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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 10:18:09 -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/2011/Nov/22/t1321975123qkp2uej57yxayh4.htm/, Retrieved Fri, 26 Apr 2024 09:29:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=146279, Retrieved Fri, 26 Apr 2024 09:29:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80

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] [ae1339cb5a7cf28362d01e7220b4a16c]
-    D    [Pearson Correlation] [WS7 - Scatterplot...] [2011-11-22 15:18:09] [e598b5cd83fcb010b35e92a01f5e81e9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1873
928
1126
1265
2214
912
899
1803
1204
1725
1080
1529
2455
1151
1173
1960
1344
988
1076
962
2100
2300
1600
1300
1700
2300
2400
1000
1800
1700
1400
1200
2100
2200
1100
1900
1500
2300
2100
1800
1100
2000
900
1500
1600
1200
1000
2000
2000
1900
2000
1500
1900
1300
1400
1300
1800
2200
1000
1900
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 time1 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 & 1 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146279&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146279&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146279&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'AstonUniversity' @ aston.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1582.78333333333187270
Biased Variance208871.93638888923552737100
Biased Standard Deviation457.025093828434153469.010226821
Covariance23780273.0508475
Correlation0.333393293637725
Determination0.11115108824261
T-Test2.69312730915106
p-value (2 sided)0.00923945586615749
p-value (1 sided)0.00461972793307874
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1582.78333333333 & 187270 \tabularnewline
Biased Variance & 208871.936388889 & 23552737100 \tabularnewline
Biased Standard Deviation & 457.025093828434 & 153469.010226821 \tabularnewline
Covariance & 23780273.0508475 \tabularnewline
Correlation & 0.333393293637725 \tabularnewline
Determination & 0.11115108824261 \tabularnewline
T-Test & 2.69312730915106 \tabularnewline
p-value (2 sided) & 0.00923945586615749 \tabularnewline
p-value (1 sided) & 0.00461972793307874 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146279&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]1582.78333333333[/C][C]187270[/C][/ROW]
[ROW][C]Biased Variance[/C][C]208871.936388889[/C][C]23552737100[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]457.025093828434[/C][C]153469.010226821[/C][/ROW]
[ROW][C]Covariance[/C][C]23780273.0508475[/C][/ROW]
[ROW][C]Correlation[/C][C]0.333393293637725[/C][/ROW]
[ROW][C]Determination[/C][C]0.11115108824261[/C][/ROW]
[ROW][C]T-Test[/C][C]2.69312730915106[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00923945586615749[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00461972793307874[/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=146279&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146279&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
Mean1582.78333333333187270
Biased Variance208871.93638888923552737100
Biased Standard Deviation457.025093828434153469.010226821
Covariance23780273.0508475
Correlation0.333393293637725
Determination0.11115108824261
T-Test2.69312730915106
p-value (2 sided)0.00923945586615749
p-value (1 sided)0.00461972793307874
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')