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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 computationTue, 03 Jul 2012 09:06:06 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jul/03/t1341320849m7wofsik46znonr.htm/, Retrieved Sat, 27 Apr 2024 06:47:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168761, Retrieved Sat, 27 Apr 2024 06:47:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2012-07-03 13:06:06] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2810
1858
1878
1332
1653
2136
16
8
983
4361
1848
2564
Dataseries Y:
Download CSV
Histogram 
2479
1466
1489
1499
1972
1961
12
15
527
3509
3453
3201

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168761&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168761&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168761&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 time2 seconds
R Server'AstonUniversity' @ aston.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1787.251798.58333333333
Biased Variance1298938.020833331369582.40972222
Biased Standard Deviation1139.709621277861170.29159175063
Covariance1251512.11363636
Correlation0.860118318873121
Determination0.739803522461124
T-Test5.33221301937398
p-value (2 sided)0.000331911253813155
p-value (1 sided)0.000165955626906578
Degrees of Freedom10
Number of Observations12

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1787.25 & 1798.58333333333 \tabularnewline
Biased Variance & 1298938.02083333 & 1369582.40972222 \tabularnewline
Biased Standard Deviation & 1139.70962127786 & 1170.29159175063 \tabularnewline
Covariance & 1251512.11363636 \tabularnewline
Correlation & 0.860118318873121 \tabularnewline
Determination & 0.739803522461124 \tabularnewline
T-Test & 5.33221301937398 \tabularnewline
p-value (2 sided) & 0.000331911253813155 \tabularnewline
p-value (1 sided) & 0.000165955626906578 \tabularnewline
Degrees of Freedom & 10 \tabularnewline
Number of Observations & 12 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168761&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]1787.25[/C][C]1798.58333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1298938.02083333[/C][C]1369582.40972222[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1139.70962127786[/C][C]1170.29159175063[/C][/ROW]
[ROW][C]Covariance[/C][C]1251512.11363636[/C][/ROW]
[ROW][C]Correlation[/C][C]0.860118318873121[/C][/ROW]
[ROW][C]Determination[/C][C]0.739803522461124[/C][/ROW]
[ROW][C]T-Test[/C][C]5.33221301937398[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000331911253813155[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000165955626906578[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]10[/C][/ROW]
[ROW][C]Number of Observations[/C][C]12[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168761&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168761&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
Mean1787.251798.58333333333
Biased Variance1298938.020833331369582.40972222
Biased Standard Deviation1139.709621277861170.29159175063
Covariance1251512.11363636
Correlation0.860118318873121
Determination0.739803522461124
T-Test5.33221301937398
p-value (2 sided)0.000331911253813155
p-value (1 sided)0.000165955626906578
Degrees of Freedom10
Number of Observations12


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
x <- x[!is.na(y)]
y <- y[!is.na(y)]
y <- y[!is.na(x)]
x <- x[!is.na(x)]
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', na.rm = T)
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')