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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationFri, 12 Aug 2016 22:01:16 +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/2016/Aug/12/t1471035793khoi52jf558ez2a.htm/, Retrieved Sun, 05 May 2024 13:49:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296479, Retrieved Sun, 05 May 2024 13:49:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Correlación entre...] [2016-08-12 21:01:16] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
72
107
66
66
38
34
72
33
29
11
36
25
26
54
93
72
43
17
18
45
50
40
132
48
37
72
74
164
73
70
111
107
112
81
37
88
63
36
40
20
34
280
179
Dataseries Y:
Download CSV
Histogram 
56
83
74
75
72
50
43
55
68
70
60
43
51
49
46
76
57
40
67
59
42
36
64
69
64
51
63
46
198
201
58
78
66
54
70
39
49
44
64
45
46
54
39

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 Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296479&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296479&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296479&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 Maurice George Kendall' @ kendall.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean67.558139534883763.5813953488372
Biased Variance2478.804759329371046.38290968091
Biased Standard Deviation49.787596440573132.3478424269828
Covariance12.3582502768549
Correlation0.00749499489647498
Determination5.6174948498186e-05
T-Test0.0479927314945958
p-value (2 sided)0.961955060306228
p-value (1 sided)0.480977530153114
95% CI of Correlation[-0.29350957825679, 0.307147443621097]
Degrees of Freedom41
Number of Observations43

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 67.5581395348837 & 63.5813953488372 \tabularnewline
Biased Variance & 2478.80475932937 & 1046.38290968091 \tabularnewline
Biased Standard Deviation & 49.7875964405731 & 32.3478424269828 \tabularnewline
Covariance & 12.3582502768549 \tabularnewline
Correlation & 0.00749499489647498 \tabularnewline
Determination & 5.6174948498186e-05 \tabularnewline
T-Test & 0.0479927314945958 \tabularnewline
p-value (2 sided) & 0.961955060306228 \tabularnewline
p-value (1 sided) & 0.480977530153114 \tabularnewline
95% CI of Correlation & [-0.29350957825679, 0.307147443621097] \tabularnewline
Degrees of Freedom & 41 \tabularnewline
Number of Observations & 43 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296479&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]67.5581395348837[/C][C]63.5813953488372[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2478.80475932937[/C][C]1046.38290968091[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]49.7875964405731[/C][C]32.3478424269828[/C][/ROW]
[ROW][C]Covariance[/C][C]12.3582502768549[/C][/ROW]
[ROW][C]Correlation[/C][C]0.00749499489647498[/C][/ROW]
[ROW][C]Determination[/C][C]5.6174948498186e-05[/C][/ROW]
[ROW][C]T-Test[/C][C]0.0479927314945958[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.961955060306228[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.480977530153114[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.29350957825679, 0.307147443621097][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]41[/C][/ROW]
[ROW][C]Number of Observations[/C][C]43[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296479&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296479&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
Mean67.558139534883763.5813953488372
Biased Variance2478.804759329371046.38290968091
Biased Standard Deviation49.787596440573132.3478424269828
Covariance12.3582502768549
Correlation0.00749499489647498
Determination5.6174948498186e-05
T-Test0.0479927314945958
p-value (2 sided)0.961955060306228
p-value (1 sided)0.480977530153114
95% CI of Correlation[-0.29350957825679, 0.307147443621097]
Degrees of Freedom41
Number of Observations43






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 95.494, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 321.4, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.173, p-value = 1.298e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 5.2505, p-value = 3.404e-13


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 95.494, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 321.4, p-value < 2.2e-16
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.173, p-value = 1.298e-05

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 5.2505, p-value = 3.404e-13

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296479&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 95.494, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 321.4, p-value < 2.2e-16
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.173, p-value = 1.298e-05

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 5.2505, p-value = 3.404e-13

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296479&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296479&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 = 95.494, p-value < 2.2e-16
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 321.4, p-value < 2.2e-16
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.173, p-value = 1.298e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 5.2505, p-value = 3.404e-13


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()