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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, 28 Jan 2009 06:53:29 -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/2009/Jan/28/t1233151032or259hyiizljwe5.htm/, Retrieved Mon, 29 Apr 2024 05:22:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36994, Retrieved Mon, 29 Apr 2024 05:22:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact241

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [teen births/crime...] [2009-01-28 13:53:29] [0a79065205ad1190aabb3fa00845df5f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
628000
617000
608000
595000
571000
571000
554000
560000
562000
537000
524000
499000
480000
478000
472000
472000
489000
518000
Dataseries Y:
Download CSV
Histogram 
1820130
1911770
1932270
1926020
1857670
1798790
1688540
1634770
1531044
1426044
1425486
1439480
1423677
1383676
1360088
1390745
1418043
1408337

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=36994&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=36994&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36994&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
Mean540833.3333333331598698.88888889
Biased Variance2557472222.2222245421723696.5432
Biased Standard Deviation50571.4565958132213123.728609799
Covariance10377501392.1569
Correlation0.909351836763583
Determination0.826920763025301
T-Test8.74318068862177
p-value (2 sided)1.71949147365069e-07
p-value (1 sided)8.59745736825346e-08
Degrees of Freedom16
Number of Observations18

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 540833.333333333 & 1598698.88888889 \tabularnewline
Biased Variance & 2557472222.22222 & 45421723696.5432 \tabularnewline
Biased Standard Deviation & 50571.4565958132 & 213123.728609799 \tabularnewline
Covariance & 10377501392.1569 \tabularnewline
Correlation & 0.909351836763583 \tabularnewline
Determination & 0.826920763025301 \tabularnewline
T-Test & 8.74318068862177 \tabularnewline
p-value (2 sided) & 1.71949147365069e-07 \tabularnewline
p-value (1 sided) & 8.59745736825346e-08 \tabularnewline
Degrees of Freedom & 16 \tabularnewline
Number of Observations & 18 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36994&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]540833.333333333[/C][C]1598698.88888889[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2557472222.22222[/C][C]45421723696.5432[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]50571.4565958132[/C][C]213123.728609799[/C][/ROW]
[ROW][C]Covariance[/C][C]10377501392.1569[/C][/ROW]
[ROW][C]Correlation[/C][C]0.909351836763583[/C][/ROW]
[ROW][C]Determination[/C][C]0.826920763025301[/C][/ROW]
[ROW][C]T-Test[/C][C]8.74318068862177[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.71949147365069e-07[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]8.59745736825346e-08[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]16[/C][/ROW]
[ROW][C]Number of Observations[/C][C]18[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36994&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36994&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
Mean540833.3333333331598698.88888889
Biased Variance2557472222.2222245421723696.5432
Biased Standard Deviation50571.4565958132213123.728609799
Covariance10377501392.1569
Correlation0.909351836763583
Determination0.826920763025301
T-Test8.74318068862177
p-value (2 sided)1.71949147365069e-07
p-value (1 sided)8.59745736825346e-08
Degrees of Freedom16
Number of Observations18


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')