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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 computationMon, 20 Oct 2008 13:53:18 -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/t1224532625g4wvotjp6u1xc8s.htm/, Retrieved Sun, 19 May 2024 14:13:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18023, Retrieved Sun, 19 May 2024 14:13:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133

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] [Q3 Clothing produ...] [2007-10-20 14:22:11] [b731da8b544846036771bbf9bf2f34ce]
F    D    [Pearson Correlation] [Repro pearson cor...] [2008-10-20 19:53:18] [21d7d81e7693ad6dde5aadefb1046611] [Current]
Feedback Forum
2008-10-25 13:52:48 [Astrid Sniekers] [reply] 
Het antwoord van de student is onduidelijk. Beter zou zijn: 0,565… is een kleine positieve correlatie. Dit wil zeggen dat als de totale productie stijgt, de productie van kleding ook zal stijgen. De totale productie heeft een associatie van 57% met de productie van de kledij.
2008-10-27 21:12:44 [Steven Symons] [reply] 
de student geeft een zeer onduidelijk antwoord. Het is zo dat we hier te maken hebben met een positieve correlatie van 0,565, deze waarde ligt dus dichter bij 1 dan bij 0. Eenvoudig trucje om de correlatie te beoordelen is een denkbeeldige lijn trekken, hoe dichter de punten erbij liggen hoe positiever de correlatie. Dit wil zeggen dat de totale productie voor 57% geassocieerd is met de productie van kleding. De lineaire samenhang is dus gemiddeld

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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 
110,40
96,40
101,90
106,20
81,00
94,70
101,00
109,40
102,30
90,70
96,20
96,10
106,00
103,10
102,00
104,70
86,00
92,10
106,90
112,60
101,70
92,00
97,40
97,00
105,40
102,70
98,10
104,50
87,40
89,90
109,80
111,70
98,60
96,90
95,10
97,00
112,70
102,90
97,40
111,40
87,40
96,80
114,10
110,30
103,90
101,60
94,60
95,90
104,70
102,80
98,10
113,90
80,90
95,70
113,20
105,90
108,80
102,30
99,00
100,70
115,50

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18023&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18023&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18023&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'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean86.8934426229508100.908196721311
Biased Variance109.89176027949564.2309164203171
Biased Standard Deviation10.48292708548028.01441928153981
Covariance48.2815546448088
Correlation0.565259717157914
Determination0.319518547841445
T-Test5.2633941884171
p-value (2 sided)2.07228182791397e-06
p-value (1 sided)1.03614091395698e-06
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 & 100.908196721311 \tabularnewline
Biased Variance & 109.891760279495 & 64.2309164203171 \tabularnewline
Biased Standard Deviation & 10.4829270854802 & 8.01441928153981 \tabularnewline
Covariance & 48.2815546448088 \tabularnewline
Correlation & 0.565259717157914 \tabularnewline
Determination & 0.319518547841445 \tabularnewline
T-Test & 5.2633941884171 \tabularnewline
p-value (2 sided) & 2.07228182791397e-06 \tabularnewline
p-value (1 sided) & 1.03614091395698e-06 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18023&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]100.908196721311[/C][/ROW]
[ROW][C]Biased Variance[/C][C]109.891760279495[/C][C]64.2309164203171[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]10.4829270854802[/C][C]8.01441928153981[/C][/ROW]
[ROW][C]Covariance[/C][C]48.2815546448088[/C][/ROW]
[ROW][C]Correlation[/C][C]0.565259717157914[/C][/ROW]
[ROW][C]Determination[/C][C]0.319518547841445[/C][/ROW]
[ROW][C]T-Test[/C][C]5.2633941884171[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.07228182791397e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.03614091395698e-06[/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=18023&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18023&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
Mean86.8934426229508100.908196721311
Biased Variance109.89176027949564.2309164203171
Biased Standard Deviation10.48292708548028.01441928153981
Covariance48.2815546448088
Correlation0.565259717157914
Determination0.319518547841445
T-Test5.2633941884171
p-value (2 sided)2.07228182791397e-06
p-value (1 sided)1.03614091395698e-06
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')