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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, 05 Apr 2008 13:23:54 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/05/t1207423577ew9qujgz6ikot88.htm/, Retrieved Sun, 12 May 2024 04:54:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10092, Retrieved Sun, 12 May 2024 04:54:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact305

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Foundation and SES] [2008-04-05 19:23:54] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12310
12310
8104
7384
7384
9284
8110
11392
11392
8699
12387
12387
8508
9024
7451
7780
7231
9467
9467
9319
7204
7446
10500
10500
10500
7308
7308
7204
8218
8179
8265
8265
8265
7259
10870
8277
8870
8870
8870
7542
7542
Dataseries Y:
Download CSV
Histogram 
3
2
46
70
68
19
12
31
40
15
4
2
31
3
11
47
51
4
3
12
12
7
9
18
6
17
14
24
11
51
2
5
12
12
26
22
9
7
14
21
30

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10092&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10092&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10092&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean8942.7317073170719.5853658536585
Biased Variance2598840.97679952313.85246876859
Biased Standard Deviation1612.0921117602217.7158818230589
Covariance-10084.3390243902
Correlation-0.344485498778087
Determination0.118670258868388
T-Test-2.29157478760068
p-value (2 sided)0.027414312375432
p-value (1 sided)0.013707156187716
Degrees of Freedom39
Number of Observations41

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 8942.73170731707 & 19.5853658536585 \tabularnewline
Biased Variance & 2598840.97679952 & 313.85246876859 \tabularnewline
Biased Standard Deviation & 1612.09211176022 & 17.7158818230589 \tabularnewline
Covariance & -10084.3390243902 \tabularnewline
Correlation & -0.344485498778087 \tabularnewline
Determination & 0.118670258868388 \tabularnewline
T-Test & -2.29157478760068 \tabularnewline
p-value (2 sided) & 0.027414312375432 \tabularnewline
p-value (1 sided) & 0.013707156187716 \tabularnewline
Degrees of Freedom & 39 \tabularnewline
Number of Observations & 41 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10092&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]8942.73170731707[/C][C]19.5853658536585[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2598840.97679952[/C][C]313.85246876859[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1612.09211176022[/C][C]17.7158818230589[/C][/ROW]
[ROW][C]Covariance[/C][C]-10084.3390243902[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.344485498778087[/C][/ROW]
[ROW][C]Determination[/C][C]0.118670258868388[/C][/ROW]
[ROW][C]T-Test[/C][C]-2.29157478760068[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.027414312375432[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.013707156187716[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]39[/C][/ROW]
[ROW][C]Number of Observations[/C][C]41[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10092&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10092&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
Mean8942.7317073170719.5853658536585
Biased Variance2598840.97679952313.85246876859
Biased Standard Deviation1612.0921117602217.7158818230589
Covariance-10084.3390243902
Correlation-0.344485498778087
Determination0.118670258868388
T-Test-2.29157478760068
p-value (2 sided)0.027414312375432
p-value (1 sided)0.013707156187716
Degrees of Freedom39
Number of Observations41


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')