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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, 07 Dec 2015 13:30:43 +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/Dec/07/t14494955378465wkhvzqfdmsu.htm/, Retrieved Thu, 16 May 2024 12:02:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285375, Retrieved Thu, 16 May 2024 12:02:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113

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 (loon en ...] [2015-12-07 13:30:43] [6a0dd4d79ba93e4b564fd6f93c05ce84] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2259
2358
2398
2494
2603
2629
2715
2796
2879
2977
3054
3129
3196
3243
Dataseries Y:
Download CSV
Histogram 
14389
15165
15728
16382
16155
15390
14213
14395
16602
14991
13711
13008
12301
11567

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'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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285375&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285375&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285375&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2766.4285714285714571.2142857143
Biased Variance97584.95918367352143152.31122449
Biased Standard Deviation312.3859138688451463.95092514213
Covariance-333215.252747253
Correlation-0.676584787144277
Determination0.457766974195066
T-Test-3.18287709385962
p-value (2 sided)0.00787900341744577
p-value (1 sided)0.00393950170872289
95% CI of Correlation[-0.88828569627508, -0.227770966079057]
Degrees of Freedom12
Number of Observations14

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2766.42857142857 & 14571.2142857143 \tabularnewline
Biased Variance & 97584.9591836735 & 2143152.31122449 \tabularnewline
Biased Standard Deviation & 312.385913868845 & 1463.95092514213 \tabularnewline
Covariance & -333215.252747253 \tabularnewline
Correlation & -0.676584787144277 \tabularnewline
Determination & 0.457766974195066 \tabularnewline
T-Test & -3.18287709385962 \tabularnewline
p-value (2 sided) & 0.00787900341744577 \tabularnewline
p-value (1 sided) & 0.00393950170872289 \tabularnewline
95% CI of Correlation & [-0.88828569627508, -0.227770966079057] \tabularnewline
Degrees of Freedom & 12 \tabularnewline
Number of Observations & 14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285375&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]2766.42857142857[/C][C]14571.2142857143[/C][/ROW]
[ROW][C]Biased Variance[/C][C]97584.9591836735[/C][C]2143152.31122449[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]312.385913868845[/C][C]1463.95092514213[/C][/ROW]
[ROW][C]Covariance[/C][C]-333215.252747253[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.676584787144277[/C][/ROW]
[ROW][C]Determination[/C][C]0.457766974195066[/C][/ROW]
[ROW][C]T-Test[/C][C]-3.18287709385962[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00787900341744577[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00393950170872289[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.88828569627508, -0.227770966079057][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]12[/C][/ROW]
[ROW][C]Number of Observations[/C][C]14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285375&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285375&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
Mean2766.4285714285714571.2142857143
Biased Variance97584.95918367352143152.31122449
Biased Standard Deviation312.3859138688451463.95092514213
Covariance-333215.252747253
Correlation-0.676584787144277
Determination0.457766974195066
T-Test-3.18287709385962
p-value (2 sided)0.00787900341744577
p-value (1 sided)0.00393950170872289
95% CI of Correlation[-0.88828569627508, -0.227770966079057]
Degrees of Freedom12
Number of Observations14






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.93721, p-value = 0.6259
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.86889, p-value = 0.6476
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.21342, p-value = 0.815

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.23518, p-value = 0.7431


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.93721, p-value = 0.6259
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.86889, p-value = 0.6476
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.21342, p-value = 0.815

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.23518, p-value = 0.7431

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285375&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.93721, p-value = 0.6259
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.86889, p-value = 0.6476
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.21342, p-value = 0.815

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.23518, p-value = 0.7431

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285375&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285375&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 = 0.93721, p-value = 0.6259
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.86889, p-value = 0.6476
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.21342, p-value = 0.815

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.23518, p-value = 0.7431


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()