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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationTue, 01 Dec 2015 17:06:36 +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/01/t1448989927kf7dnpoerc90n95.htm/, Retrieved Thu, 16 May 2024 12:33:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284754, Retrieved Thu, 16 May 2024 12:33:04 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [] [2015-10-17 09:48:33] [32b17a345b130fdf5cc88718ed94a974]
-    D    [Pearson Correlation] [Pearson correlati...] [2015-12-01 17:06:36] [9b4ece21719e6dde02765eb8dee9496c] [Current]
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Dataseries X:
171380
177473.4
165059.4
158175.7
153155.4
144994.8
106958.9
97058.6
99808.1
119600.6
149046.5
188476
178732.3
181605.1
173177.1
179099.9
179348.89339697
144680.08230441
148367.70434949
168071.0425
193012.88904801
191411.36288073
196388.75630231
191021.81435966
174411.97514088
170438.0524583
203938.35976364
216839.63785332
188331.62729734
204329.32479922
231760.56242659
241635.15924967
Dataseries Y:
217829
240241.7
239051.7
246464.5
228891.1
197867.6
162481.3
148509.1
145747.7
159647.4
185979
216834.9
210560
222582
201903.3
204623.8
195642.43812383
163769.45144036
138633.38717802
163999.575
171293.7542423
188909.78914584
194603.50086402
192177.71723536
178592.93454859
163221.72832722
175648.43522185
189041.70871173
158366.10619425
164943.77237346
185048.7637639
181858.23081587




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284754&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284754&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284754&T=0

As an alternative you can also use a 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'Herman Ole Andreas Wold' @ wold.wessa.net







Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean171493.407629079188592.668537081
Biased Variance1126810089.94772797604808.587206
Biased Standard Deviation33567.992045216528241.8981052479
Covariance261083485.929905
Correlation0.266791428734409
Determination0.0711776664461473
T-Test1.51623380586754
p-value (2 sided)0.139927626277664
p-value (1 sided)0.0699638131388319
95% CI of Correlation[-0.0903033303748818, 0.563100928890204]
Degrees of Freedom30
Number of Observations32

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 171493.407629079 & 188592.668537081 \tabularnewline
Biased Variance & 1126810089.94772 & 797604808.587206 \tabularnewline
Biased Standard Deviation & 33567.9920452165 & 28241.8981052479 \tabularnewline
Covariance & 261083485.929905 \tabularnewline
Correlation & 0.266791428734409 \tabularnewline
Determination & 0.0711776664461473 \tabularnewline
T-Test & 1.51623380586754 \tabularnewline
p-value (2 sided) & 0.139927626277664 \tabularnewline
p-value (1 sided) & 0.0699638131388319 \tabularnewline
95% CI of Correlation & [-0.0903033303748818, 0.563100928890204] \tabularnewline
Degrees of Freedom & 30 \tabularnewline
Number of Observations & 32 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284754&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]171493.407629079[/C][C]188592.668537081[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1126810089.94772[/C][C]797604808.587206[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]33567.9920452165[/C][C]28241.8981052479[/C][/ROW]
[ROW][C]Covariance[/C][C]261083485.929905[/C][/ROW]
[ROW][C]Correlation[/C][C]0.266791428734409[/C][/ROW]
[ROW][C]Determination[/C][C]0.0711776664461473[/C][/ROW]
[ROW][C]T-Test[/C][C]1.51623380586754[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.139927626277664[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0699638131388319[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.0903033303748818, 0.563100928890204][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]30[/C][/ROW]
[ROW][C]Number of Observations[/C][C]32[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284754&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284754&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean171493.407629079188592.668537081
Biased Variance1126810089.94772797604808.587206
Biased Standard Deviation33567.992045216528241.8981052479
Covariance261083485.929905
Correlation0.266791428734409
Determination0.0711776664461473
T-Test1.51623380586754
p-value (2 sided)0.139927626277664
p-value (1 sided)0.0699638131388319
95% CI of Correlation[-0.0903033303748818, 0.563100928890204]
Degrees of Freedom30
Number of Observations32







Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.87242, p-value = 0.6465
alternative hypothesis: greater
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.2233, p-value = 0.5425
alternative hypothesis: greater
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5192, p-value = 0.1734
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.28763, p-value = 0.5972

\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.87242, p-value = 0.6465
alternative hypothesis: greater
\tabularnewline
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.2233, p-value = 0.5425
alternative hypothesis: greater
\tabularnewline
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5192, p-value = 0.1734
\tabularnewline
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.28763, p-value = 0.5972
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=284754&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.87242, p-value = 0.6465
alternative hypothesis: greater
[/C][/ROW] [ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.2233, p-value = 0.5425
alternative hypothesis: greater
[/C][/ROW] [ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5192, p-value = 0.1734
[/C][/ROW] [ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.28763, p-value = 0.5972
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=284754&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284754&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.87242, p-value = 0.6465
alternative hypothesis: greater
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.2233, p-value = 0.5425
alternative hypothesis: greater
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.5192, p-value = 0.1734
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.28763, p-value = 0.5972



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()