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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_partialcorrelation.wasp
Title produced by softwarePartial Correlation
Date of computationSat, 08 Nov 2008 05:17:14 -0700
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/Nov/08/t1226146688dr64spml7qczkei.htm/, Retrieved Sat, 18 May 2024 21:27:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=22582, Retrieved Sat, 18 May 2024 21:27:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact226

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Partial Correlation] [Partial correlation] [2008-11-08 12:17:14] [00a0a665d7a07edd2e460056b0c0c354] [Current]
F RMPD    [Hierarchical Clustering] [Compete] [2008-11-09 12:18:16] [82d201ca7b4e7cd2c6f885d29b5b6937]
F    D      [Hierarchical Clustering] [Complete clustering] [2008-11-10 22:10:28] [8d78428855b119373cac369316c08983]
F   P         [Hierarchical Clustering] [Ward] [2008-11-10 22:13:06] [8d78428855b119373cac369316c08983]
- RMPD    [Hierarchical Clustering] [Ward] [2008-11-09 12:21:33] [82d201ca7b4e7cd2c6f885d29b5b6937]
F RM D    [Box-Cox Linearity Plot] [Box Cox Linearity...] [2008-11-09 12:31:54] [82d201ca7b4e7cd2c6f885d29b5b6937]
- RMPD      [Maximum-likelihood Fitting - Normal Distribution] [Maximum-likelihoo...] [2008-11-09 12:55:12] [82d201ca7b4e7cd2c6f885d29b5b6937]
F    D        [Maximum-likelihood Fitting - Normal Distribution] [Maximum-likelihoo...] [2008-11-09 12:58:19] [82d201ca7b4e7cd2c6f885d29b5b6937]
F               [Maximum-likelihood Fitting - Normal Distribution] [maximum likelihoo...] [2008-11-10 22:36:30] [8d78428855b119373cac369316c08983]
- RMPD          [Testing Mean with known Variance - Critical Value] [critical value] [2008-11-11 00:28:19] [8d78428855b119373cac369316c08983]
F RMPD          [Testing Mean with known Variance - p-value] [p-value] [2008-11-11 00:48:00] [8d78428855b119373cac369316c08983]
- RMPD          [Testing Mean with known Variance - Type II Error] [type 2 error] [2008-11-11 01:19:31] [8d78428855b119373cac369316c08983]
- RMPD          [Testing Mean with known Variance - Sample Size] [sample size] [2008-11-11 01:44:50] [8d78428855b119373cac369316c08983]
F RMPD          [Testing Population Mean with known Variance - Confidence Interval] [confidence interval] [2008-11-11 01:58:15] [8d78428855b119373cac369316c08983]
F RMPD          [Testing Sample Mean with known Variance - Confidence Interval] [confidence interval] [2008-11-11 02:12:01] [8d78428855b119373cac369316c08983]
-    D          [Maximum-likelihood Fitting - Normal Distribution] [Maximum-likelihoo...] [2008-12-10 19:20:50] [82d201ca7b4e7cd2c6f885d29b5b6937]
F           [Box-Cox Linearity Plot] [Box-Cox] [2008-11-10 22:18:08] [8d78428855b119373cac369316c08983]
F RM D    [Box-Cox Normality Plot] [Box Cox Normality] [2008-11-09 12:35:32] [82d201ca7b4e7cd2c6f885d29b5b6937]
F           [Box-Cox Normality Plot] [Box cox normality] [2008-11-10 22:32:57] [8d78428855b119373cac369316c08983]
F RM D    [Testing Mean with known Variance - Sample Size] [Testing Mean with...] [2008-11-09 13:57:54] [82d201ca7b4e7cd2c6f885d29b5b6937]
F RM D    [Testing Mean with known Variance - Critical Value] [Testing Mean with...] [2008-11-09 14:05:10] [82d201ca7b4e7cd2c6f885d29b5b6937]
F RM D    [Testing Mean with known Variance - p-value] [Testing Mean with...] [2008-11-09 14:11:56] [82d201ca7b4e7cd2c6f885d29b5b6937]
F RM D    [Testing Mean with known Variance - Type II Error] [Testing Mean with...] [2008-11-09 14:17:43] [82d201ca7b4e7cd2c6f885d29b5b6937]
F RM D    [Testing Population Mean with known Variance - Confidence Interval] [Testing Populatio...] [2008-11-09 14:21:52] [82d201ca7b4e7cd2c6f885d29b5b6937]
F RM D    [Testing Sample Mean with known Variance - Confidence Interval] [Testing Sample Me...] [2008-11-09 14:35:26] [82d201ca7b4e7cd2c6f885d29b5b6937]
Feedback Forum
2008-11-21 21:26:56 [Kim Wester] [reply] 
Bij Partial Correlatie vergelijk je drie tijdreeksen met elkaar. Hierbij wordt de invloed van 1 variabele uitgezuiverd; deze kan namelijk het beeld van de correlatie tussen de andere 2 andere reeksen vertekenen.

