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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 09:09:06 -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/t1224429115yq5r4te9n08y7po.htm/, Retrieved Fri, 17 May 2024 02:08:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16903, Retrieved Fri, 17 May 2024 02:08:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Investigating ass...] [2007-10-22 22:08:56] [8cd6641b921d30ebe00b648d1481bba0]
F    D    [Pearson Correlation] [Task 3 - Q10 - co...] [2008-10-19 15:09:06] [dafd615cb3e0decc017580d68ecea30a] [Current]
Feedback Forum
2008-10-24 15:59:02 [Bob Leysen] [reply] 
Kleine correlatie met enkele outliers
2008-10-27 08:35:09 [Jeroen Michel] [reply] 
Hier is duidelijk waar te nemen dat er een klein verband bestaat tussen de verschillende tijdreeksen. De correlatie is miniem. De vraag luidt daarom of het verstandig is om met deze grafieken verder te werken voor volgende opdrachten.
2008-10-27 18:32:10 [Jens Peeters] [reply] 
Het is inderdaad zo dat bij al de verschillende tijdreeksen de correlatie zeer laag is. Daarom is het misschien best om andere tijdreeksen te nemen hoewel deze misschien interessante resultaten kunnen opleveren.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
209
169
325
293
93
297
2125
149
106
172
107
155
751
79
149
589
44
320
270
141
314
341
101
2053
81
46
73
44
33
115
70
58
68
62
160
65
101
80
80
74
70
102
65
87
81
155
111
37
Dataseries Y:
Download CSV
Histogram 
878
346
321
116
182
189
243
270
122
138
35
456
3929
262
236
222
2010
566
122
43
477
1048
307
687
186
248
78
135
7
90
280
20
223
29
175
93
83
28
57
40
51
42
78
83
25
587
241
79

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=16903&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=16903&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16903&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
Mean234.791666666667336.729166666667
Biased Variance168367.164930556388018.947482639
Biased Standard Deviation410.325681539135622.911669085304
Covariance63871.5381205674
Correlation0.244685835337679
Determination0.059871158014898
T-Test1.71156760011369
p-value (2 sided)0.0937120685762065
p-value (1 sided)0.0468560342881033
Degrees of Freedom46
Number of Observations48

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 234.791666666667 & 336.729166666667 \tabularnewline
Biased Variance & 168367.164930556 & 388018.947482639 \tabularnewline
Biased Standard Deviation & 410.325681539135 & 622.911669085304 \tabularnewline
Covariance & 63871.5381205674 \tabularnewline
Correlation & 0.244685835337679 \tabularnewline
Determination & 0.059871158014898 \tabularnewline
T-Test & 1.71156760011369 \tabularnewline
p-value (2 sided) & 0.0937120685762065 \tabularnewline
p-value (1 sided) & 0.0468560342881033 \tabularnewline
Degrees of Freedom & 46 \tabularnewline
Number of Observations & 48 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16903&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]234.791666666667[/C][C]336.729166666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]168367.164930556[/C][C]388018.947482639[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]410.325681539135[/C][C]622.911669085304[/C][/ROW]
[ROW][C]Covariance[/C][C]63871.5381205674[/C][/ROW]
[ROW][C]Correlation[/C][C]0.244685835337679[/C][/ROW]
[ROW][C]Determination[/C][C]0.059871158014898[/C][/ROW]
[ROW][C]T-Test[/C][C]1.71156760011369[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0937120685762065[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0468560342881033[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]46[/C][/ROW]
[ROW][C]Number of Observations[/C][C]48[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16903&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16903&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
Mean234.791666666667336.729166666667
Biased Variance168367.164930556388018.947482639
Biased Standard Deviation410.325681539135622.911669085304
Covariance63871.5381205674
Correlation0.244685835337679
Determination0.059871158014898
T-Test1.71156760011369
p-value (2 sided)0.0937120685762065
p-value (1 sided)0.0468560342881033
Degrees of Freedom46
Number of Observations48


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')