FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationMon, 04 Mar 2013 13:45:42 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/04/t1362423014d4obh2pxhseqy9y.htm/, Retrieved Sun, 28 Apr 2024 22:58:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207332, Retrieved Sun, 28 Apr 2024 22:58:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Scatter Plot of G...] [2013-03-04 18:45:42] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1
1.25
1
1
1.4
1.3
2
1.6
1.2
1.6
1.5
1.8
1.6
1.5
Dataseries Y:
Download CSV
Histogram 
29
20
19
14
12
12
2
0
0
0
-1
-3
-3
-7

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207332&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207332&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207332&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'Herman Ole Andreas Wold' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1.410714285714296.71428571428571
Biased Variance0.0864923469387755109.061224489796
Biased Standard Deviation0.2940958125148610.4432382185698
Covariance-2.41593406593407
Correlation-0.730426243693816
Determination0.533522497476659
T-Test-3.70468801270237
p-value (2 sided)0.00300987701539729
p-value (1 sided)0.00150493850769864
Degrees of Freedom12
Number of Observations14

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1.41071428571429 & 6.71428571428571 \tabularnewline
Biased Variance & 0.0864923469387755 & 109.061224489796 \tabularnewline
Biased Standard Deviation & 0.29409581251486 & 10.4432382185698 \tabularnewline
Covariance & -2.41593406593407 \tabularnewline
Correlation & -0.730426243693816 \tabularnewline
Determination & 0.533522497476659 \tabularnewline
T-Test & -3.70468801270237 \tabularnewline
p-value (2 sided) & 0.00300987701539729 \tabularnewline
p-value (1 sided) & 0.00150493850769864 \tabularnewline
Degrees of Freedom & 12 \tabularnewline
Number of Observations & 14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207332&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]1.41071428571429[/C][C]6.71428571428571[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.0864923469387755[/C][C]109.061224489796[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.29409581251486[/C][C]10.4432382185698[/C][/ROW]
[ROW][C]Covariance[/C][C]-2.41593406593407[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.730426243693816[/C][/ROW]
[ROW][C]Determination[/C][C]0.533522497476659[/C][/ROW]
[ROW][C]T-Test[/C][C]-3.70468801270237[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00300987701539729[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00150493850769864[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]12[/C][/ROW]
[ROW][C]Number of Observations[/C][C]14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207332&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207332&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
Mean1.410714285714296.71428571428571
Biased Variance0.0864923469387755109.061224489796
Biased Standard Deviation0.2940958125148610.4432382185698
Covariance-2.41593406593407
Correlation-0.730426243693816
Determination0.533522497476659
T-Test-3.70468801270237
p-value (2 sided)0.00300987701539729
p-value (1 sided)0.00150493850769864
Degrees of Freedom12
Number of Observations14


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')