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 computationSat, 03 Sep 2011 08:59:18 -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/2011/Sep/03/t1315056794qpwnmwojs7c2zrb.htm/, Retrieved Fri, 17 May 2024 23:11:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124280, Retrieved Fri, 17 May 2024 23:11:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact237

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [SY rtn] [2011-09-03 12:59:18] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-3
2.5
-1.9
1.8
2.6
-2.3
-2.4
3.8
-1.2
3.2
1.1
1.1
-1.3
-.5
1.6
2.7
-.2
1.2
0
.8
.7
.6
.2
3.2
-.5
-.1
-.2
2.6
2.2
.4
.8
.3
1
.9
-1.4
.4
.5
0
1.0
1
-.3
-1.4
2.9
.9
.6
-.1
.3
.4
-.9
-.6
-.2
1
-.9
-2.5
.2
3.4
-.8
.6
.8
-.4
-6.8
-.4
-6.9
5.6
2
Dataseries Y:
Download CSV
Histogram 
-4.2
-.2
-2.2
2.6
2.4
-3.6
-5
5.4
-1.2
3.6
-.1
1.8
-3.7
-.6
-.6
3.8
.5
1.5
2.1
-.2
1.7
.9
.6
3.6
-2.1
.1
-.8
3
1.3
.3
1.1
.1
1.2
1.7
-.7
-.5
2.7
1.5
1.1
-1.7
.1
-1.2
.8
1.4
-.3
-.6
1.3
2
-1.7
-.1
-.3
-.1
-2.3
-2.2
-.1
5.6
.3
-2
2.2
-3.9
-7.1
-1.6
-4.6
4.8
-.1

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124280&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124280&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124280&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'Gwilym Jenkins' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean0.3030769230769230.115384615384615
Biased Variance4.160298224852075.90068639053254
Biased Standard Deviation2.039680912508642.42913284744424
Covariance4.22948317307692
Correlation0.840505230396115
Determination0.706449042323227
T-Test12.3131435978754
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom63
Number of Observations65

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 0.303076923076923 & 0.115384615384615 \tabularnewline
Biased Variance & 4.16029822485207 & 5.90068639053254 \tabularnewline
Biased Standard Deviation & 2.03968091250864 & 2.42913284744424 \tabularnewline
Covariance & 4.22948317307692 \tabularnewline
Correlation & 0.840505230396115 \tabularnewline
Determination & 0.706449042323227 \tabularnewline
T-Test & 12.3131435978754 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 63 \tabularnewline
Number of Observations & 65 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124280&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]0.303076923076923[/C][C]0.115384615384615[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4.16029822485207[/C][C]5.90068639053254[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.03968091250864[/C][C]2.42913284744424[/C][/ROW]
[ROW][C]Covariance[/C][C]4.22948317307692[/C][/ROW]
[ROW][C]Correlation[/C][C]0.840505230396115[/C][/ROW]
[ROW][C]Determination[/C][C]0.706449042323227[/C][/ROW]
[ROW][C]T-Test[/C][C]12.3131435978754[/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]63[/C][/ROW]
[ROW][C]Number of Observations[/C][C]65[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124280&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124280&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
Mean0.3030769230769230.115384615384615
Biased Variance4.160298224852075.90068639053254
Biased Standard Deviation2.039680912508642.42913284744424
Covariance4.22948317307692
Correlation0.840505230396115
Determination0.706449042323227
T-Test12.3131435978754
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom63
Number of Observations65


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')