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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 computationFri, 27 Nov 2015 21:34:46 +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/Nov/27/t14486605141aczbqy80yw1acr.htm/, Retrieved Wed, 15 May 2024 03:28:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284332, Retrieved Wed, 15 May 2024 03:28:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pizza Businesses] [2015-11-27 21:34:46] [973db046713346d64b5601c33e0811b1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1000
1125
1087
1070
1100
1150
1250
1150
1100
1350
1275
1375
1175
1200
1175
1300
1260
1330
1325
1200
1225
1090
1075
1080
1080
1180
1225
1175
1250
1250
750
1125
700
900
900
850
Dataseries Y:
Download CSV
Histogram 
1050
1150
1213
1275
1300
1300
1400
1400
1250
1830
1350
1450
1300
1300
1275
1375
1285
1400
1400
1285
1275
1135
1250
1275
1150
1250
1275
1225
1280
1300
1250
1175
1300
1250
1300
1200

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284332&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284332&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284332&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1134.777777777781291.05555555556
Biased Variance24450.061728395114962.8858024691
Biased Standard Deviation156.365155096636122.322875221559
Covariance9384.4126984127
Correlation0.477007251680213
Determination0.22753591815551
T-Test3.16464713745592
p-value (2 sided)0.00326626648694783
p-value (1 sided)0.00163313324347392
95% CI of Correlation[0.176063045389467, 0.696406405368175]
Degrees of Freedom34
Number of Observations36

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1134.77777777778 & 1291.05555555556 \tabularnewline
Biased Variance & 24450.0617283951 & 14962.8858024691 \tabularnewline
Biased Standard Deviation & 156.365155096636 & 122.322875221559 \tabularnewline
Covariance & 9384.4126984127 \tabularnewline
Correlation & 0.477007251680213 \tabularnewline
Determination & 0.22753591815551 \tabularnewline
T-Test & 3.16464713745592 \tabularnewline
p-value (2 sided) & 0.00326626648694783 \tabularnewline
p-value (1 sided) & 0.00163313324347392 \tabularnewline
95% CI of Correlation & [0.176063045389467, 0.696406405368175] \tabularnewline
Degrees of Freedom & 34 \tabularnewline
Number of Observations & 36 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284332&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]1134.77777777778[/C][C]1291.05555555556[/C][/ROW]
[ROW][C]Biased Variance[/C][C]24450.0617283951[/C][C]14962.8858024691[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]156.365155096636[/C][C]122.322875221559[/C][/ROW]
[ROW][C]Covariance[/C][C]9384.4126984127[/C][/ROW]
[ROW][C]Correlation[/C][C]0.477007251680213[/C][/ROW]
[ROW][C]Determination[/C][C]0.22753591815551[/C][/ROW]
[ROW][C]T-Test[/C][C]3.16464713745592[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00326626648694783[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00163313324347392[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.176063045389467, 0.696406405368175][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]34[/C][/ROW]
[ROW][C]Number of Observations[/C][C]36[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284332&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284332&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
Mean1134.777777777781291.05555555556
Biased Variance24450.061728395114962.8858024691
Biased Standard Deviation156.365155096636122.322875221559
Covariance9384.4126984127
Correlation0.477007251680213
Determination0.22753591815551
T-Test3.16464713745592
p-value (2 sided)0.00326626648694783
p-value (1 sided)0.00163313324347392
95% CI of Correlation[0.176063045389467, 0.696406405368175]
Degrees of Freedom34
Number of Observations36






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.8558, p-value = 0.03246
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 129.17, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.91414, p-value = 0.01783

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.845, p-value = 8.183e-05


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.8558, p-value = 0.03246
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 129.17, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.91414, p-value = 0.01783

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.845, p-value = 8.183e-05

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284332&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 6.8558, p-value = 0.03246
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 129.17, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.91414, p-value = 0.01783

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.845, p-value = 8.183e-05

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284332&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284332&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 = 6.8558, p-value = 0.03246
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 129.17, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.91414, p-value = 0.01783

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.845, p-value = 8.183e-05


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()