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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 computationMon, 22 Dec 2008 15:38:40 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/22/t12299855580vkyod2pfhjzgqd.htm/, Retrieved Sun, 12 May 2024 14:43:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36251, Retrieved Sun, 12 May 2024 14:43:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Paper: Pearson Co...] [2008-12-14 10:11:09] [9e54d1454d464f1bf9ee4a54d5d56945]
-    D  [Pearson Correlation] [Paper: Pearson Co...] [2008-12-14 11:39:41] [9e54d1454d464f1bf9ee4a54d5d56945]
-           [Pearson Correlation] [] [2008-12-22 22:38:40] [27189814204044fdc56e2241a9375b9f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
17,3
15,4
16,9
20,8
16,4
11,3
17,5
16,6
17,5
19,5
18,8
20,2
19,2
14,4
24,5
25,7
27,1
21
18,6
20
21,8
20,4
18
21,5
19,1
19,7
26
26,3
24,6
22,4
32
24
30
24,1
26,3
29,8
21,9
22,8
29,2
27,5
27,4
31
26,1
22,2
34
26,9
31,9
34,2
31,2
28,5
37,1
36
34,8
32,1
37,2
36,3
39,5
37,1
35,6
36,2
35,9
32,5
39,2
39,4
42,8
34,5
43,7
46,3
40,8
48,4
43,2
48,1
42,8
Dataseries Y:
Download CSV
Histogram 
1.3
1.4
1.3
1
0.8
0.7
0.6
0.8
0.9
1
1.2
1.3
1.3
1.4
1.4
1.8
1.9
2
2.4
2.5
2.5
2.3
1.7
1.1
0.7
0.2
0.3
1.1
1.6
2.2
3
3.8
4.6
5.1
5.3
5.5
5.7
5.9
6.1
6.1
6.3
6.5
6.7
6.6
6.5
6.4
6.3
6.3
6.3
6.2
6
5.6
5.3
5.1
4.5
4
3.5
3.5
3.3
3.1
2.9
2.5
2.6
2.8
2.8
2.9
3.1
3.3
3.5
3.4
3.5
3.7
3.8

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=36251&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=36251&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36251&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
Mean28.20547945205483.29589041095890
Biased Variance81.2991480577973.95135297429161
Biased Standard Deviation9.016604020239381.98780103991612
Covariance7.83710616438356
Correlation0.431270205221034
Determination0.185993989911393
T-Test4.02777149570334
p-value (2 sided)0.000139406461582503
p-value (1 sided)6.97032307912515e-05
Degrees of Freedom71
Number of Observations73

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 28.2054794520548 & 3.29589041095890 \tabularnewline
Biased Variance & 81.299148057797 & 3.95135297429161 \tabularnewline
Biased Standard Deviation & 9.01660402023938 & 1.98780103991612 \tabularnewline
Covariance & 7.83710616438356 \tabularnewline
Correlation & 0.431270205221034 \tabularnewline
Determination & 0.185993989911393 \tabularnewline
T-Test & 4.02777149570334 \tabularnewline
p-value (2 sided) & 0.000139406461582503 \tabularnewline
p-value (1 sided) & 6.97032307912515e-05 \tabularnewline
Degrees of Freedom & 71 \tabularnewline
Number of Observations & 73 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36251&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]28.2054794520548[/C][C]3.29589041095890[/C][/ROW]
[ROW][C]Biased Variance[/C][C]81.299148057797[/C][C]3.95135297429161[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]9.01660402023938[/C][C]1.98780103991612[/C][/ROW]
[ROW][C]Covariance[/C][C]7.83710616438356[/C][/ROW]
[ROW][C]Correlation[/C][C]0.431270205221034[/C][/ROW]
[ROW][C]Determination[/C][C]0.185993989911393[/C][/ROW]
[ROW][C]T-Test[/C][C]4.02777149570334[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000139406461582503[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]6.97032307912515e-05[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]71[/C][/ROW]
[ROW][C]Number of Observations[/C][C]73[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36251&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36251&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
Mean28.20547945205483.29589041095890
Biased Variance81.2991480577973.95135297429161
Biased Standard Deviation9.016604020239381.98780103991612
Covariance7.83710616438356
Correlation0.431270205221034
Determination0.185993989911393
T-Test4.02777149570334
p-value (2 sided)0.000139406461582503
p-value (1 sided)6.97032307912515e-05
Degrees of Freedom71
Number of Observations73


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')