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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, 18 Jun 2014 15:47:55 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Jun/18/t1403103030tbcujwj54wihaj9.htm/, Retrieved Mon, 13 May 2024 23:01:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235239, Retrieved Mon, 13 May 2024 23:01:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [BEMAR103A] [2014-06-18 14:47:55] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0
6
0
4
4
4
5
3
1
0
4
5
1
0
2
0
6
0
6
0
3
6
4
2
5
5
Dataseries Y:
Download CSV
Histogram 
0
8,4
1,1
7,1
6,5
11,2
11,9
10,2
8,6
0
11,2
9,8
11,6
0
6,6
0
10
1,1
12,1
1,4
12,3
13,4
10,8
6,4
16,9
7,4

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'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235239&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235239&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235239&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'Gertrude Mary Cox' @ cox.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2.923076923076927.53846153846154
Biased Variance4.9940828402366923.4592899408284
Biased Standard Deviation2.234744468666764.84347911534967
Covariance8.85507692307692
Correlation0.786635780238426
Determination0.618795850751317
T-Test6.2416657485671
p-value (2 sided)1.88646027776684e-06
p-value (1 sided)9.43230138883422e-07
Degrees of Freedom24
Number of Observations26

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2.92307692307692 & 7.53846153846154 \tabularnewline
Biased Variance & 4.99408284023669 & 23.4592899408284 \tabularnewline
Biased Standard Deviation & 2.23474446866676 & 4.84347911534967 \tabularnewline
Covariance & 8.85507692307692 \tabularnewline
Correlation & 0.786635780238426 \tabularnewline
Determination & 0.618795850751317 \tabularnewline
T-Test & 6.2416657485671 \tabularnewline
p-value (2 sided) & 1.88646027776684e-06 \tabularnewline
p-value (1 sided) & 9.43230138883422e-07 \tabularnewline
Degrees of Freedom & 24 \tabularnewline
Number of Observations & 26 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235239&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]2.92307692307692[/C][C]7.53846153846154[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4.99408284023669[/C][C]23.4592899408284[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.23474446866676[/C][C]4.84347911534967[/C][/ROW]
[ROW][C]Covariance[/C][C]8.85507692307692[/C][/ROW]
[ROW][C]Correlation[/C][C]0.786635780238426[/C][/ROW]
[ROW][C]Determination[/C][C]0.618795850751317[/C][/ROW]
[ROW][C]T-Test[/C][C]6.2416657485671[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.88646027776684e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]9.43230138883422e-07[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]24[/C][/ROW]
[ROW][C]Number of Observations[/C][C]26[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235239&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235239&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
Mean2.923076923076927.53846153846154
Biased Variance4.9940828402366923.4592899408284
Biased Standard Deviation2.234744468666764.84347911534967
Covariance8.85507692307692
Correlation0.786635780238426
Determination0.618795850751317
T-Test6.2416657485671
p-value (2 sided)1.88646027776684e-06
p-value (1 sided)9.43230138883422e-07
Degrees of Freedom24
Number of Observations26


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')