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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 computationWed, 20 Dec 2017 21:59:57 +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/2017/Dec/20/t1513803617deuychf3tq1cjpa.htm/, Retrieved Tue, 14 May 2024 18:57:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310576, Retrieved Tue, 14 May 2024 18:57:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2017-12-20 20:59:57] [e36c7bc72502ffca4997d79eaba3af3f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
35
34
55
30
44
32
31
36
37
29
45
59
57
42
46
47
39
37
56
35
34
55
30
44
32
31
36
37
29
45
59
56
42
46
47
39
37
56
35
34
55
30
44
32
31
36
37
29
45
59
55
42
46
47
39
37
56
29
28
29
Dataseries Y:
Download CSV
Histogram 
366
293
0
274
360
304
266
202
225
207
251
0
0
226
288
339
378
313
0
393
293
0
374
249
349
252
320
282
339
298
0
0
269
287
380
277
380
0
215
241
0
368
290
274
337
335
205
311
355
0
0
295
226
276
348
387
0
305
294
364

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310576&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]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310576&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310576&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 time3 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean40.9333333333333241
Biased Variance90.095555555555516830.5333333333
Biased Standard Deviation9.49186786441718129.732545389865
Covariance-970.389830508475
Correlation-0.774901273915053
Determination0.600471984315172
T-Test-9.33655699052541
p-value (2 sided)3.70923169680944e-13
p-value (1 sided)1.85461584840472e-13
95% CI of Correlation[-0.859671382450492, -0.64859921852785]
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 40.9333333333333 & 241 \tabularnewline
Biased Variance & 90.0955555555555 & 16830.5333333333 \tabularnewline
Biased Standard Deviation & 9.49186786441718 & 129.732545389865 \tabularnewline
Covariance & -970.389830508475 \tabularnewline
Correlation & -0.774901273915053 \tabularnewline
Determination & 0.600471984315172 \tabularnewline
T-Test & -9.33655699052541 \tabularnewline
p-value (2 sided) & 3.70923169680944e-13 \tabularnewline
p-value (1 sided) & 1.85461584840472e-13 \tabularnewline
95% CI of Correlation & [-0.859671382450492, -0.64859921852785] \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310576&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]40.9333333333333[/C][C]241[/C][/ROW]
[ROW][C]Biased Variance[/C][C]90.0955555555555[/C][C]16830.5333333333[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]9.49186786441718[/C][C]129.732545389865[/C][/ROW]
[ROW][C]Covariance[/C][C]-970.389830508475[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.774901273915053[/C][/ROW]
[ROW][C]Determination[/C][C]0.600471984315172[/C][/ROW]
[ROW][C]T-Test[/C][C]-9.33655699052541[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]3.70923169680944e-13[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.85461584840472e-13[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.859671382450492, -0.64859921852785][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310576&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310576&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
Mean40.9333333333333241
Biased Variance90.095555555555516830.5333333333
Biased Standard Deviation9.49186786441718129.732545389865
Covariance-970.389830508475
Correlation-0.774901273915053
Determination0.600471984315172
T-Test-9.33655699052541
p-value (2 sided)3.70923169680944e-13
p-value (1 sided)1.85461584840472e-13
95% CI of Correlation[-0.859671382450492, -0.64859921852785]
Degrees of Freedom58
Number of Observations60






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.8952, p-value = 0.0865
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 10.643, p-value = 0.004885
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6674, p-value = 0.0002492

> ad.y
	Anderson-Darling normality test
data:  y
A = 4.6432, p-value = 1.194e-11


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.8952, p-value = 0.0865
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 10.643, p-value = 0.004885
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6674, p-value = 0.0002492

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 4.6432, p-value = 1.194e-11

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310576&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 4.8952, p-value = 0.0865
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 10.643, p-value = 0.004885
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6674, p-value = 0.0002492

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 4.6432, p-value = 1.194e-11

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310576&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310576&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 = 4.8952, p-value = 0.0865
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 10.643, p-value = 0.004885
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.6674, p-value = 0.0002492

> ad.y
	Anderson-Darling normality test
data:  y
A = 4.6432, p-value = 1.194e-11


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()