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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 computationFri, 25 May 2012 15:22:31 -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/May/25/t1337973953ev0krkoq8wqg5mi.htm/, Retrieved Fri, 03 May 2024 16:19:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167528, Retrieved Fri, 03 May 2024 16:19:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact55

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2012-05-25 19:22:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8.5
5.5
7.5
5.5
8
9
4
7
7.5
7
8
4
7.5
8.5
5.5
7.5
8.5
7.5
8.5
6
7.5
8.5
4.5
6.5
5.5
8
6
6
7.5
7
6.5
7.5
Dataseries Y:
Download CSV
Histogram 
140
120
120
125
180
100
105
80
100
80
100
100
100
100
80
60
60
60
60
65
60
85
130
120
160
120
160
120
120
160
120
120

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=167528&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=167528&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167528&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
Mean6.9375106.5625
Biased Variance1.777343751025.68359375
Biased Standard Deviation1.3331705629813532.0262953485101
Covariance-9.09274193548387
Correlation-0.206307093566062
Determination0.042562616855676
T-Test-1.15483409640073
p-value (2 sided)0.257274460767403
p-value (1 sided)0.128637230383701
Degrees of Freedom30
Number of Observations32

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 6.9375 & 106.5625 \tabularnewline
Biased Variance & 1.77734375 & 1025.68359375 \tabularnewline
Biased Standard Deviation & 1.33317056298135 & 32.0262953485101 \tabularnewline
Covariance & -9.09274193548387 \tabularnewline
Correlation & -0.206307093566062 \tabularnewline
Determination & 0.042562616855676 \tabularnewline
T-Test & -1.15483409640073 \tabularnewline
p-value (2 sided) & 0.257274460767403 \tabularnewline
p-value (1 sided) & 0.128637230383701 \tabularnewline
Degrees of Freedom & 30 \tabularnewline
Number of Observations & 32 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167528&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]6.9375[/C][C]106.5625[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.77734375[/C][C]1025.68359375[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.33317056298135[/C][C]32.0262953485101[/C][/ROW]
[ROW][C]Covariance[/C][C]-9.09274193548387[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.206307093566062[/C][/ROW]
[ROW][C]Determination[/C][C]0.042562616855676[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.15483409640073[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.257274460767403[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.128637230383701[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]30[/C][/ROW]
[ROW][C]Number of Observations[/C][C]32[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167528&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167528&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
Mean6.9375106.5625
Biased Variance1.777343751025.68359375
Biased Standard Deviation1.3331705629813532.0262953485101
Covariance-9.09274193548387
Correlation-0.206307093566062
Determination0.042562616855676
T-Test-1.15483409640073
p-value (2 sided)0.257274460767403
p-value (1 sided)0.128637230383701
Degrees of Freedom30
Number of Observations32


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')