FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 22 Jan 2016 09:44:48 +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/2016/Jan/22/t1453455964hwpjt4vie7gau5s.htm/, Retrieved Wed, 08 May 2024 01:53:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=291050, Retrieved Wed, 08 May 2024 01:53:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2016-01-22 09:44:48] [d77e77dcb3e0bbaf274ceb9ae07893c0] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
18
38
15
20
18
36
20
43
45
65
43
38
33
10
50
10
50
15
53
60
18
38
15
20
18
36
20
43
45
65
43
38
33
10
50
10
50
15
53
15
37
15
18
11
35
20
40
50
36
50
38
10
75
10
85
13
50
58
58
48
12
63
10
63
13
28
35
63
13
45
9
20
18
35
20
38
50
70
40
21
19
10
33
16
5
32
23
30
45
33
25
12
53
36
5
63
43
25
73
45
52
9
30
22
56
15
45
Dataseries Y:
Download CSV
Histogram 
20.2
56
12.5
21.2
15.5
39
21
38.2
55.6
81.9
39.5
56.4
40.5
14.3
81.5
13.7
81.5
20.5
56
80.7
20
56.5
12.1
19.6
15.5
38.8
19.5
38
55
80
38.5
55.8
38.8
12.5
80.4
12.7
80.9
20.5
55
19
55.5
12.3
18.4
11.5
38
18.5
38
55.3
38.7
54.5
38
12
81.7
11.5
80
18.3
55.3
80.2
80.7
55.8
15
81
12
81.4
12.5
38.2
54.2
79.3
18.2
55.5
11.4
19.5
15.5
37.5
19.5
37.5
55.5
80
37.5
15.5
23.7
9.8
40.8
17.5
4.3
36.5
26.3
30.4
50.2
30.1
25.5
13.8
58.9
40
6
72.5
38.8
19.4
81.5
77.4
54.6
6.8
32.6
19.8
58.8
12.9
49

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=291050&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]4 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=291050&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=291050&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean33.579439252336439.0990654205607
Biased Variance342.729670713599573.301774827496
Biased Standard Deviation18.512959534164223.9437209895934
Covariance423.10149003703
Correlation0.945581893215889
Determination0.894125116777745
T-Test29.7781233635247
p-value (2 sided)0
p-value (1 sided)0
95% CI of Correlation[0.921082331302096, 0.962623675692764]
Degrees of Freedom105
Number of Observations107

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 33.5794392523364 & 39.0990654205607 \tabularnewline
Biased Variance & 342.729670713599 & 573.301774827496 \tabularnewline
Biased Standard Deviation & 18.5129595341642 & 23.9437209895934 \tabularnewline
Covariance & 423.10149003703 \tabularnewline
Correlation & 0.945581893215889 \tabularnewline
Determination & 0.894125116777745 \tabularnewline
T-Test & 29.7781233635247 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
95% CI of Correlation & [0.921082331302096, 0.962623675692764] \tabularnewline
Degrees of Freedom & 105 \tabularnewline
Number of Observations & 107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=291050&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]33.5794392523364[/C][C]39.0990654205607[/C][/ROW]
[ROW][C]Biased Variance[/C][C]342.729670713599[/C][C]573.301774827496[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]18.5129595341642[/C][C]23.9437209895934[/C][/ROW]
[ROW][C]Covariance[/C][C]423.10149003703[/C][/ROW]
[ROW][C]Correlation[/C][C]0.945581893215889[/C][/ROW]
[ROW][C]Determination[/C][C]0.894125116777745[/C][/ROW]
[ROW][C]T-Test[/C][C]29.7781233635247[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.921082331302096, 0.962623675692764][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]105[/C][/ROW]
[ROW][C]Number of Observations[/C][C]107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=291050&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=291050&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
Mean33.579439252336439.0990654205607
Biased Variance342.729670713599573.301774827496
Biased Standard Deviation18.512959534164223.9437209895934
Covariance423.10149003703
Correlation0.945581893215889
Determination0.894125116777745
T-Test29.7781233635247
p-value (2 sided)0
p-value (1 sided)0
95% CI of Correlation[0.921082331302096, 0.962623675692764]
Degrees of Freedom105
Number of Observations107






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.0927, p-value = 0.07837
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 8.788, p-value = 0.01235
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6509, p-value = 0.0002893

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.5745, p-value = 5.496e-09


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.0927, p-value = 0.07837
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 8.788, p-value = 0.01235
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6509, p-value = 0.0002893

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.5745, p-value = 5.496e-09

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=291050&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 5.0927, p-value = 0.07837
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 8.788, p-value = 0.01235
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6509, p-value = 0.0002893

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 3.5745, p-value = 5.496e-09

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=291050&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=291050&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 = 5.0927, p-value = 0.07837
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 8.788, p-value = 0.01235
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6509, p-value = 0.0002893

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.5745, p-value = 5.496e-09


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()