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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 computationSat, 26 Oct 2013 18:39:19 -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/2013/Oct/26/t1382827193m4jdmddws31p28p.htm/, Retrieved Fri, 03 May 2024 10:47:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=219744, Retrieved Fri, 03 May 2024 10:47:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2013-10-26 22:39:19] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
81
73
70
68
67
65
64
62
62
61
58
57
56
52
52
52
52
50
48
48
46
43
42
42
42
40
39
32
29
27
Dataseries Y:
Download CSV
Histogram 
14
18
17
14
4
10
10
14
7
8
4
11
12
10
13
17
10
14
10
12
16
11
16
15
12
7
13
13
6
5

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=219744&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=219744&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219744&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
Mean52.666666666666711.4333333333333
Biased Variance168.82222222222214.5788888888889
Biased Standard Deviation12.99316059402883.81823112041281
Covariance9.90804597701149
Correlation0.193057970783636
Determination0.0372713800830951
T-Test1.04115361499545
p-value (2 sided)0.306711275261603
p-value (1 sided)0.153355637630802
Degrees of Freedom28
Number of Observations30

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 52.6666666666667 & 11.4333333333333 \tabularnewline
Biased Variance & 168.822222222222 & 14.5788888888889 \tabularnewline
Biased Standard Deviation & 12.9931605940288 & 3.81823112041281 \tabularnewline
Covariance & 9.90804597701149 \tabularnewline
Correlation & 0.193057970783636 \tabularnewline
Determination & 0.0372713800830951 \tabularnewline
T-Test & 1.04115361499545 \tabularnewline
p-value (2 sided) & 0.306711275261603 \tabularnewline
p-value (1 sided) & 0.153355637630802 \tabularnewline
Degrees of Freedom & 28 \tabularnewline
Number of Observations & 30 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219744&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]52.6666666666667[/C][C]11.4333333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]168.822222222222[/C][C]14.5788888888889[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]12.9931605940288[/C][C]3.81823112041281[/C][/ROW]
[ROW][C]Covariance[/C][C]9.90804597701149[/C][/ROW]
[ROW][C]Correlation[/C][C]0.193057970783636[/C][/ROW]
[ROW][C]Determination[/C][C]0.0372713800830951[/C][/ROW]
[ROW][C]T-Test[/C][C]1.04115361499545[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.306711275261603[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.153355637630802[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]28[/C][/ROW]
[ROW][C]Number of Observations[/C][C]30[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219744&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219744&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
Mean52.666666666666711.4333333333333
Biased Variance168.82222222222214.5788888888889
Biased Standard Deviation12.99316059402883.81823112041281
Covariance9.90804597701149
Correlation0.193057970783636
Determination0.0372713800830951
T-Test1.04115361499545
p-value (2 sided)0.306711275261603
p-value (1 sided)0.153355637630802
Degrees of Freedom28
Number of Observations30


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')