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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 computationThu, 04 Sep 2014 04:01:57 +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/2014/Sep/04/t1409799753n9017zl6lxk69ve.htm/, Retrieved Mon, 13 May 2024 20:05:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235785, Retrieved Mon, 13 May 2024 20:05:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact175

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
57.89
7.69
32
71.05
38.46
32.35
41.03
100
51.28
57.89
73.68
84.62
33.33
38.46
23.08
25.64
16.22
64.1
63.16
23.08
64.1
46.15
28.21
44.74
59.46
56.41
36.67
19.44
43.24
25.64
51.28
52
48.72
65.79
16.67
28.21
38.46
34.21
33.33
46.15
57.89
13.33
60.53
64.86
27.59
15.38
54.05
50
54.05
35.9
26.67
Dataseries Y:
Download CSV
Histogram 
73
69
82
82
72
66
55
112
81
73
78
76
57
68
59
51
63
71
80
43
63
42
58
42
90
65
59
50
84
33
62
93
71
72
42
62
80
60
56
53
76
53
76
85
48
38
56
60
65
45
68

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235785&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235785&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235785&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean43.806666666666765.0588235294118
Biased Variance368.798355555556240.643598615917
Biased Standard Deviation19.204123399821115.5126915335772
Covariance198.0188
Correlation0.65166531754284
Determination0.42466768608821
T-Test6.01399779246223
p-value (2 sided)2.22705264674161e-07
p-value (1 sided)1.11352632337081e-07
Degrees of Freedom49
Number of Observations51

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 43.8066666666667 & 65.0588235294118 \tabularnewline
Biased Variance & 368.798355555556 & 240.643598615917 \tabularnewline
Biased Standard Deviation & 19.2041233998211 & 15.5126915335772 \tabularnewline
Covariance & 198.0188 \tabularnewline
Correlation & 0.65166531754284 \tabularnewline
Determination & 0.42466768608821 \tabularnewline
T-Test & 6.01399779246223 \tabularnewline
p-value (2 sided) & 2.22705264674161e-07 \tabularnewline
p-value (1 sided) & 1.11352632337081e-07 \tabularnewline
Degrees of Freedom & 49 \tabularnewline
Number of Observations & 51 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235785&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]43.8066666666667[/C][C]65.0588235294118[/C][/ROW]
[ROW][C]Biased Variance[/C][C]368.798355555556[/C][C]240.643598615917[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]19.2041233998211[/C][C]15.5126915335772[/C][/ROW]
[ROW][C]Covariance[/C][C]198.0188[/C][/ROW]
[ROW][C]Correlation[/C][C]0.65166531754284[/C][/ROW]
[ROW][C]Determination[/C][C]0.42466768608821[/C][/ROW]
[ROW][C]T-Test[/C][C]6.01399779246223[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.22705264674161e-07[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.11352632337081e-07[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]49[/C][/ROW]
[ROW][C]Number of Observations[/C][C]51[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235785&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235785&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
Mean43.806666666666765.0588235294118
Biased Variance368.798355555556240.643598615917
Biased Standard Deviation19.204123399821115.5126915335772
Covariance198.0188
Correlation0.65166531754284
Determination0.42466768608821
T-Test6.01399779246223
p-value (2 sided)2.22705264674161e-07
p-value (1 sided)1.11352632337081e-07
Degrees of Freedom49
Number of Observations51






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.4833, p-value = 0.4763
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.9138, p-value = 0.6332
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.271, p-value = 0.6604

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.1506, p-value = 0.9592


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.4833, p-value = 0.4763
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.9138, p-value = 0.6332
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.271, p-value = 0.6604

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.1506, p-value = 0.9592

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235785&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.4833, p-value = 0.4763
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.9138, p-value = 0.6332
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.271, p-value = 0.6604

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.1506, p-value = 0.9592

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235785&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235785&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 = 1.4833, p-value = 0.4763
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.9138, p-value = 0.6332
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.271, p-value = 0.6604

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.1506, p-value = 0.9592


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
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,'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()