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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 Oct 2009 06:03:37 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/23/t12562994517f6vusx7ltm0ph9.htm/, Retrieved Thu, 02 May 2024 12:53:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49915, Retrieved Thu, 02 May 2024 12:53:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
-   PD  [Bivariate Data Series] [WS 4 1 PLOTS] [2009-10-23 11:13:05] [6e4e01d7eb22a9f33d58ebb35753a195]
- RMPD    [Bivariate Explorative Data Analysis] [ws 4 part 2] [2009-10-23 11:56:36] [6e4e01d7eb22a9f33d58ebb35753a195]
- RMPD        [Pearson Correlation] [ws 4 2.2 r] [2009-10-23 12:03:37] [2e4ef2c1b76db9b31c0a03b96e94ad77] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4.608165695
4.590056548
4.55492897
4.533674184
4.523960131
4.48863637
4.458987676
4.436751534
4.415219602
4.391976966
4.404277244
4.404277244
4.417635062
4.428433007
4.456670178
4.455509411
4.456670178
4.48638665
4.49535532
4.475061501
4.480740108
4.484131858
4.510859507
4.516338972
4.558078578
4.592084946
4.604169686
4.591071262
4.608165695
4.607168189
4.609162207
4.619073091
4.634728988
4.692264893
4.713127327
4.737075257
4.802380355
4.848900371
4.866764924
4.852030264
4.816241156
4.820281566
4.847331743
4.848900371
4.855150391
4.878246106
4.906015245
4.8978398
4.973279508
4.992471323
5.016617366
5.001930853
4.951592753
4.93375425
4.94021283
4.980863136
4.99653637
5.000584958
5.017941869
5.059425458
Dataseries Y:
Download CSV
Histogram 
4.640826863
4.640923356
4.641116313
4.642176912
4.643236387
4.64352514
4.64352514
4.643621372
4.644871553
4.646599996
4.647271362
4.647367235
4.647367235
4.647654798
4.649665426
4.650621449
4.65138561
4.651576559
4.651576559
4.65167202
4.653388758
4.656718448
4.657572865
4.658047226
4.658047226
4.657952371
4.658900508
4.660510281
4.66079409
4.660983251
4.660983251
4.660983251
4.662967285
4.665041583
4.666641508
4.666923582
4.666923582
4.666829566
4.667581446
4.666171208
4.665606555
4.665606555
4.665606555
4.665606555
4.666641508
4.667581446
4.667581446
4.667957174
4.668144985
4.668802046
4.667205577
4.666923582
4.665794808
4.665418266
4.665418266
4.665700686
4.665229942
4.664193526
4.664664758
4.66428779

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49915&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49915&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49915&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'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean4.685769450016674.65807524328333
Biased Variance0.04405174340779618.32190519866406e-05
Biased Standard Deviation0.2098850719031630.0091224476971173
Covariance0.00159592216238076
Correlation0.819633186693469
Determination0.67179856072929
T-Test10.8959045651087
p-value (2 sided)1.33226762955019e-15
p-value (1 sided)6.66133814775094e-16
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 4.68576945001667 & 4.65807524328333 \tabularnewline
Biased Variance & 0.0440517434077961 & 8.32190519866406e-05 \tabularnewline
Biased Standard Deviation & 0.209885071903163 & 0.0091224476971173 \tabularnewline
Covariance & 0.00159592216238076 \tabularnewline
Correlation & 0.819633186693469 \tabularnewline
Determination & 0.67179856072929 \tabularnewline
T-Test & 10.8959045651087 \tabularnewline
p-value (2 sided) & 1.33226762955019e-15 \tabularnewline
p-value (1 sided) & 6.66133814775094e-16 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49915&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]4.68576945001667[/C][C]4.65807524328333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.0440517434077961[/C][C]8.32190519866406e-05[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.209885071903163[/C][C]0.0091224476971173[/C][/ROW]
[ROW][C]Covariance[/C][C]0.00159592216238076[/C][/ROW]
[ROW][C]Correlation[/C][C]0.819633186693469[/C][/ROW]
[ROW][C]Determination[/C][C]0.67179856072929[/C][/ROW]
[ROW][C]T-Test[/C][C]10.8959045651087[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.33226762955019e-15[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]6.66133814775094e-16[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49915&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49915&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
Mean4.685769450016674.65807524328333
Biased Variance0.04405174340779618.32190519866406e-05
Biased Standard Deviation0.2098850719031630.0091224476971173
Covariance0.00159592216238076
Correlation0.819633186693469
Determination0.67179856072929
T-Test10.8959045651087
p-value (2 sided)1.33226762955019e-15
p-value (1 sided)6.66133814775094e-16
Degrees of Freedom58
Number of Observations60


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')