667[/C][C]11.4666666666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]20.3697222222222[/C][C]84.7822222222222[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.51328286530129[/C][C]9.20772622433043[/C][/ROW]
[ROW][C]Covariance[/C][C]17.3378531073446[/C][/ROW]
[ROW][C]Correlation[/C][C]0.410252398918009[/C][/ROW]
[ROW][C]Determination[/C][C]0.168307030817981[/C][/ROW]
[ROW][C]T-Test[/C][C]3.42597043595097[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00113173258337826[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000565866291689129[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.174506611887196, 0.601515315090988][/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=308691&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308691&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
Mean61.716666666666711.4666666666667
Biased Variance20.369722222222284.7822222222222
Biased Standard Deviation4.513282865301299.20772622433043
Covariance17.3378531073446
Correlation0.410252398918009
Determination0.168307030817981
T-Test3.42597043595097
p-value (2 sided)0.00113173258337826
p-value (1 sided)0.000565866291689129
95% CI of Correlation[0.174506611887196, 0.601515315090988]
Degrees of Freedom58
Number of Observations60






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.4703, p-value = 0.2908
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 13.975, p-value = 0.0009232
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.73504, p-value = 0.05248

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.0482, p-value = 2.829e-05


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.4703, p-value = 0.2908
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 13.975, p-value = 0.0009232
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.73504, p-value = 0.05248

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.0482, p-value = 2.829e-05

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308691&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.4703, p-value = 0.2908
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 13.975, p-value = 0.0009232
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.73504, p-value = 0.05248

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 2.0482, p-value = 2.829e-05

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308691&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308691&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 = 2.4703, p-value = 0.2908
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 13.975, p-value = 0.0009232
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.73504, p-value = 0.05248

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.0482, p-value = 2.829e-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()