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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 computationWed, 11 Jun 2014 11:53:37 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Jun/11/t1402480457pdkdbo1j1l0t1i5.htm/, Retrieved Thu, 16 May 2024 01:14:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235229, Retrieved Thu, 16 May 2024 01:14:11 +0000
QR Codes:

Original text written by user:1946-1988
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact164

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Top marginal Rate...] [2014-06-11 09:53:37] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
94
86.45
86.45
82.13
82.13
91
91
92
92
91
91
91
91
91
91
91
91
91
91
77
70
70
70
75.25
77
71.75
70
70
70
70
70
70
70
70
70
70
69.13
50
50
50
50
50
38.5
Dataseries Y:
Download CSV
Histogram 
227800
249900
274800
272800
300200
347300
367700
389700
391100
426200
450100
474900
482000
522500
543300
563300
605100
638600
685800
743700
815000
861700
942500
1019900
1075900
1167800
1282400
1428500
1548800
1688900
1877600
2086000
2356600
2632100
2862500
3210900
3345000
3638100
4040700
4346700
4590100
4870200
5252600

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'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235229&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235229&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235229&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'Gwilym Jenkins' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean76.18116279069771532495.34883721
Biased Variance212.7958009734992072818273001.62
Biased Standard Deviation14.58752209847511439728.54142773
Covariance-19495244.2563677
Correlation-0.906666092804735
Determination0.822043403841804
T-Test-13.7620223136093
p-value (2 sided)5.81742493674037e-17
p-value (1 sided)2.90871246837019e-17
Degrees of Freedom41
Number of Observations43

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 76.1811627906977 & 1532495.34883721 \tabularnewline
Biased Variance & 212.795800973499 & 2072818273001.62 \tabularnewline
Biased Standard Deviation & 14.5875220984751 & 1439728.54142773 \tabularnewline
Covariance & -19495244.2563677 \tabularnewline
Correlation & -0.906666092804735 \tabularnewline
Determination & 0.822043403841804 \tabularnewline
T-Test & -13.7620223136093 \tabularnewline
p-value (2 sided) & 5.81742493674037e-17 \tabularnewline
p-value (1 sided) & 2.90871246837019e-17 \tabularnewline
Degrees of Freedom & 41 \tabularnewline
Number of Observations & 43 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235229&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]76.1811627906977[/C][C]1532495.34883721[/C][/ROW]
[ROW][C]Biased Variance[/C][C]212.795800973499[/C][C]2072818273001.62[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]14.5875220984751[/C][C]1439728.54142773[/C][/ROW]
[ROW][C]Covariance[/C][C]-19495244.2563677[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.906666092804735[/C][/ROW]
[ROW][C]Determination[/C][C]0.822043403841804[/C][/ROW]
[ROW][C]T-Test[/C][C]-13.7620223136093[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]5.81742493674037e-17[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.90871246837019e-17[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]41[/C][/ROW]
[ROW][C]Number of Observations[/C][C]43[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235229&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235229&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
Mean76.18116279069771532495.34883721
Biased Variance212.7958009734992072818273001.62
Biased Standard Deviation14.58752209847511439728.54142773
Covariance-19495244.2563677
Correlation-0.906666092804735
Determination0.822043403841804
T-Test-13.7620223136093
p-value (2 sided)5.81742493674037e-17
p-value (1 sided)2.90871246837019e-17
Degrees of Freedom41
Number of Observations43


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
x <- x[!is.na(y)]
y <- y[!is.na(y)]
y <- y[!is.na(x)]
x <- x[!is.na(x)]
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', na.rm = T)
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')