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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 computationSun, 19 Oct 2008 07:19:52 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/19/t1224422477crr2byuasmm5kbf.htm/, Retrieved Sun, 19 May 2024 16:38:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16819, Retrieved Sun, 19 May 2024 16:38:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Pearson Correlation] [Q5 Clothing Produ...] [2008-10-19 13:19:52] [6912578025c824de531bc660dd61b996] [Current]
-         [Pearson Correlation] [Q5] [2008-10-20 18:57:34] [b47fceb71c9525e79a89b5fc6d023d0e]
Feedback Forum
2008-10-21 18:41:04 [Stefan Eyckmans] [reply] 
Hier is inderdaad sprake van bijna geen correlatie. Je moet natuurlijk
altijd wel oppassen met outliers omdat die dit resultaat zwaar kunnen verstoren.
2008-10-24 20:59:07 [Kenny Simons] [reply] 
Stefan heeft gelijk, als je naar het plot ziet, zal je opmerken dat 2 outliers ons plot beïnvloeden. Als we deze outliers eruit hadden gelaten, hadden we wel degelijk een positieve relatie gehad tussen deze tijdreeksen.
2008-10-26 11:30:37 [Natascha Meeus] [reply] 
Ik ga eveneens akkoord met de bovenstaande bevindingen. Als de twee outliers linksboven niet aanwezig waren hadden we wel te maken met positieve correlatie.
2008-10-26 11:48:12 [Matthieu Blondeau] [reply] 
Ook hier ga ik helemaal akkoord met de gegeven commentaren. De outliers hebben inderdaad de uitkomst beinvloedt.
2008-10-26 17:34:38 [Chi-Kwong Man] [reply] 
Correlation = 0.0425212799870432 duidt op bijna geen correlatie.
2008-10-27 07:43:10 [c4ccf1f44d59ce687616256b9e80d6b0] [reply] 
Er is inderdaad zo goed als geen correlatie. De punten die helemaal op zichzelf staan zijn outliers. Deze beïnvloeden de correlatie. Door de outliers is er +/- geen correlatie.
2008-10-27 11:00:53 [Kim De Vos] [reply] 
De correlatiecoefficient bedraagt hier 0.42.. wat duidt op het feit dat er geen correlatie is. Dit wordt veroorzaakt door de aanwezigheid van de outliers, indien deze er niet aanwezig waren kan me spreken van een positieve correlatie.
2008-10-27 18:42:06 [Jeroen Michel] [reply] 
De student heeft het hier inderdaad bij het rechte eind. Het is wel belangrijk te stellen dat wanneer de outliers gefilterd worden er een positievere correlatie ontstaat. De correlatie in dit geval is zéér laag.
2008-10-27 19:09:49 [Niels Stas] [reply] 
De correlatie is enorm laag, waardoor er normaal maar een heel klein of zelfs geen verband bestaat. Nu zoals voorgaand al vermeld is, zijn er enkele outliers die zorgen voor een minder nauwkeurig resultaat. Indien je deze kan wegwerken zal het resultaat lichtjes wijzigen.
2008-10-28 06:48:50 [Nilay Erdogdu] [reply] 
Wanneer we een denkbeeldige rechte willen tekenen doorheen de scatterplot, zien we dat deze zo goed als horizontaal komt te liggen. Dit komt vooral door de 2 outliers in de linkerbovenhoek. Ik moet weinig veranderen en de correlatie wordt negatief.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
109,20
88,60
94,30
98,30
86,40
80,60
104,10
108,20
93,40
71,90
94,10
94,90
96,40
91,10
84,40
86,40
88,00
75,10
109,70
103,00
82,10
68,00
96,40
94,30
90,00
88,00
76,10
82,50
81,40
66,50
97,20
94,10
80,70
70,50
87,80
89,50
99,60
84,20
75,10
92,00
80,80
73,10
99,80
90,00
83,10
72,40
78,80
87,30
91,00
80,10
73,60
86,40
74,50
71,20
92,40
81,50
85,30
69,90
84,20
90,70
100,30
Dataseries Y:
Download CSV
Histogram 
72,50
59,40
85,70
88,20
62,80
87,00
79,20
112,00
79,20
132,10
40,10
69,00
59,40
73,80
57,40
81,10
46,60
41,40
71,20
67,90
72,00
145,50
39,70
51,90
73,70
70,90
60,80
61,00
54,50
39,10
66,60
58,50
59,80
80,90
37,30
44,60
48,70
54,00
49,50
61,60
35,00
35,70
51,30
49,00
41,50
72,50
42,10
44,10
45,10
50,30
40,90
47,20
36,90
40,90
38,30
46,30
28,40
78,40
36,80
50,70
42,80

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16819&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16819&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16819&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean86.893442622950859.8491803278689
Biased Variance109.891760279495494.798892770761
Biased Standard Deviation10.482927085480222.2440754532698
Covariance10.0804945355191
Correlation0.0425212799870432
Determination0.00180805925173652
T-Test0.326907817024733
p-value (2 sided)0.744894582950823
p-value (1 sided)0.372447291475412
Degrees of Freedom59
Number of Observations61

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 86.8934426229508 & 59.8491803278689 \tabularnewline
Biased Variance & 109.891760279495 & 494.798892770761 \tabularnewline
Biased Standard Deviation & 10.4829270854802 & 22.2440754532698 \tabularnewline
Covariance & 10.0804945355191 \tabularnewline
Correlation & 0.0425212799870432 \tabularnewline
Determination & 0.00180805925173652 \tabularnewline
T-Test & 0.326907817024733 \tabularnewline
p-value (2 sided) & 0.744894582950823 \tabularnewline
p-value (1 sided) & 0.372447291475412 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16819&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]86.8934426229508[/C][C]59.8491803278689[/C][/ROW]
[ROW][C]Biased Variance[/C][C]109.891760279495[/C][C]494.798892770761[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]10.4829270854802[/C][C]22.2440754532698[/C][/ROW]
[ROW][C]Covariance[/C][C]10.0804945355191[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0425212799870432[/C][/ROW]
[ROW][C]Determination[/C][C]0.00180805925173652[/C][/ROW]
[ROW][C]T-Test[/C][C]0.326907817024733[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.744894582950823[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.372447291475412[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]59[/C][/ROW]
[ROW][C]Number of Observations[/C][C]61[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16819&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16819&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
Mean86.893442622950859.8491803278689
Biased Variance109.891760279495494.798892770761
Biased Standard Deviation10.482927085480222.2440754532698
Covariance10.0804945355191
Correlation0.0425212799870432
Determination0.00180805925173652
T-Test0.326907817024733
p-value (2 sided)0.744894582950823
p-value (1 sided)0.372447291475412
Degrees of Freedom59
Number of Observations61


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
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)
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')
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,'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')