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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 14:57:13 +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/t1305557581zqqacvnec4jiaqj.htm/, Retrieved Sun, 12 May 2024 22:05:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121626, Retrieved Sun, 12 May 2024 22:05:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [3rd grade wkce an...] [2011-05-16 14:57:13] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
475
470
458
441
466
409
483
389
473
463
446
423
467
444
416
391
452
477
432
388
422
Dataseries Y:
Download CSV
Histogram 
41
41
32
34
40
25
46
30
39
36
36
34
32
38
20
38
37
36
26
24
28

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'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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121626&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121626&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121626&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'Herman Ole Andreas Wold' @ www.yougetit.org






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean442.14285714285733.9523809523809
Biased Variance890.97959183673540.8072562358277
Biased Standard Deviation29.84928126164416.38805574770819
Covariance135.157142857143
Correlation0.67506738734878
Determination0.455715977461908
T-Test3.98851413243924
p-value (2 sided)0.000786560905980505
p-value (1 sided)0.000393280452990252
Degrees of Freedom19
Number of Observations21

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 442.142857142857 & 33.9523809523809 \tabularnewline
Biased Variance & 890.979591836735 & 40.8072562358277 \tabularnewline
Biased Standard Deviation & 29.8492812616441 & 6.38805574770819 \tabularnewline
Covariance & 135.157142857143 \tabularnewline
Correlation & 0.67506738734878 \tabularnewline
Determination & 0.455715977461908 \tabularnewline
T-Test & 3.98851413243924 \tabularnewline
p-value (2 sided) & 0.000786560905980505 \tabularnewline
p-value (1 sided) & 0.000393280452990252 \tabularnewline
Degrees of Freedom & 19 \tabularnewline
Number of Observations & 21 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121626&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]442.142857142857[/C][C]33.9523809523809[/C][/ROW]
[ROW][C]Biased Variance[/C][C]890.979591836735[/C][C]40.8072562358277[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]29.8492812616441[/C][C]6.38805574770819[/C][/ROW]
[ROW][C]Covariance[/C][C]135.157142857143[/C][/ROW]
[ROW][C]Correlation[/C][C]0.67506738734878[/C][/ROW]
[ROW][C]Determination[/C][C]0.455715977461908[/C][/ROW]
[ROW][C]T-Test[/C][C]3.98851413243924[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000786560905980505[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000393280452990252[/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=121626&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121626&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
Mean442.14285714285733.9523809523809
Biased Variance890.97959183673540.8072562358277
Biased Standard Deviation29.84928126164416.38805574770819
Covariance135.157142857143
Correlation0.67506738734878
Determination0.455715977461908
T-Test3.98851413243924
p-value (2 sided)0.000786560905980505
p-value (1 sided)0.000393280452990252
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')