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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 16:05:40 +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/t13055618072zis2xrirdkgjfn.htm/, Retrieved Sun, 12 May 2024 22:24:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121643, Retrieved Sun, 12 May 2024 22:24:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83

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 16:05:40] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
501
569
499
501
491
441
520
468
484
576
482
570
484
472
525
477
613
473
505
508
548
Dataseries Y:
Download CSV
Histogram 
28
45
26
28
31
24
36
6
28
38
35
40
27
26
36
22
45
21
28
25
35

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 0 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121643&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121643&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121643&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 time0 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean509.85714285714330
Biased Variance1764.3129251700775.047619047619
Biased Standard Deviation42.00372513444578.66300288858425
Covariance307
Correlation0.80351281821524
Determination0.645632849036198
T-Test5.88359650522338
p-value (2 sided)1.15058296419335e-05
p-value (1 sided)5.75291482096674e-06
Degrees of Freedom19
Number of Observations21

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 509.857142857143 & 30 \tabularnewline
Biased Variance & 1764.31292517007 & 75.047619047619 \tabularnewline
Biased Standard Deviation & 42.0037251344457 & 8.66300288858425 \tabularnewline
Covariance & 307 \tabularnewline
Correlation & 0.80351281821524 \tabularnewline
Determination & 0.645632849036198 \tabularnewline
T-Test & 5.88359650522338 \tabularnewline
p-value (2 sided) & 1.15058296419335e-05 \tabularnewline
p-value (1 sided) & 5.75291482096674e-06 \tabularnewline
Degrees of Freedom & 19 \tabularnewline
Number of Observations & 21 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121643&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]509.857142857143[/C][C]30[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1764.31292517007[/C][C]75.047619047619[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]42.0037251344457[/C][C]8.66300288858425[/C][/ROW]
[ROW][C]Covariance[/C][C]307[/C][/ROW]
[ROW][C]Correlation[/C][C]0.80351281821524[/C][/ROW]
[ROW][C]Determination[/C][C]0.645632849036198[/C][/ROW]
[ROW][C]T-Test[/C][C]5.88359650522338[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.15058296419335e-05[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]5.75291482096674e-06[/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=121643&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121643&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
Mean509.85714285714330
Biased Variance1764.3129251700775.047619047619
Biased Standard Deviation42.00372513444578.66300288858425
Covariance307
Correlation0.80351281821524
Determination0.645632849036198
T-Test5.88359650522338
p-value (2 sided)1.15058296419335e-05
p-value (1 sided)5.75291482096674e-06
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')