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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 computationMon, 16 May 2011 14:40:47 +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/2011/May/16/t1305556596rg6bnvyepo5vh26.htm/, Retrieved Mon, 13 May 2024 11:59:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121614, Retrieved Mon, 13 May 2024 11:59:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [5th grade math an...] [2011-05-16 14:40:47] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
553
530
504
522
530
509
432
564
441
548
511
515
529
489
430
501
618
541
525
532
596
Dataseries Y:
Download CSV
Histogram 
42
38
34
43
40
36
27
39
32
47
44
40
42
28
23
32
34
27
39
41
43

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'George Udny Yule' @ 216.218.223.82

\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 & 'George Udny Yule' @ 216.218.223.82 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121614&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]'George Udny Yule' @ 216.218.223.82[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121614&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121614&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'George Udny Yule' @ 216.218.223.82






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean52036.7142857142857
Biased Variance209440.8707482993197
Biased Standard Deviation45.76024475459026.39302340831939
Covariance176.5
Correlation0.574593590713489
Determination0.330157794489021
T-Test3.06021066078386
p-value (2 sided)0.00644110966034517
p-value (1 sided)0.00322055483017258
Degrees of Freedom19
Number of Observations21

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 520 & 36.7142857142857 \tabularnewline
Biased Variance & 2094 & 40.8707482993197 \tabularnewline
Biased Standard Deviation & 45.7602447545902 & 6.39302340831939 \tabularnewline
Covariance & 176.5 \tabularnewline
Correlation & 0.574593590713489 \tabularnewline
Determination & 0.330157794489021 \tabularnewline
T-Test & 3.06021066078386 \tabularnewline
p-value (2 sided) & 0.00644110966034517 \tabularnewline
p-value (1 sided) & 0.00322055483017258 \tabularnewline
Degrees of Freedom & 19 \tabularnewline
Number of Observations & 21 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121614&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]520[/C][C]36.7142857142857[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2094[/C][C]40.8707482993197[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]45.7602447545902[/C][C]6.39302340831939[/C][/ROW]
[ROW][C]Covariance[/C][C]176.5[/C][/ROW]
[ROW][C]Correlation[/C][C]0.574593590713489[/C][/ROW]
[ROW][C]Determination[/C][C]0.330157794489021[/C][/ROW]
[ROW][C]T-Test[/C][C]3.06021066078386[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00644110966034517[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00322055483017258[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]19[/C][/ROW]
[ROW][C]Number of Observations[/C][C]21[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121614&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121614&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
Mean52036.7142857142857
Biased Variance209440.8707482993197
Biased Standard Deviation45.76024475459026.39302340831939
Covariance176.5
Correlation0.574593590713489
Determination0.330157794489021
T-Test3.06021066078386
p-value (2 sided)0.00644110966034517
p-value (1 sided)0.00322055483017258
Degrees of Freedom19
Number of Observations21


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')