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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 computationSat, 06 Dec 2008 07:58:38 -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/06/t1228575549dke6b29xv8rew8k.htm/, Retrieved Sun, 19 May 2024 12:38:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29680, Retrieved Sun, 19 May 2024 12:38:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Back to Back Histogram] [] [2008-12-06 14:15:54] [4c8dfb519edec2da3492d7e6be9a5685]
-   PD  [Back to Back Histogram] [] [2008-12-06 14:41:51] [4c8dfb519edec2da3492d7e6be9a5685]
- RMP     [Pearson Correlation] [] [2008-12-06 14:47:15] [4c8dfb519edec2da3492d7e6be9a5685]
-    D      [Pearson Correlation] [] [2008-12-06 14:54:12] [4c8dfb519edec2da3492d7e6be9a5685]
-    D          [Pearson Correlation] [] [2008-12-06 14:58:38] [6d40a467de0f28bd2350f82ac9522c51] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
641
550
542
629
687
612
588
567
564
570
635
591
634
576
352
508
586
666
694
651
655
734
648
678
816
591
564
743
694
729
749
539
569
693
581
507
613
443
523
597
534
523
559
431
538
612
428
522
531
426
410
551
556
460
289
392
401
399
355
338
379
334
322
450
486
422
406
420
432
418
Dataseries Y:
Download CSV
Histogram 
15107
15024
12083
15761
16943
15070
13660
14769
14725
15998
15371
14957
15470
15102
11704
16284
16727
14969
14861
14583
15306
17904
16379
15420
17871
15913
13867
17823
17872
17422
16705
15991
16584
19124
17839
17209
18587
16258
15142
19202
17747
19090
18040
17516
17752
21073
17170
19440
19795
17575
16165
19465
19932
19961
17343
18924
18574
21351
18595
19823
20844
19640
17735
19814
22239
20682
17819
21872
22117
21866

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29680&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29680&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29680&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 time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean540.47142857142917393.5
Biased Variance13977.87775510205501545.76428571
Biased Standard Deviation118.2280751560392345.53741481259
Covariance-94198.384057971
Correlation-0.334835517580087
Determination0.112114823833125
T-Test-2.93026955705175
p-value (2 sided)0.0046074255636657
p-value (1 sided)0.00230371278183285
Degrees of Freedom68
Number of Observations70

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 540.471428571429 & 17393.5 \tabularnewline
Biased Variance & 13977.8777551020 & 5501545.76428571 \tabularnewline
Biased Standard Deviation & 118.228075156039 & 2345.53741481259 \tabularnewline
Covariance & -94198.384057971 \tabularnewline
Correlation & -0.334835517580087 \tabularnewline
Determination & 0.112114823833125 \tabularnewline
T-Test & -2.93026955705175 \tabularnewline
p-value (2 sided) & 0.0046074255636657 \tabularnewline
p-value (1 sided) & 0.00230371278183285 \tabularnewline
Degrees of Freedom & 68 \tabularnewline
Number of Observations & 70 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29680&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]540.471428571429[/C][C]17393.5[/C][/ROW]
[ROW][C]Biased Variance[/C][C]13977.8777551020[/C][C]5501545.76428571[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]118.228075156039[/C][C]2345.53741481259[/C][/ROW]
[ROW][C]Covariance[/C][C]-94198.384057971[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.334835517580087[/C][/ROW]
[ROW][C]Determination[/C][C]0.112114823833125[/C][/ROW]
[ROW][C]T-Test[/C][C]-2.93026955705175[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0046074255636657[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00230371278183285[/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=29680&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29680&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
Mean540.47142857142917393.5
Biased Variance13977.87775510205501545.76428571
Biased Standard Deviation118.2280751560392345.53741481259
Covariance-94198.384057971
Correlation-0.334835517580087
Determination0.112114823833125
T-Test-2.93026955705175
p-value (2 sided)0.0046074255636657
p-value (1 sided)0.00230371278183285
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')