FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationMon, 20 Oct 2008 15:03:23 -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/20/t12245366473xl654ofp45q5jx.htm/, Retrieved Sun, 19 May 2024 15:23:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18148, Retrieved Sun, 19 May 2024 15:23:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129

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 Relationship b...] [2007-10-20 14:40:02] [b731da8b544846036771bbf9bf2f34ce]
F    D    [Pearson Correlation] [Repro q5] [2008-10-20 21:03:23] [21d7d81e7693ad6dde5aadefb1046611] [Current]
Feedback Forum
2008-10-25 13:54:22 [Astrid Sniekers] [reply] 
We hebben hier te maken met een kleine positieve correlatie, omdat 2 ‘outliers’ de correlatie helemaal verpesten. Dit kunnen we afleiden aan de hand van de grafiek. Dit heeft de student spijtig genoeg niet opgemerkt.
2008-10-25 13:55:10 [Astrid Sniekers] [reply] 
Q6:
Het antwoord van de student is niet reproduceerbaar!!!


Q7:
Het antwoord van de student is niet reproduceerbaar!!!
2008-10-26 22:53:41 [Elias Van Deun] [reply] 
Er is eigenlijk wel een sterke correlatie, alleen zijn er 2 outliers (links bovenaan) die een grote invloed hebben op de correlatie.
2008-10-27 09:07:36 [Stéphanie Claes] [reply] 
Klopt. Als we naar de tekening kijken dan lijkt deze redelijk stijgend te zijn maar de outliers links vanboven zorgen ervoor dat het correlatiecijfer zwak is.
2008-10-27 21:27:11 [Steven Symons] [reply] 
de correlatie is zeer klein 0,04, wat extreem dicht bij 0 is. De investeringen zijn dus slecht voor 4% geassocieerd met de productie van kleding, er bestaat geen samenhang tussen de 2 reeksen.

Maar als we de denkbeeldige lijn bekijken zien we dat deze horizontaal verloopt, als we dan bovenaan enkele punten zouden bijzetten zouden we meteen een negatief verband hebben (dalende lijn). Hier kan je dus zien dat outliers zéér sterk beïnvloeden.

Post a new message

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=18148&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=18148&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18148&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=18148&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=18148&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18148&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):
par1 = ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')