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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, 14 Dec 2010 22:09:52 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/14/t1292364510nb52wdly07jvec5.htm/, Retrieved Thu, 02 May 2024 19:08:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110239, Retrieved Thu, 02 May 2024 19:08:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Competence to learn] [2010-11-17 07:43:53] [b98453cac15ba1066b407e146608df68]
- R PD  [Multiple Regression] [Workshop 7 - Firs...] [2010-11-19 10:36:36] [8b017ffbf7b0eded54d8efebfb3e4cfa]
-   P     [Multiple Regression] [Workshop 7 - Firs...] [2010-11-19 10:41:24] [8b017ffbf7b0eded54d8efebfb3e4cfa]
- R PD      [Multiple Regression] [] [2010-11-23 16:27:22] [1ad9dd03b6c5806e9fe90049663fcef1]
- RMPD          [Pearson Correlation] [correlatie PS - L...] [2010-12-14 22:09:52] [5f761c4a622da19727fd2adf71158b48] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2
1,8
0,7
3,9
1
3,6
1,4
1,5
0,7
2,1
0
4,1
1,2
0,5
3,4
1,5
3,4
0,8
0,8
1,4
2
1,9
1,3
2
5,6
3,1
1,8
0,9
1,8
1,9
0,9
2,6
2,4
1,2
0,9
0,5
0,6
2,3
0,5
2,6
0,6
6,6
Dataseries Y:
Download CSV
Histogram 
4,5
69
27
19
30,4
28
50
7
30
3,5
50
6
10,4
20
3,9
41
9
7,6
46
2,6
24
100
3,2
2
5
6,5
12
20,2
13
27
18
4,7
9,8
29
7
6
20
4,5
7,5
2,3
24
3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110239&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110239&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110239&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1.919.3714285714286
Biased Variance1.88285714285714400.581088435374
Biased Standard Deviation1.3721724173212120.0145219387168
Covariance-7.54926829268293
Correlation-0.268340064645849
Determination0.0720063902941386
T-Test-1.76174489987959
p-value (2 sided)0.0857543140388109
p-value (1 sided)0.0428771570194054
Degrees of Freedom40
Number of Observations42

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1.9 & 19.3714285714286 \tabularnewline
Biased Variance & 1.88285714285714 & 400.581088435374 \tabularnewline
Biased Standard Deviation & 1.37217241732121 & 20.0145219387168 \tabularnewline
Covariance & -7.54926829268293 \tabularnewline
Correlation & -0.268340064645849 \tabularnewline
Determination & 0.0720063902941386 \tabularnewline
T-Test & -1.76174489987959 \tabularnewline
p-value (2 sided) & 0.0857543140388109 \tabularnewline
p-value (1 sided) & 0.0428771570194054 \tabularnewline
Degrees of Freedom & 40 \tabularnewline
Number of Observations & 42 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110239&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]1.9[/C][C]19.3714285714286[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.88285714285714[/C][C]400.581088435374[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.37217241732121[/C][C]20.0145219387168[/C][/ROW]
[ROW][C]Covariance[/C][C]-7.54926829268293[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.268340064645849[/C][/ROW]
[ROW][C]Determination[/C][C]0.0720063902941386[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.76174489987959[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0857543140388109[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0428771570194054[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]40[/C][/ROW]
[ROW][C]Number of Observations[/C][C]42[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110239&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110239&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
Mean1.919.3714285714286
Biased Variance1.88285714285714400.581088435374
Biased Standard Deviation1.3721724173212120.0145219387168
Covariance-7.54926829268293
Correlation-0.268340064645849
Determination0.0720063902941386
T-Test-1.76174489987959
p-value (2 sided)0.0857543140388109
p-value (1 sided)0.0428771570194054
Degrees of Freedom40
Number of Observations42


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = pearson ;
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')