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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 14:44:18 +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/t1305556848jvk9j5gl3txgv64.htm/, Retrieved Sun, 12 May 2024 23:09:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121617, Retrieved Sun, 12 May 2024 23:09:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81

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 14:44:18] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
478
372
450
426
418
459
436
389
478
469
435
363
422
407
510
509
493
432
489
413
452
Dataseries Y:
Download CSV
Histogram 
73
65
68
40
54
59
55
58
58
54
69
41
69
46
72
64
56
52
66
62
40

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121617&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121617&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121617&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean442.85714285714358.1428571428571
Biased Variance1672.1224489795999.5510204081633
Biased Standard Deviation40.89159386695019.97752576584813
Covariance164.821428571429
Correlation0.384740121871967
Determination0.148024961378056
T-Test1.81689923999876
p-value (2 sided)0.0850417637310665
p-value (1 sided)0.0425208818655333
Degrees of Freedom19
Number of Observations21

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 442.857142857143 & 58.1428571428571 \tabularnewline
Biased Variance & 1672.12244897959 & 99.5510204081633 \tabularnewline
Biased Standard Deviation & 40.8915938669501 & 9.97752576584813 \tabularnewline
Covariance & 164.821428571429 \tabularnewline
Correlation & 0.384740121871967 \tabularnewline
Determination & 0.148024961378056 \tabularnewline
T-Test & 1.81689923999876 \tabularnewline
p-value (2 sided) & 0.0850417637310665 \tabularnewline
p-value (1 sided) & 0.0425208818655333 \tabularnewline
Degrees of Freedom & 19 \tabularnewline
Number of Observations & 21 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121617&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]442.857142857143[/C][C]58.1428571428571[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1672.12244897959[/C][C]99.5510204081633[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]40.8915938669501[/C][C]9.97752576584813[/C][/ROW]
[ROW][C]Covariance[/C][C]164.821428571429[/C][/ROW]
[ROW][C]Correlation[/C][C]0.384740121871967[/C][/ROW]
[ROW][C]Determination[/C][C]0.148024961378056[/C][/ROW]
[ROW][C]T-Test[/C][C]1.81689923999876[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0850417637310665[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0425208818655333[/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=121617&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121617&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
Mean442.85714285714358.1428571428571
Biased Variance1672.1224489795999.5510204081633
Biased Standard Deviation40.89159386695019.97752576584813
Covariance164.821428571429
Correlation0.384740121871967
Determination0.148024961378056
T-Test1.81689923999876
p-value (2 sided)0.0850417637310665
p-value (1 sided)0.0425208818655333
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')