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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, 22 Dec 2010 11:19:10 +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/2010/Dec/22/t1293016761kqa3iwoj005g3r6.htm/, Retrieved Mon, 06 May 2024 06:41:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114168, Retrieved Mon, 06 May 2024 06:41:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson Correlati...] [2010-12-22 11:19:10] [55fca7c82a53ae69fe96aa1750b06058] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.57
0.60
0.62
0.69
0.74
0.74
0.75
0.78
0.80
0.87
0.94
1.05
1.13
1.24
1.31
1.38
1.50
1.70
1.98
2.20
2.51
3.15
3.64
4.05
4.43
4.69
5.06
5.51
6.07
6.41
6.74
7.02
7.32
7.35
7.51
7.69
8.12
8.50
9.00
9.39
9.79
10.17
9.76
9.97
10.18
10.74
11.52
11.86
12.29
12.57
13.12
13.50
13.89
Dataseries Y:
Download CSV
Histogram 
716
677
710
839
886
891
917
820
793
932
906
844
801
957
1159
1264
1097
1240
1411
1535
1862
1894
2239
2465
2423
2692
2856
3450
4162
4260
4225
4092
4160
3896
3628
3754
3749
3907
4449
5272
6197
6446
7157
7559
7674
6929
7156
6805
7095
7222
7593
7910
7878

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'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114168&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114168&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114168&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean5.568113207547173442.47169811321
Biased Variance18.36922662869356176445.45674617
Biased Standard Deviation4.285933577261022485.24555260565
Covariance10610.0928301887
Correlation0.977309040699289
Determination0.955132961032564
T-Test32.9498392271946
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom51
Number of Observations53

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 5.56811320754717 & 3442.47169811321 \tabularnewline
Biased Variance & 18.3692266286935 & 6176445.45674617 \tabularnewline
Biased Standard Deviation & 4.28593357726102 & 2485.24555260565 \tabularnewline
Covariance & 10610.0928301887 \tabularnewline
Correlation & 0.977309040699289 \tabularnewline
Determination & 0.955132961032564 \tabularnewline
T-Test & 32.9498392271946 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 51 \tabularnewline
Number of Observations & 53 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114168&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]5.56811320754717[/C][C]3442.47169811321[/C][/ROW]
[ROW][C]Biased Variance[/C][C]18.3692266286935[/C][C]6176445.45674617[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.28593357726102[/C][C]2485.24555260565[/C][/ROW]
[ROW][C]Covariance[/C][C]10610.0928301887[/C][/ROW]
[ROW][C]Correlation[/C][C]0.977309040699289[/C][/ROW]
[ROW][C]Determination[/C][C]0.955132961032564[/C][/ROW]
[ROW][C]T-Test[/C][C]32.9498392271946[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]51[/C][/ROW]
[ROW][C]Number of Observations[/C][C]53[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114168&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114168&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
Mean5.568113207547173442.47169811321
Biased Variance18.36922662869356176445.45674617
Biased Standard Deviation4.285933577261022485.24555260565
Covariance10610.0928301887
Correlation0.977309040699289
Determination0.955132961032564
T-Test32.9498392271946
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom51
Number of Observations53


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')