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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 computationThu, 17 Dec 2009 22:11:40 +0100
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/Dec/17/t1261084314iwd2wuslnzke8gv.htm/, Retrieved Tue, 30 Apr 2024 06:11:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69114, Retrieved Tue, 30 Apr 2024 06:11:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2009-12-17 19:09:08] [b98453cac15ba1066b407e146608df68]
- RMPD    [Pearson Correlation] [] [2009-12-17 21:11:40] [d76b387543b13b5e3afd8ff9e5fdc89f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.7
7.5
8.3
7.8
7.9
6.6
7
8.2
8.2
9.1
9
7.1
8.9
8.5
9.8
8.8
9.2
7.4
8.3
9.7
9.7
10.8
9.8
7.9
9.8
9
10.5
9.5
9.7
8.1
10.1
11.1
11.2
12.6
12.2
9.9
11.8
11.1
12.6
11.9
11.9
10
10.8
12.9
12.5
13.8
13.1
10.5
12.9
12.9
14.4
12.7
13.3
11
11.9
14.1
14.4
14.9
15.7
12
14.3
14.2
17.4
15.1
15.3
12.6
14
16.6
16.7
17.6
18.3
13.6
15.8
16.1
18.6
17.3
17
13.9
15.2
17.8
18
19.4
21.8
16.2
19.2
19.5
22
20
19.2
16.9
20
20.4
21.8
25
25.8
19.4
22.6
24.1
26.9
24.9
23.3
20.3
22.3
23.7
24.3
31.7
32.2
25.4
28.6
28.7
30.9
31.4
29.1
26.3
28.9
28.9
31
33.4
35.9
25.8
31.2
31.7
36.2
32
32.1
28.1
31.1
31.9
32
36.6
38.1
28.1
32.9
30.7
35.4
33.7
31.6
27.9
32.2
32.3
35.3
37.2
39.6
28.4
33.9
33.7
38.3
34.6
32.7
29.5
32
33.2
36.7
38.6
38.1
29.8
35.6
33.2
38.9
34.8
37.2
29.7
32.2
32.1
36.3
38.4
40.8
31.3
36.2
35.1
44.1
39.3
34.1
32.4
36.3
36.8
40.5
46
43.9
37.2
40.7
42
49.2
42.3
40.8
37.6
Dataseries Y:
Download CSV
Histogram 
277
260.6
291.6
275.4
275.3
231.7
238.8
274.2
277.8
299.1
286.6
232.3
294.1
267.5
309.7
280.7
287.3
235.7
256.4
289
290.8
321.9
291.8
241.4
295.5
258.2
306.1
281.5
283.1
237.4
274.8
299.3
300.4
340.9
318.8
265.7
322.7
281.6
323.5
312.6
310.8
262.8
273.8
320
310.3
342.2
320.1
265.6
327
300.7
346.4
317.3
326.2
270.7
278.2
324.6
321.8
343.5
354
278.2
330.2
307.3
375.9
335.3
339.3
280.3
293.7
341.2
345.1
368.7
369.4
288.4
341
319.1
374.2
344.5
337.3
281
282.2
321
325.4
366.3
380.3
300.7
359.3
327.6
383.6
352.4
329.4
294.5
333.5
334.3
358
396.1
387
307.2
363.9
344.7
397.6
376.8
337.1
299.3
323.1
329.1
347
462
436.5
360.4
415.5
382.1
432.2
424.3
386.7
354.5
375.8
368
402.4
426.5
433.3
338.5
416.8
381.1
445.7
412.4
394
348.2
380.1
373.7
393.6
434.2
430.7
344.5
411.9
370.5
437.3
411.3
385.5
341.3
384.2
373.2
415.8
448.6
454.3
350.3
419.1
398
456.1
430.1
399.8
362.7
384.9
385.3
432.3
468.9
442.7
370.2
439.4
393.9
468.7
438.8
430.1
366.3
391
380.9
431.4
465.4
471.5
387.5
446.4
421.5
504.8
492.1
421.3
396.7
428
421.9
465.6
525.8
499.9
435.3
479.5
473
554.4
489.6
462.2
420.3

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69114&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69114&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69114&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'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean22.9301075268817358.083333333333
Biased Variance124.6735021389764487.01364695341
Biased Standard Deviation11.165728912121066.9851748296099
Covariance709.453477477477
Correlation0.943445747298256
Determination0.890089878095164
T-Test38.6017503702943
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom184
Number of Observations186

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 22.9301075268817 & 358.083333333333 \tabularnewline
Biased Variance & 124.673502138976 & 4487.01364695341 \tabularnewline
Biased Standard Deviation & 11.1657289121210 & 66.9851748296099 \tabularnewline
Covariance & 709.453477477477 \tabularnewline
Correlation & 0.943445747298256 \tabularnewline
Determination & 0.890089878095164 \tabularnewline
T-Test & 38.6017503702943 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 184 \tabularnewline
Number of Observations & 186 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69114&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]22.9301075268817[/C][C]358.083333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]124.673502138976[/C][C]4487.01364695341[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]11.1657289121210[/C][C]66.9851748296099[/C][/ROW]
[ROW][C]Covariance[/C][C]709.453477477477[/C][/ROW]
[ROW][C]Correlation[/C][C]0.943445747298256[/C][/ROW]
[ROW][C]Determination[/C][C]0.890089878095164[/C][/ROW]
[ROW][C]T-Test[/C][C]38.6017503702943[/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]184[/C][/ROW]
[ROW][C]Number of Observations[/C][C]186[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69114&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69114&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
Mean22.9301075268817358.083333333333
Biased Variance124.6735021389764487.01364695341
Biased Standard Deviation11.165728912121066.9851748296099
Covariance709.453477477477
Correlation0.943445747298256
Determination0.890089878095164
T-Test38.6017503702943
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom184
Number of Observations186


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 1 ;
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')