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 20:24:47 +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/t1512329114rpejvhoq6g6tkt8.htm/, Retrieved Tue, 14 May 2024 21:40:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308487, Retrieved Tue, 14 May 2024 21:40:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102

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 19:24:47] [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
0
1
9
40
141
302
558
971
1177
1200
11302
1319
958
927
773
700

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308487&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]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308487&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308487&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 time5 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean42.51132.11111111111
Biased Variance672.9166666666676303429.32098765
Biased Standard Deviation25.94063736045562510.66312375588
Covariance21327.9411764706
Correlation0.309283153106643
Determination0.0956560687955872
T-Test1.30091655789173
p-value (2 sided)0.211711340763203
p-value (1 sided)0.105855670381602
95% CI of Correlation[-0.18418187069964, 0.678221412965399]
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 & 1132.11111111111 \tabularnewline
Biased Variance & 672.916666666667 & 6303429.32098765 \tabularnewline
Biased Standard Deviation & 25.9406373604556 & 2510.66312375588 \tabularnewline
Covariance & 21327.9411764706 \tabularnewline
Correlation & 0.309283153106643 \tabularnewline
Determination & 0.0956560687955872 \tabularnewline
T-Test & 1.30091655789173 \tabularnewline
p-value (2 sided) & 0.211711340763203 \tabularnewline
p-value (1 sided) & 0.105855670381602 \tabularnewline
95% CI of Correlation & [-0.18418187069964, 0.678221412965399] \tabularnewline
Degrees of Freedom & 16 \tabularnewline
Number of Observations & 18 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308487&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]1132.11111111111[/C][/ROW]
[ROW][C]Biased Variance[/C][C]672.916666666667[/C][C]6303429.32098765[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]25.9406373604556[/C][C]2510.66312375588[/C][/ROW]
[ROW][C]Covariance[/C][C]21327.9411764706[/C][/ROW]
[ROW][C]Correlation[/C][C]0.309283153106643[/C][/ROW]
[ROW][C]Determination[/C][C]0.0956560687955872[/C][/ROW]
[ROW][C]T-Test[/C][C]1.30091655789173[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.211711340763203[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.105855670381602[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.18418187069964, 0.678221412965399][/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=308487&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308487&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
Mean42.51132.11111111111
Biased Variance672.9166666666676303429.32098765
Biased Standard Deviation25.94063736045562510.66312375588
Covariance21327.9411764706
Correlation0.309283153106643
Determination0.0956560687955872
T-Test1.30091655789173
p-value (2 sided)0.211711340763203
p-value (1 sided)0.105855670381602
95% CI of Correlation[-0.18418187069964, 0.678221412965399]
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 = 147.6, p-value < 2.2e-16
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 = 4.0325, p-value = 1.667e-10


\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 = 147.6, p-value < 2.2e-16
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 = 4.0325, p-value = 1.667e-10

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308487&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 = 147.6, p-value < 2.2e-16
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 = 4.0325, p-value = 1.667e-10

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308487&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308487&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 = 147.6, p-value < 2.2e-16
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 = 4.0325, p-value = 1.667e-10


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()