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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 computationWed, 14 Dec 2011 11:50:57 -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/Dec/14/t1323881494f7n3vrsjgp0fi79.htm/, Retrieved Wed, 01 May 2024 20:26:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=155126, Retrieved Wed, 01 May 2024 20:26:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Pearson Correlation] [Screen dimensions] [2010-09-25 10:10:17] [b98453cac15ba1066b407e146608df68]
- R  D  [Pearson Correlation] [Paper: Scatterplot] [2011-12-14 16:38:52] [54b1f171ce7a12209ffa11b565e1dcf5]
-    D    [Pearson Correlation] [Paper: Scatterplo...] [2011-12-14 16:45:58] [54b1f171ce7a12209ffa11b565e1dcf5]
-    D        [Pearson Correlation] [Paper: Scatterplo...] [2011-12-14 16:50:57] [70041e5e9044b1d424b6896a10522877] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1366
1280
1280
1280
1280
1280
1680
1280
1680
1440
2560
1280
1280
1280
1280
1440
1920
1280
1440
1920
1280
1024
1024
1280
1280
1366
1344
1024
1366
1024
1280
1280
1366
1173
1680
1280
1120
1280
1920
1440
1280
1366
1024
1600
1280
1024
1280
1280
1280
1280
1280
1680
1366
1280
1525
1920
1366
1280
1920
1024
1024
1280
1440
1440
1280
1366
1024
1280
1440
1920
1366
1280
1920
1024
1920
1366
1280
1280
1280
1366
1600
1280
1366
1280
1344
1024
1280
1280
1920
1024
1280
1920
1366
1366
1280
1366
1280
1280
Dataseries Y:
Download CSV
Histogram 
768
800
800
1024
800
1024
1050
720
1050
900
1440
1024
800
1024
800
900
1080
1024
900
1200
800
768
768
800
800
768
840
768
768
768
1024
800
768
939
1050
800
700
800
1080
900
800
768
768
900
800
768
800
768
800
1024
1024
1050
768
720
858
1080
768
800
1200
768
768
800
900
900
1024
768
600
800
900
1200
768
1024
1200
768
1200
768
800
1024
1024
768
900
1024
768
768
840
768
800
800
1200
768
800
1080
768
768
800
768
1024
800

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=155126&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=155126&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155126&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
Mean1375.55102040816882.826530612245
Biased Variance70064.267805081222150.1841940858
Biased Standard Deviation264.696557977396148.829379472219
Covariance30854.6532716179
Correlation0.775227845931927
Determination0.600978213108255
T-Test12.0244902900325
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom96
Number of Observations98

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1375.55102040816 & 882.826530612245 \tabularnewline
Biased Variance & 70064.2678050812 & 22150.1841940858 \tabularnewline
Biased Standard Deviation & 264.696557977396 & 148.829379472219 \tabularnewline
Covariance & 30854.6532716179 \tabularnewline
Correlation & 0.775227845931927 \tabularnewline
Determination & 0.600978213108255 \tabularnewline
T-Test & 12.0244902900325 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 96 \tabularnewline
Number of Observations & 98 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155126&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]1375.55102040816[/C][C]882.826530612245[/C][/ROW]
[ROW][C]Biased Variance[/C][C]70064.2678050812[/C][C]22150.1841940858[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]264.696557977396[/C][C]148.829379472219[/C][/ROW]
[ROW][C]Covariance[/C][C]30854.6532716179[/C][/ROW]
[ROW][C]Correlation[/C][C]0.775227845931927[/C][/ROW]
[ROW][C]Determination[/C][C]0.600978213108255[/C][/ROW]
[ROW][C]T-Test[/C][C]12.0244902900325[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]96[/C][/ROW]
[ROW][C]Number of Observations[/C][C]98[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155126&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155126&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
Mean1375.55102040816882.826530612245
Biased Variance70064.267805081222150.1841940858
Biased Standard Deviation264.696557977396148.829379472219
Covariance30854.6532716179
Correlation0.775227845931927
Determination0.600978213108255
T-Test12.0244902900325
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom96
Number of Observations98


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')