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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 computationSun, 21 Oct 2007 07:04:49 -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/2007/Oct/21/w1h1743u9lilrud1192975253.htm/, Retrieved Thu, 09 May 2024 14:56:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1308, Retrieved Thu, 09 May 2024 14:56:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS2Q10UITTOT
Estimated Impact166

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [WS2Q10UITTOT] [2007-10-21 14:04:49] [e0964b90cb3acfe235da067e79729c23] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
352,8
458,2
461,4
422,5
338,1
326,9
414,6
412,7
369,7
409,5
354,2
351,8
333
390,7
384,4
405,6
308,8
339,4
407
371,1
374,4
393,3
328
332,6
300,4
376,1
379
377
272,8
332,4
398,4
327,2
349,1
370,4
293,4
311,9
285,6
297,9
364,2
356,8
244,1
319,5
330,1
297
310,8
315,2
295,4
297,6
264,7
347,8
394,2
343
242,9
310,8
322,9
302,9
319,1
336,4
301
296,7
258,1
320,4
365,1
325
261,1
309,3
347,1
319,8
314,5
345,8
307,6
327
Dataseries Y:
Download CSV
Histogram 
467,037
460,07
447,988
442,867
436,087
431,328
484,015
509,673
512,927
502,831
470,984
471,067
476,049
474,605
470,439
461,251
454,724
455,626
516,847
525,192
522,975
518,585
509,239
512,238
519,164
517,009
509,933
509,127
500,857
506,971
569,323
579,714
577,992
565,464
547,344
554,788
562,325
560,854
555,332
543,599
536,662
542,722
593,53
610,763
612,613
611,324
594,167
595,454
590,865
589,379
584,428
573,1
567,456
569,028
620,735
628,884
628,232
612,117
595,404
597,141
593,408
590,072
579,799
574,205
572,775
572,942
619,567
625,809
619,916
587,625
565,742
557,274

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1308&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1308&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1308&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean339.252777777778543.438583333333
Biased Variance2145.968325617283010.70215174306
Biased Standard Deviation46.324597414519354.8698656071168
Covariance-1277.72022276995
Correlation-0.49569674895472
Determination0.245715266924279
T-Test-4.7752644979825
p-value (2 sided)9.53793492510315e-06
p-value (1 sided)4.76896746255157e-06
Degrees of Freedom70
Number of Observations72

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 339.252777777778 & 543.438583333333 \tabularnewline
Biased Variance & 2145.96832561728 & 3010.70215174306 \tabularnewline
Biased Standard Deviation & 46.3245974145193 & 54.8698656071168 \tabularnewline
Covariance & -1277.72022276995 \tabularnewline
Correlation & -0.49569674895472 \tabularnewline
Determination & 0.245715266924279 \tabularnewline
T-Test & -4.7752644979825 \tabularnewline
p-value (2 sided) & 9.53793492510315e-06 \tabularnewline
p-value (1 sided) & 4.76896746255157e-06 \tabularnewline
Degrees of Freedom & 70 \tabularnewline
Number of Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1308&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]339.252777777778[/C][C]543.438583333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2145.96832561728[/C][C]3010.70215174306[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]46.3245974145193[/C][C]54.8698656071168[/C][/ROW]
[ROW][C]Covariance[/C][C]-1277.72022276995[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.49569674895472[/C][/ROW]
[ROW][C]Determination[/C][C]0.245715266924279[/C][/ROW]
[ROW][C]T-Test[/C][C]-4.7752644979825[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]9.53793492510315e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]4.76896746255157e-06[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]70[/C][/ROW]
[ROW][C]Number of Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1308&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1308&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
Mean339.252777777778543.438583333333
Biased Variance2145.968325617283010.70215174306
Biased Standard Deviation46.324597414519354.8698656071168
Covariance-1277.72022276995
Correlation-0.49569674895472
Determination0.245715266924279
T-Test-4.7752644979825
p-value (2 sided)9.53793492510315e-06
p-value (1 sided)4.76896746255157e-06
Degrees of Freedom70
Number of Observations72


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')