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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_correlation.wasp

Title produced by software

Pearson Correlation

Date of computation

Wed, 28 Oct 2009 16:01:13 -0600

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/28/t1256767439nj25wmdeuv2t1n0.htm/, Retrieved Sun, 05 May 2024 21:24:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51883, Retrieved Sun, 05 May 2024 21:24:03 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

WSD2M2PC

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Bivariate Explorative Data Analysis] [Workshop 4: deel ...] [2009-10-28 16:09:47] [7c2a5b25a196bd646844b8f5223c9b3e]
- RMPD    [Pearson Correlation] [Workshop 4: deel ...] [2009-10-28 22:01:13] [3d2053c5f7c50d3c075d87ce0bd87294] [Current]

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Dataseries X:

Download CSV

Histogram

Boxplots

3.109060959
3.310543013
3.310543013
3.414442608
3.56671182
3.234749174
3.310543013
3.27336401
3.478158423
3.346389145
3.346389145
3.414442608
3.5085559
3.310543013
3.152736022
3.015534901
3.109060959
3.194583132
3.194583132
3.27336401
3.380994674
3.346389145
3.109060959
2.912350665
3.234749174
3.310543013
3.152736022
2.734367509
2.965273066
3.27336401
3.414442608
3.310543013
3.310543013
3.063390922
3.310543013
3.414442608
3.538056564
3.5085559
3.594568775
3.56671182
3.621670704
3.5085559
3.56671182
3.478158423
3.346389145
3.346389145
3.446807893
3.5085559
3.5085559
3.346389145
3.478158423
3.414442608
3.346389145
3.27336401
3.310543013
3.194583132
2.965273066
3.152736022
2.912350665
2.912350665
2.517696473
2.341805806
2.00148
1
2.174751721
2.186051277
2.564949357
2.884800713
2.587764035

Dataseries Y:

Download CSV

Histogram

3.861884491
3.86432807
3.864492015
3.863257308
3.860453306
3.849318732
3.844063366
3.844181192
3.845531265
3.835138386
3.840896665
3.843161358
3.848062114
3.850490024
3.851442229
3.853087325
3.851779838
3.840943954
3.834650174
3.835185604
3.840041333
3.85185285
3.855980758
3.85724753
3.854755941
3.861171308
3.865913967
3.869739954
3.86908917
3.85765146
3.84534727
3.838506216
3.853366873
3.8585208
3.864809349
3.865086762
3.871043125
3.873953266
3.871181262
3.874806751
3.874289451
3.854408916
3.840662338
3.833562198
3.850478329
3.861866435
3.865858029
3.872258448
3.872886015
3.876970667
3.873825677
3.878687726
3.872366111
3.860679016
3.848518938
3.84031302
3.86456395
3.879947833
3.893237105
3.903049256
3.912810243
3.919609086
3.930075738
3.933031449
3.933305731
3.926413182
3.910060531
3.903890717
3.922433331

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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=51883&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=51883&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51883&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	3.16266084897101	3.8665575772029
Biased Variance	0.190802804697886	0.000648168941304216
Biased Standard Deviation	0.436809803802394	0.025459162227069
Covariance	-0.00842987551270384
Correlation	-0.747041102733847
Determination	0.558070409173803
T-Test	-9.19825315211065
p-value (2 sided)	1.69204946588564e-13
p-value (1 sided)	8.46024732942818e-14
Degrees of Freedom	67
Number of Observations	69

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 3.16266084897101 & 3.8665575772029 \tabularnewline
Biased Variance & 0.190802804697886 & 0.000648168941304216 \tabularnewline
Biased Standard Deviation & 0.436809803802394 & 0.025459162227069 \tabularnewline
Covariance & -0.00842987551270384 \tabularnewline
Correlation & -0.747041102733847 \tabularnewline
Determination & 0.558070409173803 \tabularnewline
T-Test & -9.19825315211065 \tabularnewline
p-value (2 sided) & 1.69204946588564e-13 \tabularnewline
p-value (1 sided) & 8.46024732942818e-14 \tabularnewline
Degrees of Freedom & 67 \tabularnewline
Number of Observations & 69 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51883&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]3.16266084897101[/C][C]3.8665575772029[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.190802804697886[/C][C]0.000648168941304216[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.436809803802394[/C][C]0.025459162227069[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.00842987551270384[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.747041102733847[/C][/ROW]
[ROW][C]Determination[/C][C]0.558070409173803[/C][/ROW]
[ROW][C]T-Test[/C][C]-9.19825315211065[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.69204946588564e-13[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]8.46024732942818e-14[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]67[/C][/ROW]
[ROW][C]Number of Observations[/C][C]69[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51883&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51883&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	3.16266084897101	3.8665575772029
Biased Variance	0.190802804697886	0.000648168941304216
Biased Standard Deviation	0.436809803802394	0.025459162227069
Covariance	-0.00842987551270384
Correlation	-0.747041102733847
Determination	0.558070409173803
T-Test	-9.19825315211065
p-value (2 sided)	1.69204946588564e-13
p-value (1 sided)	8.46024732942818e-14
Degrees of Freedom	67
Number of Observations	69

Figure 1

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code