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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 computationMon, 20 Jan 2020 06:59:52 +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/2020/Jan/20/t1579500173tkj8cywwjfatv5h.htm/, Retrieved Sat, 20 Apr 2024 11:31:49 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 20 Apr 2024 11:31:49 +0200
QR Codes:

Original text written by user:
IsPrivate?This computation is private
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5000
4400
7200
6786
4789
6030
6487
8745
3200
3200
5200
4000
4800
6160
5200
5733
6540
6400
5714
4800
4800
3200
5362
2440
6360
5359
2438
NA
NA
Dataseries Y:
Download CSV
Histogram 
5094.9
5459.9
5037.8
5476.7
3817.3
4768.6
4715.6
4569.6
4605.7
4718.1
5351.1
4950.5
3727.4
5592.0
5891.2
5951.6
5936.9
6363.6
5698.3
5306.4
4961.5
5484.3
5329.6
4711.9
5266.8
5121.7
5104.3
NA

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 time1 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean5197.888888888895148.64074074074
Biased Variance2131309.06172839349805.315006859
Biased Standard Deviation1459.90036020558591.443416572421
Covariance189079.366239316
Correlation0.210871216799279
Determination0.0444666700744084
T-Test1.07860986557911
p-value (2 sided)0.291059084973553
p-value (1 sided)0.145529542486776
95% CI of Correlation[-0.18387759783183, 0.547048031644156]
Degrees of Freedom25
Number of Observations27

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 5197.88888888889 & 5148.64074074074 \tabularnewline
Biased Variance & 2131309.06172839 & 349805.315006859 \tabularnewline
Biased Standard Deviation & 1459.90036020558 & 591.443416572421 \tabularnewline
Covariance & 189079.366239316 \tabularnewline
Correlation & 0.210871216799279 \tabularnewline
Determination & 0.0444666700744084 \tabularnewline
T-Test & 1.07860986557911 \tabularnewline
p-value (2 sided) & 0.291059084973553 \tabularnewline
p-value (1 sided) & 0.145529542486776 \tabularnewline
95% CI of Correlation & [-0.18387759783183, 0.547048031644156] \tabularnewline
Degrees of Freedom & 25 \tabularnewline
Number of Observations & 27 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]5197.88888888889[/C][C]5148.64074074074[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2131309.06172839[/C][C]349805.315006859[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1459.90036020558[/C][C]591.443416572421[/C][/ROW]
[ROW][C]Covariance[/C][C]189079.366239316[/C][/ROW]
[ROW][C]Correlation[/C][C]0.210871216799279[/C][/ROW]
[ROW][C]Determination[/C][C]0.0444666700744084[/C][/ROW]
[ROW][C]T-Test[/C][C]1.07860986557911[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.291059084973553[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.145529542486776[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.18387759783183, 0.547048031644156][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]25[/C][/ROW]
[ROW][C]Number of Observations[/C][C]27[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
Mean5197.888888888895148.64074074074
Biased Variance2131309.06172839349805.315006859
Biased Standard Deviation1459.90036020558591.443416572421
Covariance189079.366239316
Correlation0.210871216799279
Determination0.0444666700744084
T-Test1.07860986557911
p-value (2 sided)0.291059084973553
p-value (1 sided)0.145529542486776
95% CI of Correlation[-0.18387759783183, 0.547048031644156]
Degrees of Freedom25
Number of Observations27






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.0097065, p-value = 0.9952
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.89443, p-value = 0.6394
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.33717, p-value = 0.4789

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.30355, p-value = 0.5486


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.0097065, p-value = 0.9952
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.89443, p-value = 0.6394
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.33717, p-value = 0.4789

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.30355, p-value = 0.5486

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

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.0097065, p-value = 0.9952
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.89443, p-value = 0.6394
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.33717, p-value = 0.4789

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.30355, p-value = 0.5486

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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 = 0.0097065, p-value = 0.9952
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.89443, p-value = 0.6394
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.33717, p-value = 0.4789

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.30355, p-value = 0.5486


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()