In dit geval is de correlatie tussen x en y 0.426980633094778. Wanneer reeks z wordt toegevoegd is te zien dat deze reeks vrijwel geen invloed heeft op de correlatie tussen x en y. Dit betekent dat de correlatie geen vertekend beeld geeft.

Dit is echter niet het geval bij reeks x en z waarbij reeks y wordt toegevoegd. Dit levert een negatieve correlatie op, waardoor het lijkt alsof er en negatief verband is. Dit is echter niet zo!
2008-11-23 10:47:27 [Inge Meelberghs] [reply] 
Partiële correlatie kunne we omschrijven als correlatie tussen twee variabelen na correctie voor een derde variable.

Als eerst berekent het model de correlatie tussen twee variabelen(XY,XZ,UZ). Daarna wordt er een derde variable geïntroduceerd, Z. Deze dient om na te gaan of Z al dat niet een invloed heeft. Als de waarde van de simpele correlatie kort bij die van de partiële correlatie ligt, dan kunnen we zeggen dat Z geen invloedrijke variable is. Is het net andersom en liggen beide waarden relatief ver uit elkaar, dan is Z wél een invloedrijke variable en kunnen we zeggen dat de correlatie een vertekend beeld geeft.

In dit voorbeeld bedraagt de correlatie voor r(xy) 0.426980633094778 en -0.136684024705862 voor r(yz). Als we hierna de derde variabele Z toevoegen kunnen we stellen dat deze geen invloed heeft op de twee correlaties (want de waarden van de partiële correlatie zijn praktisch hetzelfde als die van de simpele correlatie) wat wil zeggen dat de correlatie geen vertekend beeld geeft.

Maar als we dan naar de correlatie van r(xz) kijken na toevoeging van de derde variabele Z, kunnen we zien dat deze wél een invloed heeft. Hier ligt de waarde van de partiële correlatie beduidend hoger dan die van de simpele correlatie. IIn dit geval geeft de correlatie dus wel een vertekend beeld.
2008-11-23 17:25:16 [Michaël De Kuyer] [reply] 
De conclusie van Inge is naar mijn mening correct.
2008-11-24 11:57:24 [Bonifer Spillemaeckers] [reply] 
Ik ga hier akkoord met bovenstaande opmerkingen. De techniek van de partial correlation wordt hier prima verwoord.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
116.1
102.5
102.0
101.3
100.6
100.9
104.2
108.3
108.9
109.9
106.8
112.7
113.4
101.3
97.8
95.0
93.8
94.5
101.4
105.8
106.6
109.7
108.8
113.4
113.7
103.6
98.2
95.5
94.4
95.9
103.2
104.1
127.6
130.3
133.0
140.4
123.5
116.9
115.9
113.1
112.1
112.4
118.9
117.4
115.6
120.7
114.9
122.0
119.6
114.6
118.4
110.9
111.6
114.6
112.1
117.4
114.8
123.4
118.1
121.9
123.3
Dataseries Y:
Download CSV
Histogram 
117.1
107.0
107.0
111.0
108.2
96.3
100.9
107.7
106.2
118.7
116.1
118.1
118.4
110.8
106.4
112.2
108.3
96.0
100.6
107.8
108.4
120.9
117.3
119.7
119.6
111.8
108.1
111.8
105.5
93.6
103.9
100.3
106.6
118.4
106.6
109.8
115.9
111.7
119.8
116.1
103.2
99.0
112.3
104.2
114.0
121.7
107.2
112.8
117.8
113.3
116.1
111.8
110.2
110.0
102.9
110.1
102.7
118.7
109.0
115.7
118.1
Dataseries Z:
Download CSV
Histogram 
118.9
108.8
115.6
95.0
92.8
108.9
109.8
106.1
102.8
98.4
85.7
114.6
129.4
117.7
126.6
103.8
101.5
118.7
119.6
114.8
109.9
106.3
95.0
124.5
140.4
128.8
137.5
113.3
110.3
129.1
128.4
120.3
113.6
96.9
124.7
126.4
131.9
122.5
113.1
99.8
116.0
115.0
114.0
111.0
91.7
90.6
103.3
106.7
111.2
102.9
126.5
115.1
110.2
110.1
103.3
107.7
103.9
114.0
117.2
117.0
116.5

