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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, 22 Nov 2011 10:13:55 -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/2011/Nov/22/t1321974893rsvgmatm5zpu3co.htm/, Retrieved Tue, 23 Apr 2024 08:56:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=146273, Retrieved Tue, 23 Apr 2024 08:56:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [WS7 - Scatterplot...] [2011-11-22 15:13:55] [e598b5cd83fcb010b35e92a01f5e81e9] [Current]
-    D    [Pearson Correlation] [WS7 - Scatterplot...] [2011-11-22 15:17:07] [ae1339cb5a7cf28362d01e7220b4a16c]
-    D    [Pearson Correlation] [WS7 - Scatterplot...] [2011-11-22 15:18:09] [ae1339cb5a7cf28362d01e7220b4a16c]
- RMPD    [Multiple Regression] [WS 7 Mini-Tutorial] [2011-11-22 16:50:45] [ae1339cb5a7cf28362d01e7220b4a16c]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5960
9000
9500
10000
18000
8500
8000
23000
8100
9000
7300
8000
20000
8000
8000
10500
4000
45000
3400
1500
17800
18500
6700
44200
3400
29400
43200
2900
28900
21000
8700
34100
28100
38400
33900
5100
14600
17400
30900
25500
33900
33700
19900
26800
30500
19500
42500
12200
6600
2800
7600
37700
28200
20600
23000
15900
20800
10000
22000
40300
Dataseries Y:
Download CSV
Histogram 
68900
48500
55500
62000
116500
45000
38000
83000
59000
47500
40500
40000
97000
45500
40900
80000
56000
37000
50000
22400
241100
82200
234400
233700
177700
65900
117600
22500
326600
377900
290700
108200
488100
496600
493100
236900
420600
328200
313200
40200
318300
374100
144400
298300
404200
134600
270600
181800
492300
203000
464300
137200
95100
481300
112300
29500
76200
323800
40600
425700

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'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146273&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146273&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146273&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'AstonUniversity' @ aston.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean18866187270
Biased Variance153633737.33333323552737100
Biased Standard Deviation12394.9077178224153469.010226821
Covariance644442793.220339
Correlation0.333135674654653
Determination0.110979377727611
T-Test2.69078638676644
p-value (2 sided)0.00929714814528193
p-value (1 sided)0.00464857407264097
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 18866 & 187270 \tabularnewline
Biased Variance & 153633737.333333 & 23552737100 \tabularnewline
Biased Standard Deviation & 12394.9077178224 & 153469.010226821 \tabularnewline
Covariance & 644442793.220339 \tabularnewline
Correlation & 0.333135674654653 \tabularnewline
Determination & 0.110979377727611 \tabularnewline
T-Test & 2.69078638676644 \tabularnewline
p-value (2 sided) & 0.00929714814528193 \tabularnewline
p-value (1 sided) & 0.00464857407264097 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146273&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]18866[/C][C]187270[/C][/ROW]
[ROW][C]Biased Variance[/C][C]153633737.333333[/C][C]23552737100[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]12394.9077178224[/C][C]153469.010226821[/C][/ROW]
[ROW][C]Covariance[/C][C]644442793.220339[/C][/ROW]
[ROW][C]Correlation[/C][C]0.333135674654653[/C][/ROW]
[ROW][C]Determination[/C][C]0.110979377727611[/C][/ROW]
[ROW][C]T-Test[/C][C]2.69078638676644[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00929714814528193[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00464857407264097[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146273&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146273&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
Mean18866187270
Biased Variance153633737.33333323552737100
Biased Standard Deviation12394.9077178224153469.010226821
Covariance644442793.220339
Correlation0.333135674654653
Determination0.110979377727611
T-Test2.69078638676644
p-value (2 sided)0.00929714814528193
p-value (1 sided)0.00464857407264097
Degrees of Freedom58
Number of Observations60


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')