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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 computationSat, 16 Jun 2012 16:41:10 -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/Jun/16/t1339879554i45rb0yc2qkqfk2.htm/, Retrieved Tue, 30 Apr 2024 05:23:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168741, Retrieved Tue, 30 Apr 2024 05:23:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Age vs VJ] [2012-06-16 20:41:10] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
18
20
21
21
21
19
20
19
20
19
18
21
20
Dataseries Y:
Download CSV
Histogram 
18
16
18
16
19
20
16
18
20
20
20
19
16

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=168741&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=168741&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168741&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
Mean19.769230769230818.1538461538462
Biased Variance1.100591715976332.59171597633136
Biased Standard Deviation1.049090899768141.60988073357357
Covariance-0.628205128205128
Correlation-0.34334643966478
Determination0.117886777630481
T-Test-1.21245806009056
p-value (2 sided)0.250734896644528
p-value (1 sided)0.125367448322264
Degrees of Freedom11
Number of Observations13

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 19.7692307692308 & 18.1538461538462 \tabularnewline
Biased Variance & 1.10059171597633 & 2.59171597633136 \tabularnewline
Biased Standard Deviation & 1.04909089976814 & 1.60988073357357 \tabularnewline
Covariance & -0.628205128205128 \tabularnewline
Correlation & -0.34334643966478 \tabularnewline
Determination & 0.117886777630481 \tabularnewline
T-Test & -1.21245806009056 \tabularnewline
p-value (2 sided) & 0.250734896644528 \tabularnewline
p-value (1 sided) & 0.125367448322264 \tabularnewline
Degrees of Freedom & 11 \tabularnewline
Number of Observations & 13 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168741&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]19.7692307692308[/C][C]18.1538461538462[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.10059171597633[/C][C]2.59171597633136[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.04909089976814[/C][C]1.60988073357357[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.628205128205128[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.34334643966478[/C][/ROW]
[ROW][C]Determination[/C][C]0.117886777630481[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.21245806009056[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.250734896644528[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.125367448322264[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]11[/C][/ROW]
[ROW][C]Number of Observations[/C][C]13[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168741&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168741&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
Mean19.769230769230818.1538461538462
Biased Variance1.100591715976332.59171597633136
Biased Standard Deviation1.049090899768141.60988073357357
Covariance-0.628205128205128
Correlation-0.34334643966478
Determination0.117886777630481
T-Test-1.21245806009056
p-value (2 sided)0.250734896644528
p-value (1 sided)0.125367448322264
Degrees of Freedom11
Number of Observations13


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')