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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 computationFri, 23 Dec 2011 11:06:41 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t1324656419oqr2e6vefs0uoob.htm/, Retrieved Mon, 29 Apr 2024 21:37:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160538, Retrieved Mon, 29 Apr 2024 21:37:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85

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-correlation] [2011-12-23 15:23:48] [c2267e575f67090c7e8d960bdccd246a]
- R  D    [Pearson Correlation] [paper-correlation] [2011-12-23 16:06:41] [fe2dc4bc83c881ccd49ef12feaba2b65] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
590
580
574
573
573
620
626
620
588
566
557
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581
564
558
575
580
575
563
552
537
545
601
604
586
564
549
551
556
548
540
531
521
519
572
581
563
548
539
Dataseries Y:
Download CSV
Histogram 
29.506
34.506
27.165
26.736
23.691
18.157
17.328
18.205
20.995
17.382
9.367
31.124
26.551
30.651
25.859
25.100
25.778
20.418
18.688
20.424
24.776
19.814
12.738
31.566
30.111
30.019
31.934
25.826
26.835
20.205
17.789
20.520
22.518
15.572
11.509
25.447
24.090
27.786
26.195
20.516
22.759
19.028
16.971
20.036
22.485
18.730
14.538
27.561
25.985
34.670
32.066
27.186
29.586
21.359
21.553
19.573
24.256
22.380
16.167
27.297
28.287
33.474
28.229
28.785
25.597
18.130
20.198
22.849
23.118
21.925

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'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160538&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160538&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160538&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'Herman Ole Andreas Wold' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean548.54285714285723.5453571428571
Biased Variance1131.1338775510230.3732053153061
Biased Standard Deviation33.63233381065045.51118910175528
Covariance-43.0257329192547
Correlation-0.228811058365891
Determination0.052354500430519
T-Test-1.93824429375667
p-value (2 sided)0.056746185121248
p-value (1 sided)0.028373092560624
Degrees of Freedom68
Number of Observations70

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 548.542857142857 & 23.5453571428571 \tabularnewline
Biased Variance & 1131.13387755102 & 30.3732053153061 \tabularnewline
Biased Standard Deviation & 33.6323338106504 & 5.51118910175528 \tabularnewline
Covariance & -43.0257329192547 \tabularnewline
Correlation & -0.228811058365891 \tabularnewline
Determination & 0.052354500430519 \tabularnewline
T-Test & -1.93824429375667 \tabularnewline
p-value (2 sided) & 0.056746185121248 \tabularnewline
p-value (1 sided) & 0.028373092560624 \tabularnewline
Degrees of Freedom & 68 \tabularnewline
Number of Observations & 70 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160538&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]548.542857142857[/C][C]23.5453571428571[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1131.13387755102[/C][C]30.3732053153061[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]33.6323338106504[/C][C]5.51118910175528[/C][/ROW]
[ROW][C]Covariance[/C][C]-43.0257329192547[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.228811058365891[/C][/ROW]
[ROW][C]Determination[/C][C]0.052354500430519[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.93824429375667[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.056746185121248[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.028373092560624[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]68[/C][/ROW]
[ROW][C]Number of Observations[/C][C]70[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160538&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160538&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
Mean548.54285714285723.5453571428571
Biased Variance1131.1338775510230.3732053153061
Biased Standard Deviation33.63233381065045.51118910175528
Covariance-43.0257329192547
Correlation-0.228811058365891
Determination0.052354500430519
T-Test-1.93824429375667
p-value (2 sided)0.056746185121248
p-value (1 sided)0.028373092560624
Degrees of Freedom68
Number of Observations70


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')