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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, 25 Oct 2017 12:47:00 +0200
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/Oct/25/t1508929583v7q3mqdjg7k5n80.htm/, Retrieved Sat, 11 May 2024 22:25:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308046, Retrieved Sat, 11 May 2024 22:25:32 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2017-10-25 10:47:00] [b4ce4907781ca48e64ab853e8b6ed861] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2570
2669
2450
2842
3440
2678
2981
2260
2844
2546
2456
2295
2379
2471
2057
2280
2351
2276
2548
2311
2201
2725
2408
2139
1898
2539
2070
2063
2565
2443
2196
2799
2076
2628
2292
2155
2476
2138
1854
2081
1795
1756
2237
1960
1829
2524
2077
2366
2185
2098
1836
1863
2044
2136
2931
3263
3328
3570
2313
1623
1316
1507
1419
1660
1790
1733
2086
1814
2241
1943
1773
2143
2087
1805
1913
2296
2500
2210
2526
2249
2024
2091
2045
1882
1831
1964
1763
1688
2149
1823
2094
2145
1791
1996
2097
1796
1963
2042
1746
2210
2968
3126
3708
3015
1569
1518
1393
1615
1777
1648
1463
1779
Dataseries Y:
Download CSV
Histogram 
2.88
2.62
2.39
1.7
1.96
2.2
1.87
1.61
1.63
1.23
1.21
1.49
1.64
1.67
1.77
1.81
1.78
1.28
1.29
1.37
1.12
1.5
2.24
2.95
3.08
3.46
3.65
4.39
4.16
5.21
5.8
5.9
5.39
5.47
4.72
3.14
2.63
2.32
1.93
0.62
0.6
-0.37
-1.1
-1.68
-0.77
-1.2
-0.97
-0.12
0.26
0.62
0.7
1.65
1.79
2.28
2.46
2.57
2.32
2.91
3.01
2.87
3.11
3.22
3.38
3.52
3.41
3.35
3.68
3.75
3.6
3.56
3.57
3.85
3.48
3.65
3.66
3.36
3.19
2.81
2.25
2.32
2.85
2.75
2.78
2.26
2.23
1.46
1.19
1.11
1
1.18
1.59
1.51
1.01
0.9
0.63
0.81
0.97
1.14
0.97
0.89
0.62
0.36
0.27
0.34
0.02
-0.12
0.09
-0.11
-0.38
-0.65
-0.4
-0.4

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308046&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]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308046&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308046&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 time4 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2195.660714285711.95089285714286
Biased Variance217080.8848852042.46015991709184
Biased Standard Deviation465.9193974124751.56848969301422
Covariance79.2812966537967
Correlation0.107518510627635
Determination0.011560230127585
T-Test1.1342387409363
p-value (2 sided)0.259160163857129
p-value (1 sided)0.129580081928565
95% CI of Correlation[-0.0796258546265897, 0.287341624909086]
Degrees of Freedom110
Number of Observations112

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2195.66071428571 & 1.95089285714286 \tabularnewline
Biased Variance & 217080.884885204 & 2.46015991709184 \tabularnewline
Biased Standard Deviation & 465.919397412475 & 1.56848969301422 \tabularnewline
Covariance & 79.2812966537967 \tabularnewline
Correlation & 0.107518510627635 \tabularnewline
Determination & 0.011560230127585 \tabularnewline
T-Test & 1.1342387409363 \tabularnewline
p-value (2 sided) & 0.259160163857129 \tabularnewline
p-value (1 sided) & 0.129580081928565 \tabularnewline
95% CI of Correlation & [-0.0796258546265897, 0.287341624909086] \tabularnewline
Degrees of Freedom & 110 \tabularnewline
Number of Observations & 112 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308046&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]2195.66071428571[/C][C]1.95089285714286[/C][/ROW]
[ROW][C]Biased Variance[/C][C]217080.884885204[/C][C]2.46015991709184[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]465.919397412475[/C][C]1.56848969301422[/C][/ROW]
[ROW][C]Covariance[/C][C]79.2812966537967[/C][/ROW]
[ROW][C]Correlation[/C][C]0.107518510627635[/C][/ROW]
[ROW][C]Determination[/C][C]0.011560230127585[/C][/ROW]
[ROW][C]T-Test[/C][C]1.1342387409363[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.259160163857129[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.129580081928565[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.0796258546265897, 0.287341624909086][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]110[/C][/ROW]
[ROW][C]Number of Observations[/C][C]112[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308046&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308046&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
Mean2195.660714285711.95089285714286
Biased Variance217080.8848852042.46015991709184
Biased Standard Deviation465.9193974124751.56848969301422
Covariance79.2812966537967
Correlation0.107518510627635
Determination0.011560230127585
T-Test1.1342387409363
p-value (2 sided)0.259160163857129
p-value (1 sided)0.129580081928565
95% CI of Correlation[-0.0796258546265897, 0.287341624909086]
Degrees of Freedom110
Number of Observations112






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 17.663, p-value = 0.0001461
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.56728, p-value = 0.753
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4115, p-value = 0.001134

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.25726, p-value = 0.7147


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 17.663, p-value = 0.0001461
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.56728, p-value = 0.753
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4115, p-value = 0.001134

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.25726, p-value = 0.7147

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308046&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 17.663, p-value = 0.0001461
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.56728, p-value = 0.753
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4115, p-value = 0.001134

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.25726, p-value = 0.7147

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308046&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308046&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 = 17.663, p-value = 0.0001461
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 0.56728, p-value = 0.753
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4115, p-value = 0.001134

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.25726, p-value = 0.7147


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()