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 computationSun, 03 Dec 2017 20:16:53 +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/03/t15123286543osp8ovjclicezp.htm/, Retrieved Tue, 14 May 2024 23:38:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308484, Retrieved Tue, 14 May 2024 23:38:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94

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 Correlati...] [2017-12-03 19:16:53] [dc50920429733eb8e80244e6ce50bf79] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
Dataseries Y:
Download CSV
Histogram 
0
0
3
7
8
16
16
23
36
74
113
204
313
325
300
424
455
540

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308484&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]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308484&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308484&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 time4 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean42.5158.722222222222
Biased Variance672.91666666666732269.200617284
Biased Standard Deviation25.9406373604556179.636300945226
Covariance4541.32352941176
Correlation0.920415901116216
Determination0.847165431027576
T-Test9.41744962997331
p-value (2 sided)6.28965583585571e-08
p-value (1 sided)3.14482791792786e-08
95% CI of Correlation[0.795296283075185, 0.970323683060864]
Degrees of Freedom16
Number of Observations18

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 42.5 & 158.722222222222 \tabularnewline
Biased Variance & 672.916666666667 & 32269.200617284 \tabularnewline
Biased Standard Deviation & 25.9406373604556 & 179.636300945226 \tabularnewline
Covariance & 4541.32352941176 \tabularnewline
Correlation & 0.920415901116216 \tabularnewline
Determination & 0.847165431027576 \tabularnewline
T-Test & 9.41744962997331 \tabularnewline
p-value (2 sided) & 6.28965583585571e-08 \tabularnewline
p-value (1 sided) & 3.14482791792786e-08 \tabularnewline
95% CI of Correlation & [0.795296283075185, 0.970323683060864] \tabularnewline
Degrees of Freedom & 16 \tabularnewline
Number of Observations & 18 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308484&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]42.5[/C][C]158.722222222222[/C][/ROW]
[ROW][C]Biased Variance[/C][C]672.916666666667[/C][C]32269.200617284[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]25.9406373604556[/C][C]179.636300945226[/C][/ROW]
[ROW][C]Covariance[/C][C]4541.32352941176[/C][/ROW]
[ROW][C]Correlation[/C][C]0.920415901116216[/C][/ROW]
[ROW][C]Determination[/C][C]0.847165431027576[/C][/ROW]
[ROW][C]T-Test[/C][C]9.41744962997331[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]6.28965583585571e-08[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]3.14482791792786e-08[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.795296283075185, 0.970323683060864][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]16[/C][/ROW]
[ROW][C]Number of Observations[/C][C]18[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308484&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308484&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
Mean42.5158.722222222222
Biased Variance672.91666666666732269.200617284
Biased Standard Deviation25.9406373604556179.636300945226
Covariance4541.32352941176
Correlation0.920415901116216
Determination0.847165431027576
T-Test9.41744962997331
p-value (2 sided)6.28965583585571e-08
p-value (1 sided)3.14482791792786e-08
95% CI of Correlation[0.795296283075185, 0.970323683060864]
Degrees of Freedom16
Number of Observations18






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.0934, p-value = 0.5789
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.4113, p-value = 0.2995
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.2021, p-value = 0.8564

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4061, p-value = 0.0008388


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.0934, p-value = 0.5789
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.4113, p-value = 0.2995
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.2021, p-value = 0.8564

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4061, p-value = 0.0008388

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308484&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.0934, p-value = 0.5789
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.4113, p-value = 0.2995
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.2021, p-value = 0.8564

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4061, p-value = 0.0008388

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308484&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308484&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 = 1.0934, p-value = 0.5789
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.4113, p-value = 0.2995
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.2021, p-value = 0.8564

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4061, p-value = 0.0008388


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()