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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationTue, 15 Nov 2011 14:52:44 -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/2011/Nov/15/t13213867744oovwcqeujgwf8r.htm/, Retrieved Fri, 26 Apr 2024 15:04:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143458, Retrieved Fri, 26 Apr 2024 15:04:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-19 12:03:37] [74be16979710d4c4e7c6647856088456]
- RM D  [Pearson Correlation] [Scatterplot] [2010-11-12 15:51:23] [9894f466352df31a128e82ec8d720241]
- RMPD    [Notched Boxplots] [assignment - outl...] [2010-11-12 17:56:50] [9894f466352df31a128e82ec8d720241]
-   P       [Notched Boxplots] [] [2010-11-25 15:47:40] [2e1e44f0ae3cb9513dc28781dfdb387b]
- RMPD          [Pearson Correlation] [] [2011-11-15 19:52:44] [ef12b3094dcc95645ac503919f1fca4e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Dataseries Y:
Download CSV
Histogram 
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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=143458&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=143458&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143458&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
Mean20.64197530864223.037037037037
Biased Variance13.291571406797710.0109739368999
Biased Standard Deviation3.645760744590593.16401231617386
Covariance5.30526800092017
Correlation0.457079621785582
Determination0.20892178065165
T-Test6.50043076456109
p-value (2 sided)9.70824087787037e-10
p-value (1 sided)4.85412043893518e-10
Degrees of Freedom160
Number of Observations162

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 20.641975308642 & 23.037037037037 \tabularnewline
Biased Variance & 13.2915714067977 & 10.0109739368999 \tabularnewline
Biased Standard Deviation & 3.64576074459059 & 3.16401231617386 \tabularnewline
Covariance & 5.30526800092017 \tabularnewline
Correlation & 0.457079621785582 \tabularnewline
Determination & 0.20892178065165 \tabularnewline
T-Test & 6.50043076456109 \tabularnewline
p-value (2 sided) & 9.70824087787037e-10 \tabularnewline
p-value (1 sided) & 4.85412043893518e-10 \tabularnewline
Degrees of Freedom & 160 \tabularnewline
Number of Observations & 162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143458&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]20.641975308642[/C][C]23.037037037037[/C][/ROW]
[ROW][C]Biased Variance[/C][C]13.2915714067977[/C][C]10.0109739368999[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.64576074459059[/C][C]3.16401231617386[/C][/ROW]
[ROW][C]Covariance[/C][C]5.30526800092017[/C][/ROW]
[ROW][C]Correlation[/C][C]0.457079621785582[/C][/ROW]
[ROW][C]Determination[/C][C]0.20892178065165[/C][/ROW]
[ROW][C]T-Test[/C][C]6.50043076456109[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]9.70824087787037e-10[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]4.85412043893518e-10[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]160[/C][/ROW]
[ROW][C]Number of Observations[/C][C]162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143458&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143458&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
Mean20.64197530864223.037037037037
Biased Variance13.291571406797710.0109739368999
Biased Standard Deviation3.645760744590593.16401231617386
Covariance5.30526800092017
Correlation0.457079621785582
Determination0.20892178065165
T-Test6.50043076456109
p-value (2 sided)9.70824087787037e-10
p-value (1 sided)4.85412043893518e-10
Degrees of Freedom160
Number of Observations162


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
R code (references can be found in the software module):
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')
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')