FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationThu, 20 Dec 2007 09:00:56 -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/2007/Dec/20/t1198165427bnh8gvyj8u0053z.htm/, Retrieved Mon, 29 Apr 2024 08:02:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4745, Retrieved Mon, 29 Apr 2024 08:02:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact201

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [PAPER, TIM, GIEL,...] [2007-12-13 15:05:38] [beddef6ae4019f3e51da5e10d233ec85]
-    D    [Pearson Correlation] [Paper Tim, Giel, Rik] [2007-12-20 16:00:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
513
503
471
471
476
475
470
461
455
456
517
525
523
519
509
512
519
517
510
509
501
507
569
580
578
565
547
555
562
561
555
544
537
543
594
611
613
611
594
595
591
589
584
573
567
569
621
629
628
612
595
597
593
590
580
574
573
573
620
626
620
588
566
557
561
549
532
526
511
499
555
565
542
Dataseries Y:
Download CSV
Histogram 
6,6
7,8
7,4
7,4
7,5
7,4
7,4
7
6,9
6,9
7,6
7,7
7,6
8,2
8
8,1
8,3
8,2
8,1
7,7
7,6
7,7
8,2
8,4
8,4
8,6
8,4
8,5
8,7
8,7
8,6
7,4
7,3
7,4
9
9,2
9,2
8,5
8,3
8,3
8,6
8,6
8,5
8,1
8,1
8
8,6
8,7
8,7
8,6
8,4
8,4
8,7
8,7
8,5
8,3
8,3
8,3
8,1
8,2
8,1
8,1
7,9
7,7
8,1
8
7,7
7,8
7,6
7,4
7,7
7,8
7,5

Tables (Output of Computation)





Summary of compuational 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 compuational 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=4745&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]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=4745&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4745&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean551.8904109589048.05479452054795
Biased Variance2124.59072996810.295079752298743
Biased Standard Deviation46.09328291593150.543212437540547
Covariance19.7352549467275
Correlation0.777400885924052
Determination0.6043521374355
T-Test10.4140532412360
p-value (2 sided)4.44089209850063e-16
p-value (1 sided)2.22044604925031e-16
Degrees of Freedom71
Number of Observations73

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 551.890410958904 & 8.05479452054795 \tabularnewline
Biased Variance & 2124.5907299681 & 0.295079752298743 \tabularnewline
Biased Standard Deviation & 46.0932829159315 & 0.543212437540547 \tabularnewline
Covariance & 19.7352549467275 \tabularnewline
Correlation & 0.777400885924052 \tabularnewline
Determination & 0.6043521374355 \tabularnewline
T-Test & 10.4140532412360 \tabularnewline
p-value (2 sided) & 4.44089209850063e-16 \tabularnewline
p-value (1 sided) & 2.22044604925031e-16 \tabularnewline
Degrees of Freedom & 71 \tabularnewline
Number of Observations & 73 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4745&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]551.890410958904[/C][C]8.05479452054795[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2124.5907299681[/C][C]0.295079752298743[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]46.0932829159315[/C][C]0.543212437540547[/C][/ROW]
[ROW][C]Covariance[/C][C]19.7352549467275[/C][/ROW]
[ROW][C]Correlation[/C][C]0.777400885924052[/C][/ROW]
[ROW][C]Determination[/C][C]0.6043521374355[/C][/ROW]
[ROW][C]T-Test[/C][C]10.4140532412360[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]4.44089209850063e-16[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.22044604925031e-16[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]71[/C][/ROW]
[ROW][C]Number of Observations[/C][C]73[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4745&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4745&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
Mean551.8904109589048.05479452054795
Biased Variance2124.59072996810.295079752298743
Biased Standard Deviation46.09328291593150.543212437540547
Covariance19.7352549467275
Correlation0.777400885924052
Determination0.6043521374355
T-Test10.4140532412360
p-value (2 sided)4.44089209850063e-16
p-value (1 sided)2.22044604925031e-16
Degrees of Freedom71
Number of Observations73


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')