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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 computationThu, 21 Nov 2013 02:47:56 -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/2013/Nov/21/t1385020082z2dga9ujvlafoda.htm/, Retrieved Fri, 03 May 2024 13:58:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226780, Retrieved Fri, 03 May 2024 13:58:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2013-11-21 07:47:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21
20
20
23
16
16
17
20
20
15
19
15
14
17
20
9
12
16
16
18
18
15
15
20
23
25
17
24
28
28
27
26
18
26
12
20
18
17
15
11
21
11
5
13
8
13
9
17
12
10
2
Dataseries Y:
Download CSV
Histogram 
3
3
3
3
7
6
5
4
6
4
5
5
7
4
5
4
6
5
5
6
6
5
3
3
3
6
4
4
4
6
5
5
6
4
4
6
6
8
9
5
4
4
5
4
8
6
5
3
5
6
7

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=226780&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=226780&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226780&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
Mean17.01960784313735
Biased Variance31.98000768935022
Biased Standard Deviation5.655086886100891.4142135623731
Covariance-2.32
Correlation-0.284402581007406
Determination0.0808848280836739
T-Test-2.07657014502414
p-value (2 sided)0.0431072834596182
p-value (1 sided)0.0215536417298091
Degrees of Freedom49
Number of Observations51

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 17.0196078431373 & 5 \tabularnewline
Biased Variance & 31.9800076893502 & 2 \tabularnewline
Biased Standard Deviation & 5.65508688610089 & 1.4142135623731 \tabularnewline
Covariance & -2.32 \tabularnewline
Correlation & -0.284402581007406 \tabularnewline
Determination & 0.0808848280836739 \tabularnewline
T-Test & -2.07657014502414 \tabularnewline
p-value (2 sided) & 0.0431072834596182 \tabularnewline
p-value (1 sided) & 0.0215536417298091 \tabularnewline
Degrees of Freedom & 49 \tabularnewline
Number of Observations & 51 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226780&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]17.0196078431373[/C][C]5[/C][/ROW]
[ROW][C]Biased Variance[/C][C]31.9800076893502[/C][C]2[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]5.65508688610089[/C][C]1.4142135623731[/C][/ROW]
[ROW][C]Covariance[/C][C]-2.32[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.284402581007406[/C][/ROW]
[ROW][C]Determination[/C][C]0.0808848280836739[/C][/ROW]
[ROW][C]T-Test[/C][C]-2.07657014502414[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0431072834596182[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0215536417298091[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]49[/C][/ROW]
[ROW][C]Number of Observations[/C][C]51[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226780&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226780&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
Mean17.01960784313735
Biased Variance31.98000768935022
Biased Standard Deviation5.655086886100891.4142135623731
Covariance-2.32
Correlation-0.284402581007406
Determination0.0808848280836739
T-Test-2.07657014502414
p-value (2 sided)0.0431072834596182
p-value (1 sided)0.0215536417298091
Degrees of Freedom49
Number of Observations51


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')