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 computationWed, 18 Jun 2014 10:41:15 +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/t14030845658vj5c0xrnoii3k5.htm/, Retrieved Tue, 14 May 2024 19:50:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235235, Retrieved Tue, 14 May 2024 19:50:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [BEMAR104A ] [2014-06-18 09:41:15] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5
0
5
4
0
0
0
3
1
0
0
4
2
0
0
0
0
0
2
0
2
5
5
0
4
4
1
0
5
4
Dataseries Y:
Download CSV
Histogram 
2,4
2,3
9,9
7,3
0
0
0
13,4
13,3
5,7
1,4
9,5
13,9
0
2,9
0
9
9,1
5,1
1,1
0
6,7
10,7
14,8
12,7
8,3
9,1
6,9
15,1
6,6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 & 0 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235235&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]0 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=235235&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235235&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 time0 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1.866666666666676.57333333333333
Biased Variance4.1155555555555625.0159555555556
Biased Standard Deviation2.028683207293735.00159530105701
Covariance4.62390804597701
Correlation0.440517483296126
Determination0.194055653089553
T-Test2.59650784074784
p-value (2 sided)0.0148364785762976
p-value (1 sided)0.00741823928814878
Degrees of Freedom28
Number of Observations30

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1.86666666666667 & 6.57333333333333 \tabularnewline
Biased Variance & 4.11555555555556 & 25.0159555555556 \tabularnewline
Biased Standard Deviation & 2.02868320729373 & 5.00159530105701 \tabularnewline
Covariance & 4.62390804597701 \tabularnewline
Correlation & 0.440517483296126 \tabularnewline
Determination & 0.194055653089553 \tabularnewline
T-Test & 2.59650784074784 \tabularnewline
p-value (2 sided) & 0.0148364785762976 \tabularnewline
p-value (1 sided) & 0.00741823928814878 \tabularnewline
Degrees of Freedom & 28 \tabularnewline
Number of Observations & 30 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235235&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]1.86666666666667[/C][C]6.57333333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4.11555555555556[/C][C]25.0159555555556[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.02868320729373[/C][C]5.00159530105701[/C][/ROW]
[ROW][C]Covariance[/C][C]4.62390804597701[/C][/ROW]
[ROW][C]Correlation[/C][C]0.440517483296126[/C][/ROW]
[ROW][C]Determination[/C][C]0.194055653089553[/C][/ROW]
[ROW][C]T-Test[/C][C]2.59650784074784[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0148364785762976[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00741823928814878[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]28[/C][/ROW]
[ROW][C]Number of Observations[/C][C]30[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235235&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235235&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
Mean1.866666666666676.57333333333333
Biased Variance4.1155555555555625.0159555555556
Biased Standard Deviation2.028683207293735.00159530105701
Covariance4.62390804597701
Correlation0.440517483296126
Determination0.194055653089553
T-Test2.59650784074784
p-value (2 sided)0.0148364785762976
p-value (1 sided)0.00741823928814878
Degrees of Freedom28
Number of Observations30


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')