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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 computationSun, 01 Nov 2009 11:05:30 -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/2009/Nov/01/t1257098812t7p2v5pvf1xjbyd.htm/, Retrieved Mon, 06 May 2024 12:43:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=52378, Retrieved Mon, 06 May 2024 12:43:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [SHW_WS5_Correlation] [2009-10-29 18:55:36] [8b1aef4e7013bd33fbc2a5833375c5f5]
-  M D    [Pearson Correlation] [ws 5] [2009-11-01 18:05:30] [f7d3e79b917995ba1c8c80042fc22ef9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-8.420276058
5.603810549
7.227897157
-0.439987367
-8.023929628
-10.08378528
-10.65969868
-2.827583199
-3.339265638
-2.699121292
5.708907577
-19.42686147
-11.31080373
5.505254006
2.529340614
3.06145609
-4.822486171
-5.698399564
-5.450226349
7.438091212
0.070206688
5.602322165
8.934437641
-17.34950462
-6.409360275
9.214726333
12.15487068
5.578957286
1.503043893
-0.488927238
-0.46484063
12.15121711
4.459245977
6.675303715
11.79939032
-12.67652307
-2.168494201
10.64756354
14.39573675
8.711794491
-0.832003425
4.284054313
7.172371874
9.140978126
10.51323795
9.58549777
13.30155551
-10.16632902
-1.210126931
10.14607515
8.762132891
-0.865607287
-10.54954955
-12.32546294
-11.6094052
-0.077289726
-10.75320312
-6.588972166
-1.932770082
-22.20868347
Dataseries Y:
Download CSV
Histogram 
0.650033625
0.669304839
0.088576053
-0.385728995
-0.272881519
-0.04076283
0.078508384
0.004203336
-0.225135547
-0.293016857
-0.486593119
0.264796785
0.37764426
0.390491736
0.20976295
0.135457902
0.248305378
0.467576592
0.506119019
0.476780137
0.402475088
0.22817004
-0.046135008
0.166712468
0.098831158
0.118102371
0.050221061
-0.030507725
-0.011236511
0.095187227
0.114458441
0.027305917
0.133729654
-0.15342287
-0.634151656
-0.314880442
-0.508456704
-0.795609228
-0.7570668
-0.744219325
-0.499253159
-0.386405683
-0.515744566
-0.680846069
-1.023032427
-1.265218786
-0.85237131
0.373323642
0.618289807
0.263255973
-0.323896551
-0.56608291
-0.253235434
0.56603578
0.878883256
0.904578208
0.623849422
0.275239325
0.420205491
1.139476705

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52378&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=52378&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52378&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1.66666878215205e-11-1.66666648743815e-11
Biased Variance78.18865240705730.249383350019018
Biased Standard Deviation8.842434755600820.499382969292123
Covariance-2.34188495494372
Correlation-0.521507701627666
Determination0.271970282856971
T-Test-4.65479082668502
p-value (2 sided)1.93101111329821e-05
p-value (1 sided)9.65505556649103e-06
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1.66666878215205e-11 & -1.66666648743815e-11 \tabularnewline
Biased Variance & 78.1886524070573 & 0.249383350019018 \tabularnewline
Biased Standard Deviation & 8.84243475560082 & 0.499382969292123 \tabularnewline
Covariance & -2.34188495494372 \tabularnewline
Correlation & -0.521507701627666 \tabularnewline
Determination & 0.271970282856971 \tabularnewline
T-Test & -4.65479082668502 \tabularnewline
p-value (2 sided) & 1.93101111329821e-05 \tabularnewline
p-value (1 sided) & 9.65505556649103e-06 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52378&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]1.66666878215205e-11[/C][C]-1.66666648743815e-11[/C][/ROW]
[ROW][C]Biased Variance[/C][C]78.1886524070573[/C][C]0.249383350019018[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]8.84243475560082[/C][C]0.499382969292123[/C][/ROW]
[ROW][C]Covariance[/C][C]-2.34188495494372[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.521507701627666[/C][/ROW]
[ROW][C]Determination[/C][C]0.271970282856971[/C][/ROW]
[ROW][C]T-Test[/C][C]-4.65479082668502[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.93101111329821e-05[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]9.65505556649103e-06[/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=52378&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52378&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
Mean1.66666878215205e-11-1.66666648743815e-11
Biased Variance78.18865240705730.249383350019018
Biased Standard Deviation8.842434755600820.499382969292123
Covariance-2.34188495494372
Correlation-0.521507701627666
Determination0.271970282856971
T-Test-4.65479082668502
p-value (2 sided)1.93101111329821e-05
p-value (1 sided)9.65505556649103e-06
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')