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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 computationMon, 09 May 2011 16:04:04 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/09/t13049568370guc49700zx7n4o.htm/, Retrieved Mon, 13 May 2024 21:15:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121293, Retrieved Mon, 13 May 2024 21:15:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsCerebral N1
Estimated Impact101

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Correlation Aplys...] [2011-05-09 16:04:04] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5
8
7
3
6
16
Dataseries Y:
Download CSV
Histogram 
3
7
8
3
5
14

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'Gwilym Jenkins' @ www.wessa.org

\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 & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121293&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]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121293&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121293&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'Gwilym Jenkins' @ www.wessa.org






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean7.56.66666666666667
Biased Variance16.916666666666714.2222222222222
Biased Standard Deviation4.112987559751023.77123616632825
Covariance18
Correlation0.967052680415864
Determination0.935190886699508
T-Test7.59734920642528
p-value (2 sided)0.00161040621782749
p-value (1 sided)0.000805203108913743
Degrees of Freedom4
Number of Observations6

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 7.5 & 6.66666666666667 \tabularnewline
Biased Variance & 16.9166666666667 & 14.2222222222222 \tabularnewline
Biased Standard Deviation & 4.11298755975102 & 3.77123616632825 \tabularnewline
Covariance & 18 \tabularnewline
Correlation & 0.967052680415864 \tabularnewline
Determination & 0.935190886699508 \tabularnewline
T-Test & 7.59734920642528 \tabularnewline
p-value (2 sided) & 0.00161040621782749 \tabularnewline
p-value (1 sided) & 0.000805203108913743 \tabularnewline
Degrees of Freedom & 4 \tabularnewline
Number of Observations & 6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121293&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]7.5[/C][C]6.66666666666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]16.9166666666667[/C][C]14.2222222222222[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.11298755975102[/C][C]3.77123616632825[/C][/ROW]
[ROW][C]Covariance[/C][C]18[/C][/ROW]
[ROW][C]Correlation[/C][C]0.967052680415864[/C][/ROW]
[ROW][C]Determination[/C][C]0.935190886699508[/C][/ROW]
[ROW][C]T-Test[/C][C]7.59734920642528[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00161040621782749[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000805203108913743[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]4[/C][/ROW]
[ROW][C]Number of Observations[/C][C]6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121293&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121293&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
Mean7.56.66666666666667
Biased Variance16.916666666666714.2222222222222
Biased Standard Deviation4.112987559751023.77123616632825
Covariance18
Correlation0.967052680415864
Determination0.935190886699508
T-Test7.59734920642528
p-value (2 sided)0.00161040621782749
p-value (1 sided)0.000805203108913743
Degrees of Freedom4
Number of Observations6


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')