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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 computationSun, 19 Oct 2008 16:39:24 -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/t1224456010cj6qoch5877p31t.htm/, Retrieved Sun, 19 May 2024 14:42:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17115, Retrieved Sun, 19 May 2024 14:42:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact193

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] [Pearson correlati...] [2008-10-19 22:39:24] [14a75ec03b2c0d8ddd8b141a7b1594fd] [Current]
Feedback Forum
2008-10-23 15:51:32 [Kenny Simons] [reply] 
Als we hier naar het cijfer van de correlatie zien, ligt deze wel zeer dicht bij 0. Dit wil inderdaad zeggen dat er geen correlatie is. Als we het scatter plot bekijken, zien we hier dat er outliers zijn die ons plot beïnvloeden. Als we deze outliers eruit hadden gehaald, hadden we waarschijnlijk wel te maken met een positieve relatie. We kunnen dus besluiten dat er hier geen relatie is tussen de tijdreeksen, omdat deze worden beïnvloed door outliers.
2008-10-27 10:57:48 [Joris Deboel] [reply] 
Ook hier weer afgaande op het coefficient is er geen verband maar als we de grafiek gaan bekijken zien we duidelijk een positief verband. Het coefficient is duidelijk beinvloed door de outliners.

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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=17115&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=17115&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17115&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=17115&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=17115&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17115&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')