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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, 26 Nov 2018 12:11:43 +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/2018/Nov/26/t1543230753ccsdc5c1c94d3lc.htm/, Retrieved Fri, 03 May 2024 00:15:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=315701, Retrieved Fri, 03 May 2024 00:15:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130

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 Corr] [2018-11-26 11:11:43] [ed325faff554f097403cb8f6ee07a063] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
78
79
81
80
76
78
82
79
76
79
82
85
86
83
84
82
80
78
84
86
85
87
94
92
95
96
94
96
91
90
Dataseries Y:
Download CSV
Histogram 
41
56
63
68
69
65
61
47
32
24
28
26
32
40
55
63
72
72
67
60
44
40
32
27
28
33
41
52
64
71

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time9 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 time9 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315701&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]9 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=315701&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315701&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 time9 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean84.649.1
Biased Variance37.7066666666667260.69
Biased Standard Deviation6.1405754344903816.1458973117012
Covariance-33.3034482758621
Correlation-0.324709271597262
Determination0.105436111061225
T-Test-1.81663644911232
p-value (2 sided)0.0799929917763979
p-value (1 sided)0.039996495888199
95% CI of Correlation[-0.613239989600027, 0.0402709587769368]
Degrees of Freedom28
Number of Observations30

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 84.6 & 49.1 \tabularnewline
Biased Variance & 37.7066666666667 & 260.69 \tabularnewline
Biased Standard Deviation & 6.14057543449038 & 16.1458973117012 \tabularnewline
Covariance & -33.3034482758621 \tabularnewline
Correlation & -0.324709271597262 \tabularnewline
Determination & 0.105436111061225 \tabularnewline
T-Test & -1.81663644911232 \tabularnewline
p-value (2 sided) & 0.0799929917763979 \tabularnewline
p-value (1 sided) & 0.039996495888199 \tabularnewline
95% CI of Correlation & [-0.613239989600027, 0.0402709587769368] \tabularnewline
Degrees of Freedom & 28 \tabularnewline
Number of Observations & 30 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315701&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]84.6[/C][C]49.1[/C][/ROW]
[ROW][C]Biased Variance[/C][C]37.7066666666667[/C][C]260.69[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]6.14057543449038[/C][C]16.1458973117012[/C][/ROW]
[ROW][C]Covariance[/C][C]-33.3034482758621[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.324709271597262[/C][/ROW]
[ROW][C]Determination[/C][C]0.105436111061225[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.81663644911232[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0799929917763979[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.039996495888199[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.613239989600027, 0.0402709587769368][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]28[/C][/ROW]
[ROW][C]Number of Observations[/C][C]30[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315701&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315701&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
Mean84.649.1
Biased Variance37.7066666666667260.69
Biased Standard Deviation6.1405754344903816.1458973117012
Covariance-33.3034482758621
Correlation-0.324709271597262
Determination0.105436111061225
T-Test-1.81663644911232
p-value (2 sided)0.0799929917763979
p-value (1 sided)0.039996495888199
95% CI of Correlation[-0.613239989600027, 0.0402709587769368]
Degrees of Freedom28
Number of Observations30






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.4956, p-value = 0.2871
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.839, p-value = 0.2418
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.81204, p-value = 0.03153

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.95166, p-value = 0.01397


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.4956, p-value = 0.2871
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.839, p-value = 0.2418
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.81204, p-value = 0.03153

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.95166, p-value = 0.01397

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315701&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.4956, p-value = 0.2871
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.839, p-value = 0.2418
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.81204, p-value = 0.03153

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.95166, p-value = 0.01397

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315701&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315701&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 = 2.4956, p-value = 0.2871
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.839, p-value = 0.2418
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.81204, p-value = 0.03153

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.95166, p-value = 0.01397


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()