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22582&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22582&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22582&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Partial Correlation - Ungrouped Data
StatisticValue
Correlation r(xy)0.426980633094778
Partial Correlation r(xy.z)0.437225424203568
Correlation r(xz)0.0421186875074862
Partial Correlation r(xz.y)0.112171282083215
Correlation r(yz)-0.136684024705862
Partial Correlation r(yz.x)-0.171195373921222

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Partial Correlation - Ungrouped Data \tabularnewline
Statistic & Value \tabularnewline
Correlation r(xy) & 0.426980633094778 \tabularnewline
Partial Correlation r(xy.z) & 0.437225424203568 \tabularnewline
Correlation r(xz) & 0.0421186875074862 \tabularnewline
Partial Correlation r(xz.y) & 0.112171282083215 \tabularnewline
Correlation r(yz) & -0.136684024705862 \tabularnewline
Partial Correlation r(yz.x) & -0.171195373921222 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22582&T=1

[TABLE]
[ROW][C]Pearson Product Moment Partial Correlation - Ungrouped Data[/C][/ROW]
[ROW][C]Statistic[/C][C]Value[/C][/ROW]
[ROW][C]Correlation r(xy)[/C][C]0.426980633094778[/C][/ROW]
[ROW][C]Partial Correlation r(xy.z)[/C][C]0.437225424203568[/C][/ROW]
[ROW][C]Correlation r(xz)[/C][C]0.0421186875074862[/C][/ROW]
[ROW][C]Partial Correlation r(xz.y)[/C][C]0.112171282083215[/C][/ROW]
[ROW][C]Correlation r(yz)[/C][C]-0.136684024705862[/C][/ROW]
[ROW][C]Partial Correlation r(yz.x)[/C][C]-0.171195373921222[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22582&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22582&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 Partial Correlation - Ungrouped Data
StatisticValue
Correlation r(xy)0.426980633094778
Partial Correlation r(xy.z)0.437225424203568
Correlation r(xz)0.0421186875074862
Partial Correlation r(xz.y)0.112171282083215
Correlation r(yz)-0.136684024705862
Partial Correlation r(yz.x)-0.171195373921222


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
(rho12 <- cor(x, y))
(rho23 <- cor(y, z))
(rho13 <- cor(x, z))
(rhoxy_z <- (rho12-(rho13*rho23))/(sqrt(1-(rho13*rho13)) * sqrt(1-(rho23*rho23))))
(rhoxz_y <- (rho13-(rho12*rho23))/(sqrt(1-(rho12*rho12)) * sqrt(1-(rho23*rho23))))
(rhoyz_x <- (rho23-(rho12*rho13))/(sqrt(1-(rho12*rho12)) * sqrt(1-(rho13*rho13))))
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Partial Correlation - Ungrouped Data',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Value',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Correlation r(xy)',header=TRUE)
a<-table.element(a,rho12)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('partial_correlation1.htm','Partial Correlation r(xy.z)',''),header=TRUE)
a<-table.element(a,rhoxy_z)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Correlation r(xz)',header=TRUE)
a<-table.element(a,rho13)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('partial_correlation1.htm','Partial Correlation r(xz.y)',''),header=TRUE)
a<-table.element(a,rhoxz_y)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Correlation r(yz)',header=TRUE)
a<-table.element(a,rho23)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('partial_correlation1.htm','Partial Correlation r(yz.x)',''),header=TRUE)
a<-table.element(a,rhoyz_x)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')