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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 02:44:09 -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/t13850198687bjbmm89qi1143o.htm/, Retrieved Fri, 03 May 2024 06:00:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226778, Retrieved Fri, 03 May 2024 06:00:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102

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 07:44:09] [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 
183.8
134.7
30.5
41.3
146.3
59.5
50.2
34.7
40.4
46.3
57.9
181.1
184.9
87.3
158.3
189.6
117
132
196.5
134.4
122.4
100
76.4
176.1
59.1
177.6
139
196.5
81.5
185.7
95.4
90
88.8
167.2
145.9
104.2
212.4
181.5
131.3
162.2
73.4
74.1
160.2
59.1
173.4
112
188.8
131.3
162.2
142.9
155

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=226778&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=226778&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226778&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
Mean17.0196078431373124.162745098039
Biased Variance31.98000768935022677.00586697424
Biased Standard Deviation5.6550868861008951.7397899780647
Covariance-60.0112549019608
Correlation-0.201079868835012
Determination0.0404331136507056
T-Test-1.43690814657076
p-value (2 sided)0.157099037281916
p-value (1 sided)0.0785495186409579
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 & 124.162745098039 \tabularnewline
Biased Variance & 31.9800076893502 & 2677.00586697424 \tabularnewline
Biased Standard Deviation & 5.65508688610089 & 51.7397899780647 \tabularnewline
Covariance & -60.0112549019608 \tabularnewline
Correlation & -0.201079868835012 \tabularnewline
Determination & 0.0404331136507056 \tabularnewline
T-Test & -1.43690814657076 \tabularnewline
p-value (2 sided) & 0.157099037281916 \tabularnewline
p-value (1 sided) & 0.0785495186409579 \tabularnewline
Degrees of Freedom & 49 \tabularnewline
Number of Observations & 51 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226778&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]124.162745098039[/C][/ROW]
[ROW][C]Biased Variance[/C][C]31.9800076893502[/C][C]2677.00586697424[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]5.65508688610089[/C][C]51.7397899780647[/C][/ROW]
[ROW][C]Covariance[/C][C]-60.0112549019608[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.201079868835012[/C][/ROW]
[ROW][C]Determination[/C][C]0.0404331136507056[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.43690814657076[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.157099037281916[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0785495186409579[/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=226778&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226778&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
Mean17.0196078431373124.162745098039
Biased Variance31.98000768935022677.00586697424
Biased Standard Deviation5.6550868861008951.7397899780647
Covariance-60.0112549019608
Correlation-0.201079868835012
Determination0.0404331136507056
T-Test-1.43690814657076
p-value (2 sided)0.157099037281916
p-value (1 sided)0.0785495186409579
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')