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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 computationThu, 17 Dec 2015 14:06:27 +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/17/t1450361324cm6spzzs414se9w.htm/, Retrieved Thu, 16 May 2024 11:25:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286807, Retrieved Thu, 16 May 2024 11:25:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2015-12-17 14:06:27] [7b81fac622814275349f5d25cf6bd6bd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104
81
101
92
83
101
64
57
108
121
99
109
96
88
91
71
85
93
64
48
96
95
74
91
Dataseries Y:
Download CSV
Histogram 
33
40
38
47
32
46
51
11
68
39
27
40
25
27
32
25
35
37
18
18
58
38
27
48

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=286807&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=286807&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286807&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
Mean8835.8333333333333
Biased Variance298.416666666667164.472222222222
Biased Standard Deviation17.274740711995312.8246724021404
Covariance125.304347826087
Correlation0.542031987947043
Determination0.293798675957823
T-Test3.02532470449471
p-value (2 sided)0.0062183012467758
p-value (1 sided)0.0031091506233879
95% CI of Correlation[0.177431335265508, 0.775797526915802]
Degrees of Freedom22
Number of Observations24

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 88 & 35.8333333333333 \tabularnewline
Biased Variance & 298.416666666667 & 164.472222222222 \tabularnewline
Biased Standard Deviation & 17.2747407119953 & 12.8246724021404 \tabularnewline
Covariance & 125.304347826087 \tabularnewline
Correlation & 0.542031987947043 \tabularnewline
Determination & 0.293798675957823 \tabularnewline
T-Test & 3.02532470449471 \tabularnewline
p-value (2 sided) & 0.0062183012467758 \tabularnewline
p-value (1 sided) & 0.0031091506233879 \tabularnewline
95% CI of Correlation & [0.177431335265508, 0.775797526915802] \tabularnewline
Degrees of Freedom & 22 \tabularnewline
Number of Observations & 24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286807&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]88[/C][C]35.8333333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]298.416666666667[/C][C]164.472222222222[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]17.2747407119953[/C][C]12.8246724021404[/C][/ROW]
[ROW][C]Covariance[/C][C]125.304347826087[/C][/ROW]
[ROW][C]Correlation[/C][C]0.542031987947043[/C][/ROW]
[ROW][C]Determination[/C][C]0.293798675957823[/C][/ROW]
[ROW][C]T-Test[/C][C]3.02532470449471[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0062183012467758[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0031091506233879[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.177431335265508, 0.775797526915802][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]22[/C][/ROW]
[ROW][C]Number of Observations[/C][C]24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286807&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286807&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
Mean8835.8333333333333
Biased Variance298.416666666667164.472222222222
Biased Standard Deviation17.274740711995312.8246724021404
Covariance125.304347826087
Correlation0.542031987947043
Determination0.293798675957823
T-Test3.02532470449471
p-value (2 sided)0.0062183012467758
p-value (1 sided)0.0031091506233879
95% CI of Correlation[0.177431335265508, 0.775797526915802]
Degrees of Freedom22
Number of Observations24






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1472, p-value = 0.5635
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.69036, p-value = 0.7081
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.42842, p-value = 0.2861

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.2272, p-value = 0.7916


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1472, p-value = 0.5635
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.69036, p-value = 0.7081
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.42842, p-value = 0.2861

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.2272, p-value = 0.7916

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286807&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1472, p-value = 0.5635
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.69036, p-value = 0.7081
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.42842, p-value = 0.2861

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.2272, p-value = 0.7916

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286807&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286807&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 = 1.1472, p-value = 0.5635
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.69036, p-value = 0.7081
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.42842, p-value = 0.2861

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.2272, p-value = 0.7916


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()