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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationWed, 28 Oct 2009 09:19:35 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/28/t1256743246xz3n8d8dyooe7wq.htm/, Retrieved Mon, 06 May 2024 00:23:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51410, Retrieved Mon, 06 May 2024 00:23:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
- RMPD  [Bivariate Kernel Density Estimation] [] [2009-10-28 15:17:58] [ba905ddf7cdf9ecb063c35348c4dab2e]
- RMP       [Pearson Correlation] [] [2009-10-28 15:19:35] [244731fa3e7e6c85774b8c0902c58f85] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
79.21
67.24
57.76
59.29
65.61
68.89
68.89
62.41
60.84
64
72.25
73.96
72.25
64
60.84
64
67.24
68.89
67.24
65.61
64
60.84
60.84
59.29
57.76
57.76
57.76
60.84
64
64
62.41
59.29
54.76
47.61
44.89
42.25
40.96
44.89
46.24
47.61
47.61
44.89
40.96
38.44
34.81
37.21
44.89
46.24
43.56
40.96
40.96
44.89
50.41
50.41
47.61
40.96
36
36
Dataseries Y:
Download CSV
Histogram 
3071
3388
2652
3190
2885
3295
3818
3226
3953
3810
2877
3515
3708
3450
3360
4110
4385
3729
4309
3506
3690
3911
2952
3324
3417
3498
2770
2907
3179
3014
3483
3016
2617
3534
2849
3129
2578
3626
2813
2591
2890
3369
2926
3016
2878
3198
2560
2573
3121
2658
2869
3076
2168
2341
2570
2626
2490
2756

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51410&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51410&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51410&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean55.09017241379313158.96551724138
Biased Variance130.521639625446239868.585017836
Biased Standard Deviation11.4246067602104489.76380533665
Covariance3113.27719903206
Correlation0.546810324560293
Determination0.299001531045732
T-Test4.8873358587567
p-value (2 sided)8.95455130067724e-06
p-value (1 sided)4.47727565033862e-06
Degrees of Freedom56
Number of Observations58

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 55.0901724137931 & 3158.96551724138 \tabularnewline
Biased Variance & 130.521639625446 & 239868.585017836 \tabularnewline
Biased Standard Deviation & 11.4246067602104 & 489.76380533665 \tabularnewline
Covariance & 3113.27719903206 \tabularnewline
Correlation & 0.546810324560293 \tabularnewline
Determination & 0.299001531045732 \tabularnewline
T-Test & 4.8873358587567 \tabularnewline
p-value (2 sided) & 8.95455130067724e-06 \tabularnewline
p-value (1 sided) & 4.47727565033862e-06 \tabularnewline
Degrees of Freedom & 56 \tabularnewline
Number of Observations & 58 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51410&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]55.0901724137931[/C][C]3158.96551724138[/C][/ROW]
[ROW][C]Biased Variance[/C][C]130.521639625446[/C][C]239868.585017836[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]11.4246067602104[/C][C]489.76380533665[/C][/ROW]
[ROW][C]Covariance[/C][C]3113.27719903206[/C][/ROW]
[ROW][C]Correlation[/C][C]0.546810324560293[/C][/ROW]
[ROW][C]Determination[/C][C]0.299001531045732[/C][/ROW]
[ROW][C]T-Test[/C][C]4.8873358587567[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]8.95455130067724e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]4.47727565033862e-06[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]56[/C][/ROW]
[ROW][C]Number of Observations[/C][C]58[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51410&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51410&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
Mean55.09017241379313158.96551724138
Biased Variance130.521639625446239868.585017836
Biased Standard Deviation11.4246067602104489.76380533665
Covariance3113.27719903206
Correlation0.546810324560293
Determination0.299001531045732
T-Test4.8873358587567
p-value (2 sided)8.95455130067724e-06
p-value (1 sided)4.47727565033862e-06
Degrees of Freedom56
Number of Observations58


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')