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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 computationWed, 16 Jan 2008 03:21:25 -0700
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/Jan/16/t1200478785aq6501zmcj87s44.htm/, Retrieved Thu, 16 May 2024 01:17:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7977, Retrieved Thu, 16 May 2024 01:17:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact275

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2008-01-16 10:21:25] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,88
0,87
0,88
0,89
0,92
0,96
0,99
0,98
0,98
0,98
1,00
1,02
1,06
1,08
1,08
1,08
1,16
1,17
1,14
1,11
1,12
1,17
1,17
1,23
1,26
1,26
1,23
1,20
1,20
1,21
1,23
1,22
1,22
1,25
1,30
1,34
1,31
1,30
1,32
1,29
1,27
1,22
1,20
1,23
1,23
1,20
1,18
1,19
1,21
1,19
1,20
1,23
1,28
1,27
1,27
1,28
1,27
1,26
1,29
1,32
Dataseries Y:
Download CSV
Histogram 
281
295
294
302
314
321
313
310
319
316
319
333
356
358
340
328
355
356
351
359
378
378
389.
407
413
404
406
402
383
392
398
400
405
420
439
441
424
423
434
429
421
430
424
437
456
469
476
510
549
554
557
610
675
596
633
632
596
585
627
629

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7977&T=0

[TABLE]
[ROW][C]Summary of compuational 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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7977&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7977&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1.16416666666667425.85
Biased Variance0.016090972222222210522.8608333333
Biased Standard Deviation0.126850195988111102.580996453209
Covariance9.37741525423729
Correlation0.708640310638407
Determination0.502171089861698
T-Test7.64891427008378
p-value (2 sided)2.37870834141063e-10
p-value (1 sided)1.18935417070531e-10
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1.16416666666667 & 425.85 \tabularnewline
Biased Variance & 0.0160909722222222 & 10522.8608333333 \tabularnewline
Biased Standard Deviation & 0.126850195988111 & 102.580996453209 \tabularnewline
Covariance & 9.37741525423729 \tabularnewline
Correlation & 0.708640310638407 \tabularnewline
Determination & 0.502171089861698 \tabularnewline
T-Test & 7.64891427008378 \tabularnewline
p-value (2 sided) & 2.37870834141063e-10 \tabularnewline
p-value (1 sided) & 1.18935417070531e-10 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7977&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]1.16416666666667[/C][C]425.85[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.0160909722222222[/C][C]10522.8608333333[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.126850195988111[/C][C]102.580996453209[/C][/ROW]
[ROW][C]Covariance[/C][C]9.37741525423729[/C][/ROW]
[ROW][C]Correlation[/C][C]0.708640310638407[/C][/ROW]
[ROW][C]Determination[/C][C]0.502171089861698[/C][/ROW]
[ROW][C]T-Test[/C][C]7.64891427008378[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.37870834141063e-10[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.18935417070531e-10[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7977&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7977&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
Mean1.16416666666667425.85
Biased Variance0.016090972222222210522.8608333333
Biased Standard Deviation0.126850195988111102.580996453209
Covariance9.37741525423729
Correlation0.708640310638407
Determination0.502171089861698
T-Test7.64891427008378
p-value (2 sided)2.37870834141063e-10
p-value (1 sided)1.18935417070531e-10
Degrees of Freedom58
Number of Observations60


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')