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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 computationFri, 12 Dec 2014 10:24:13 +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/2014/Dec/12/t141837986343725a7ubng9tau.htm/, Retrieved Thu, 16 May 2024 09:53:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266477, Retrieved Thu, 16 May 2024 09:53:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Pearson Correlation] [Screen dimensions] [2010-09-25 10:10:17] [b98453cac15ba1066b407e146608df68]
- RM D  [Pearson Correlation] [] [2014-12-12 10:21:33] [93cb0d178904cf975da218b7c929e42d]
-    D      [Pearson Correlation] [] [2014-12-12 10:24:13] [0935be2dcbf70771a0c3533f1d231b96] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.5
6.5
1.0
1.0
5.5
8.5
6.5
4.5
2.0
5.0
0.5
5.0
2.5
5.0
5.5
3.5
4.0
6.5
4.5
5.5
4.0
7.5
4.0
5.5
2.5
5.5
3.5
4.5
4.5
6.0
5.0
6.5
5.0
6.0
4.5
5.0
5.0
6.5
7.0
4.5
8.5
3.5
6.0
1.5
3.5
7.5
5.0
6.5
6.5
6.5
7.0
1.5
4.0
4.5
0.0
3.5
4.5
0.0
3.0
3.5
3.0
1.0
5.5
Dataseries Y:
Download CSV
Histogram 
149
148
158
128
224
159
105
159
167
165
159
176
54
91
163
124
121
148
221
149
244
148
150
153
94
156
132
105
151
131
157
162
163
59
187
116
148
155
125
116
138
164
162
99
186
188
177
139
162
108
159
110
96
87
97
127
74
114
95
121
130
52
118

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=266477&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=266477&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266477&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
Mean4.58730158730159138.460317460317
Biased Variance4.043965734441931439.51826656589
Biased Standard Deviation2.0109613955623137.9409839957517
Covariance21.4027137736815
Correlation0.276062654707034
Determination0.0762105893238948
T-Test2.24329344676868
p-value (2 sided)0.0285204333097937
p-value (1 sided)0.0142602166548969
Degrees of Freedom61
Number of Observations63

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 4.58730158730159 & 138.460317460317 \tabularnewline
Biased Variance & 4.04396573444193 & 1439.51826656589 \tabularnewline
Biased Standard Deviation & 2.01096139556231 & 37.9409839957517 \tabularnewline
Covariance & 21.4027137736815 \tabularnewline
Correlation & 0.276062654707034 \tabularnewline
Determination & 0.0762105893238948 \tabularnewline
T-Test & 2.24329344676868 \tabularnewline
p-value (2 sided) & 0.0285204333097937 \tabularnewline
p-value (1 sided) & 0.0142602166548969 \tabularnewline
Degrees of Freedom & 61 \tabularnewline
Number of Observations & 63 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266477&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]4.58730158730159[/C][C]138.460317460317[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4.04396573444193[/C][C]1439.51826656589[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.01096139556231[/C][C]37.9409839957517[/C][/ROW]
[ROW][C]Covariance[/C][C]21.4027137736815[/C][/ROW]
[ROW][C]Correlation[/C][C]0.276062654707034[/C][/ROW]
[ROW][C]Determination[/C][C]0.0762105893238948[/C][/ROW]
[ROW][C]T-Test[/C][C]2.24329344676868[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0285204333097937[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0142602166548969[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]61[/C][/ROW]
[ROW][C]Number of Observations[/C][C]63[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266477&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266477&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
Mean4.58730158730159138.460317460317
Biased Variance4.043965734441931439.51826656589
Biased Standard Deviation2.0109613955623137.9409839957517
Covariance21.4027137736815
Correlation0.276062654707034
Determination0.0762105893238948
T-Test2.24329344676868
p-value (2 sided)0.0285204333097937
p-value (1 sided)0.0142602166548969
Degrees of Freedom61
Number of Observations63


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')