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 computationMon, 30 Nov 2015 13:16:47 +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/Nov/30/t1448889752e4hkimse2ft8jw0.htm/, Retrieved Tue, 14 May 2024 07:58:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284586, Retrieved Tue, 14 May 2024 07:58:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Sterftes bij vrou...] [2015-11-30 12:50:02] [25ff470ac0d6ae34c6063067ee270158]
- RMPD    [Pearson Correlation] [Verschil sterftes...] [2015-11-30 13:16:47] [f5873c2f4f82c50a280588900254fbac] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
166.06
154.50
146.87
145.10
143.32
137.03
132.42
130.71
128.60
130.39
138.43
154.74
184.35
163.39
149.06
147.10
138.06
134.13
139.87
133.68
125.47
137.03
140.50
157.13
159.55
160.36
156.48
153.03
138.03
139.70
138.23
145.68
139.90
142.06
145.77
171.19
171.61
150.21
144.65
140.33
129.61
130.40
128.13
125.35
129.73
136.84
137.80
153.00
165.03
172.25
177.06
142.10
136.16
135.87
119.84
119.84
126.13
133.58
132.27
153.77
161.90
155.11
156.55
138.47
130.16
133.20
152.71
121.87
129.57
127.52
132.90
143.10
154.94
166.86
147.10
142.97
127.77
131.43
126.84
123.10
127.80
133.23
148.90
143.45
Dataseries Y:
Download CSV
Histogram 
159.81
147.75
147.13
140.33
142.87
139.67
135.35
136.32
129.27
126.81
137.17
150.94
173.71
156.68
146.84
144.17
134.81
135.13
131.45
133.77
134.87
140.90
136.57
155.52
160.16
158.04
148.42
150.70
135.26
134.63
132.23
132.55
134.13
136.94
141.73
165.68
162.48
145.86
142.19
137.30
131.71
133.67
133.81
127.48
128.10
134.32
135.83
151.87
158.87
163.86
158.58
140.13
136.87
134.20
126.19
122.52
124.20
133.87
136.53
148.90
151.19
151.29
149.06
138.80
134.77
135.43
141.19
126.77
126.43
131.00
134.00
138.13
151.06
158.61
144.03
139.57
128.74
127.20
125.90
122.06
127.23
135.13
144.83
134.94

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 Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284586&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284586&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284586&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 Ronald Aylmer Fisher' @ fisher.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean142.820595238095140.416785714286
Biased Variance198.592165121882124.228071811225
Biased Standard Deviation14.092273241811711.1457647477068
Covariance152.112523623064
Correlation0.956913871778821
Determination0.915684158002733
T-Test29.841811712023
p-value (2 sided)0
p-value (1 sided)0
95% CI of Correlation[0.934171107622084, 0.971913493843366]
Degrees of Freedom82
Number of Observations84

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 142.820595238095 & 140.416785714286 \tabularnewline
Biased Variance & 198.592165121882 & 124.228071811225 \tabularnewline
Biased Standard Deviation & 14.0922732418117 & 11.1457647477068 \tabularnewline
Covariance & 152.112523623064 \tabularnewline
Correlation & 0.956913871778821 \tabularnewline
Determination & 0.915684158002733 \tabularnewline
T-Test & 29.841811712023 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
95% CI of Correlation & [0.934171107622084, 0.971913493843366] \tabularnewline
Degrees of Freedom & 82 \tabularnewline
Number of Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284586&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]142.820595238095[/C][C]140.416785714286[/C][/ROW]
[ROW][C]Biased Variance[/C][C]198.592165121882[/C][C]124.228071811225[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]14.0922732418117[/C][C]11.1457647477068[/C][/ROW]
[ROW][C]Covariance[/C][C]152.112523623064[/C][/ROW]
[ROW][C]Correlation[/C][C]0.956913871778821[/C][/ROW]
[ROW][C]Determination[/C][C]0.915684158002733[/C][/ROW]
[ROW][C]T-Test[/C][C]29.841811712023[/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][0.934171107622084, 0.971913493843366][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]82[/C][/ROW]
[ROW][C]Number of Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284586&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284586&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
Mean142.820595238095140.416785714286
Biased Variance198.592165121882124.228071811225
Biased Standard Deviation14.092273241811711.1457647477068
Covariance152.112523623064
Correlation0.956913871778821
Determination0.915684158002733
T-Test29.841811712023
p-value (2 sided)0
p-value (1 sided)0
95% CI of Correlation[0.934171107622084, 0.971913493843366]
Degrees of Freedom82
Number of Observations84






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.9512, p-value = 0.03094
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 7.4587, p-value = 0.02401
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.1164, p-value = 0.006005

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.6968, p-value = 0.0002186


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.9512, p-value = 0.03094
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 7.4587, p-value = 0.02401
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.1164, p-value = 0.006005

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.6968, p-value = 0.0002186

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284586&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.9512, p-value = 0.03094
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 7.4587, p-value = 0.02401
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.1164, p-value = 0.006005

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.6968, p-value = 0.0002186

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284586&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284586&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 = 6.9512, p-value = 0.03094
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 7.4587, p-value = 0.02401
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.1164, p-value = 0.006005

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.6968, p-value = 0.0002186


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()