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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 06:28:50 -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/tdzguli9j6e2zn41192973091.htm/, Retrieved Thu, 09 May 2024 13:41:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1298, Retrieved Thu, 09 May 2024 13:41:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS2Q10BASMET
Estimated Impact196

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [WS2Q10BASMET] [2007-10-21 13:28:50] [e0964b90cb3acfe235da067e79729c23] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,354
2,318
2,25
2,219
2,206
2,146
2,212
2,243
2,275
2,291
2,141
2,134
2,18
2,183
2,169
2,132
2,092
2,069
2,099
2,073
2,051
2,082
2,059
2,101
2,158
2,153
2,145
2,149
2,135
2,097
2,143
2,13
2,132
2,142
2,094
2,147
2,203
2,244
2,26
2,254
2,231
2,211
2,209
2,191
2,21
2,257
2,252
2,266
2,264
2,265
2,255
2,28
2,288
2,284
2,282
2,271
2,296
2,303
2,316
2,325
2,415
2,402
2,425
2,4
2,424
2,393
2,419
2,415
2,425
2,421
2,378
2,364
Dataseries Y:
Download CSV
Histogram 
7,322
7,141
6,907
6,834
6,751
6,507
6,785
6,913
6,903
7,067
6,808
7,011
7,506
7,594
7,702
7,656
7,549
7,452
8,126
8,37
8,29
8,492
8,548
9,026
9,513
9,565
9,602
9,846
9,612
9,789
10,583
10,7
10,384
10,486
10,24
10,819
11,38
11,702
11,787
11,676
11,58
11,355
11,991
12,338
11,963
12,317
12,098
12,551
12,551
12,447
12,5
12,326
12,206
12,142
12,66
12,727
12,641
12,61
12,249
12,657
12,221
12,359
12,155
12,509
12,363
12,251
12,742
12,487
12,108
11,463
11,193
11,368

Tables (Output of Computation)





Summary of compuational 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 compuational 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=1298&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]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=1298&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1298&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2.2333611111111110.251
Biased Variance0.01110484182098774.68315261111111
Biased Standard Deviation0.1053795132888162.16405929010993
Covariance0.124884366197183
Correlation0.540018431081597
Determination0.291619905907830
T-Test5.36814735159564
p-value (2 sided)9.79811613177617e-07
p-value (1 sided)4.89905806588808e-07
Degrees of Freedom70
Number of Observations72

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2.23336111111111 & 10.251 \tabularnewline
Biased Variance & 0.0111048418209877 & 4.68315261111111 \tabularnewline
Biased Standard Deviation & 0.105379513288816 & 2.16405929010993 \tabularnewline
Covariance & 0.124884366197183 \tabularnewline
Correlation & 0.540018431081597 \tabularnewline
Determination & 0.291619905907830 \tabularnewline
T-Test & 5.36814735159564 \tabularnewline
p-value (2 sided) & 9.79811613177617e-07 \tabularnewline
p-value (1 sided) & 4.89905806588808e-07 \tabularnewline
Degrees of Freedom & 70 \tabularnewline
Number of Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1298&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]2.23336111111111[/C][C]10.251[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.0111048418209877[/C][C]4.68315261111111[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.105379513288816[/C][C]2.16405929010993[/C][/ROW]
[ROW][C]Covariance[/C][C]0.124884366197183[/C][/ROW]
[ROW][C]Correlation[/C][C]0.540018431081597[/C][/ROW]
[ROW][C]Determination[/C][C]0.291619905907830[/C][/ROW]
[ROW][C]T-Test[/C][C]5.36814735159564[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]9.79811613177617e-07[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]4.89905806588808e-07[/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=1298&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1298&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
Mean2.2333611111111110.251
Biased Variance0.01110484182098774.68315261111111
Biased Standard Deviation0.1053795132888162.16405929010993
Covariance0.124884366197183
Correlation0.540018431081597
Determination0.291619905907830
T-Test5.36814735159564
p-value (2 sided)9.79811613177617e-07
p-value (1 sided)4.89905806588808e-07
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')