FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationWed, 28 Oct 2009 10:48:25 -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/2009/Oct/28/t12567487312otsgsz5ie3pxja.htm/, Retrieved Mon, 06 May 2024 03:19:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51554, Retrieved Mon, 06 May 2024 03:19:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Workshop4_part2_l...] [2009-10-28 16:48:25] [7a6d96edf94be87996de99db5f42363b] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12.27798392 
 12.25821433 
 12.25330445 
 12.3759884 
 12.39702766 
 12.39618875 
 12.39925583 
 12.38231325 
 12.38979738 
 12.40800073 
 12.40728138 
 12.39492284 
 12.39064583 
 12.37196413 
 12.37580276 
 12.48589516 
 12.507469 
 12.50486156 
 12.4951425 
 12.46115275 
 12.47919803 
 12.49654956 
 12.49637379 
 12.48664324 
 12.46405424 
 12.44840687 
 12.44850104 
 12.53273622 
 12.56147528 
 12.56584977 
 12.55335058 
 12.53064218 
 12.53507059 
 12.53223477 
 12.53214456 
 12.52466091 
 12.50673264 
 12.49552814 
 12.48745869 
 12.56813953 
 12.58171752 
 12.58553595 
 12.57136138 
 12.54780602 
 12.55198589 
 12.54322322 
 12.54400096 
 12.53118055 
 12.52531152 
 12.52216723 
 12.51102104 
 12.57695321 
 12.58013652 
 12.58553595 
 12.53719488 
 12.50553259 
 12.49072889 
 12.50259304 
 12.48437083 
 12.44979499 
 12.44253905 
 12.4133185 
 12.36892252 
 12.46286758 
 12.47224887 
 12.44769638 
 12.43178489 
 12.40255184 
 12.41756863 
 12.4233631 
 12.40917266 
 12.37615292 
 12.37617401 
 12.32631488 
 12.33199579 
 12.42091786 
 12.42252587 
 12.4170181 
 12.40941341 
 12.41415535 
 12.45201433 
 12.48491199 
 12.5000362 
 12.51739556 
 12.52074834 
 12.49661313 
 12.51353161
Dataseries Y:
Download CSV
Histogram 
12.41446392 
 12.40500137 
 12.41289574 
 12.54185178 
 12.55359433 
 12.54645508 
 12.5280257 
 12.50874431 
 12.51319331 
 12.52238591 
 12.51514799 
 12.50008837 
 12.50092644 
 12.48660925 
 12.50608094 
 12.62722736 
 12.64227709 
 12.63898105 
 12.60628063 
 12.57498096 
 12.58442346 
 12.59443229 
 12.58959203 
 12.57954817 
 12.55931771 
 12.54901675 
 12.57020869 
 12.66432942 
 12.69284735 
 12.6946864 
 12.70162827 
 12.6681701 
 12.66835592 
 12.65631033 
 12.65164269 
 12.64236113 
 12.62132305 
 12.61259053 
 12.62489811 
 12.71732618 
 12.72990728 
 12.72466404 
 12.68828581 
 12.65691575 
 12.65869166 
 12.65465471 
 12.64324312 
 12.62136596 
 12.60816206 
 12.60626722 
 12.61695969 
 12.70613556 
 12.72213354 
 12.69959747 
 12.6414816 
 12.59783091 
 12.58249678 
 12.58293936 
 12.559114 
 12.52987568 
 12.51563607 
 12.4874134 
 12.48101137 
 12.60083401 
 12.62345974 
 12.56721659 
 12.52970205 
 12.4928443 
 12.49557681 
 12.50016289 
 12.47809017 
 12.45114206 
 12.44176908 
 12.4041158 
 12.43217581 
 12.54413291 
 12.56114581 
 12.50978554 
 12.47256683 
 12.45138074 
 12.46988202 
 12.48333689 
 12.48480605 
 12.48095819 
 12.47828061 
 12.45358485 
 12.48454115

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=51554&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=51554&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51554&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
Mean12.466426078046012.5677528051724
Biased Variance0.005693669691572990.0072819983106519
Biased Standard Deviation0.07545640921467830.0853346255083591
Covariance0.00556077013284435
Correlation0.853675308641104
Determination0.728761532583485
T-Test15.1121599709992
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom85
Number of Observations87

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 12.4664260780460 & 12.5677528051724 \tabularnewline
Biased Variance & 0.00569366969157299 & 0.0072819983106519 \tabularnewline
Biased Standard Deviation & 0.0754564092146783 & 0.0853346255083591 \tabularnewline
Covariance & 0.00556077013284435 \tabularnewline
Correlation & 0.853675308641104 \tabularnewline
Determination & 0.728761532583485 \tabularnewline
T-Test & 15.1121599709992 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 85 \tabularnewline
Number of Observations & 87 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51554&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]12.4664260780460[/C][C]12.5677528051724[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.00569366969157299[/C][C]0.0072819983106519[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.0754564092146783[/C][C]0.0853346255083591[/C][/ROW]
[ROW][C]Covariance[/C][C]0.00556077013284435[/C][/ROW]
[ROW][C]Correlation[/C][C]0.853675308641104[/C][/ROW]
[ROW][C]Determination[/C][C]0.728761532583485[/C][/ROW]
[ROW][C]T-Test[/C][C]15.1121599709992[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]85[/C][/ROW]
[ROW][C]Number of Observations[/C][C]87[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51554&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51554&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
Mean12.466426078046012.5677528051724
Biased Variance0.005693669691572990.0072819983106519
Biased Standard Deviation0.07545640921467830.0853346255083591
Covariance0.00556077013284435
Correlation0.853675308641104
Determination0.728761532583485
T-Test15.1121599709992
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom85
Number of Observations87


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')