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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, 11 Dec 2008 07:19:51 -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/11/t1229005247x53vg6l2ipvjhzl.htm/, Retrieved Sun, 19 May 2024 07:09:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32254, Retrieved Sun, 19 May 2024 07:09:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson Correlati...] [2008-12-11 14:19:51] [d96f761aa3e94002e7c05c3c847d2c79] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
492865
480961
461935
456608
441977
439148
488180
520564
501492
485025
464196
460170
467037
460070
447988
442867
436087
431328
484015
509673
512927
502831
470984
471067
476049
474605
470439
461251
454724
455626
516847
525192
522975
518585
509239
512238
519164
517009
509933
509127
500857
506971
569323
579714
577992
565464
547344
554788
562325
560854
555332
543599
536662
542722
593530
610763
612613
611324
594167
595454
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274
Dataseries Y:
Download CSV
Histogram 
9 733
9 259
9 864
9 215
10 103
9 380
9 896
10 117
9 451
9 700
9 081
9 084
9 743
8 587
9 731
9 563
9 998
9 437
10 038
9 918
9 252
9 737
9 035
9 133
9 487
8 700
9 627
8 947
9 283
8 829
9 947
9 628
9 318
9 605
8 640
9 214
9 567
8 547
9 185
9 470
9 123
9 278
10 170
9 434
9 655
9 429
8 739
9 552
9 687
9 019
9 672
9 206
9 069
9 788
10 312
10 105
9 863
9 656
9 295
9 946
9 701
9 049
10 190
9 706
9 765
9 893
9 994
10 433
10 073
10 112
9 266
9 820
10 097
9 115
10 411
9 678
10 408
10 153
10 368
10 581
10 597
10 680
9 738
9 556

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32254&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32254&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32254&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'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean533579.759612.27380952381
Biased Variance3242642902.78274235091.960742630
Biased Standard Deviation56944.2086851924484.862826727963
Covariance13343465.4307229
Correlation0.477528162927569
Determination0.228033146388979
T-Test4.92160312375768
p-value (2 sided)4.36725199515209e-06
p-value (1 sided)2.18362599757604e-06
Degrees of Freedom82
Number of Observations84

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 533579.75 & 9612.27380952381 \tabularnewline
Biased Variance & 3242642902.78274 & 235091.960742630 \tabularnewline
Biased Standard Deviation & 56944.2086851924 & 484.862826727963 \tabularnewline
Covariance & 13343465.4307229 \tabularnewline
Correlation & 0.477528162927569 \tabularnewline
Determination & 0.228033146388979 \tabularnewline
T-Test & 4.92160312375768 \tabularnewline
p-value (2 sided) & 4.36725199515209e-06 \tabularnewline
p-value (1 sided) & 2.18362599757604e-06 \tabularnewline
Degrees of Freedom & 82 \tabularnewline
Number of Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32254&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]533579.75[/C][C]9612.27380952381[/C][/ROW]
[ROW][C]Biased Variance[/C][C]3242642902.78274[/C][C]235091.960742630[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]56944.2086851924[/C][C]484.862826727963[/C][/ROW]
[ROW][C]Covariance[/C][C]13343465.4307229[/C][/ROW]
[ROW][C]Correlation[/C][C]0.477528162927569[/C][/ROW]
[ROW][C]Determination[/C][C]0.228033146388979[/C][/ROW]
[ROW][C]T-Test[/C][C]4.92160312375768[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]4.36725199515209e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.18362599757604e-06[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]82[/C][/ROW]
[ROW][C]Number of Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32254&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32254&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
Mean533579.759612.27380952381
Biased Variance3242642902.78274235091.960742630
Biased Standard Deviation56944.2086851924484.862826727963
Covariance13343465.4307229
Correlation0.477528162927569
Determination0.228033146388979
T-Test4.92160312375768
p-value (2 sided)4.36725199515209e-06
p-value (1 sided)2.18362599757604e-06
Degrees of Freedom82
Number of Observations84


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')