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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 computationTue, 27 Oct 2009 11:08:00 -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/27/t1256663333btwfn8wzzp2vol7.htm/, Retrieved Tue, 07 May 2024 15:05:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51063, Retrieved Tue, 07 May 2024 15:05:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsHSWWS4Q2
Estimated Impact96

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2009-10-27 17:08:00] [4563e36d4b7005634fe3557528d9fcab] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9356
9337
10149
9788
9770
9911
9429
8775
10189
10529
9914
9790
9625
9729
10589
9611
9388
9510
9690
8434
9844
10601
9942
10229
9381
9635
11228
9999
10089
11622
10533
9965
11567
11321
11686
11747
10595
10751
12199
11690
10978
11753
10839
10518
12183
11967
12363
12359
12162
12096
14325
12670
13865
13563
12734
12464
13389
13961
14088
13143
13413
13579
15388
13708
14689
14883
13991
13854
14364
15672
15904
14016
Dataseries Y:
Download CSV
Histogram 
14271
14013
15912
14290
14744
14721
13918
13263
15660
15629
15113
14526
15132
14908
16167
14122
13985
14236
13921
12394
15454
16146
15107
14593
14695
14513
17071
15179
15460
17173
15938
15003
18216
17847
18029
17281
16706
16750
18912
17763
16736
18061
16713
16769
19514
19251
19951
19052
19555
19083
22534
18854
19801
20346
18169
19087
20842
21602
22360
20334
21215
20530
23152
20134
21193
21628
20823
20493
22106
24178
24958
21620

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51063&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51063&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51063&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean11569.694444444417630.625
Biased Variance3533674.712191368712304.59548611
Biased Standard Deviation1879.807094409252951.66132804665
Covariance5526973.74295775
Correlation0.9822757987588
Determination0.96486574482724
T-Test43.8446985514657
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom70
Number of Observations72

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 11569.6944444444 & 17630.625 \tabularnewline
Biased Variance & 3533674.71219136 & 8712304.59548611 \tabularnewline
Biased Standard Deviation & 1879.80709440925 & 2951.66132804665 \tabularnewline
Covariance & 5526973.74295775 \tabularnewline
Correlation & 0.9822757987588 \tabularnewline
Determination & 0.96486574482724 \tabularnewline
T-Test & 43.8446985514657 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 70 \tabularnewline
Number of Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51063&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]11569.6944444444[/C][C]17630.625[/C][/ROW]
[ROW][C]Biased Variance[/C][C]3533674.71219136[/C][C]8712304.59548611[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1879.80709440925[/C][C]2951.66132804665[/C][/ROW]
[ROW][C]Covariance[/C][C]5526973.74295775[/C][/ROW]
[ROW][C]Correlation[/C][C]0.9822757987588[/C][/ROW]
[ROW][C]Determination[/C][C]0.96486574482724[/C][/ROW]
[ROW][C]T-Test[/C][C]43.8446985514657[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/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=51063&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51063&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
Mean11569.694444444417630.625
Biased Variance3533674.712191368712304.59548611
Biased Standard Deviation1879.807094409252951.66132804665
Covariance5526973.74295775
Correlation0.9822757987588
Determination0.96486574482724
T-Test43.8446985514657
p-value (2 sided)0
p-value (1 sided)0
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')