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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, 26 Nov 2010 08:45:54 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/26/t1290761031auumgq6ggevgu4o.htm/, Retrieved Sat, 04 May 2024 01:06:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101706, Retrieved Sat, 04 May 2024 01:06:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Testing Mean with unknown Variance - Critical Value] [] [2010-10-25 13:12:27] [b98453cac15ba1066b407e146608df68]
- RMPD    [Pearson Correlation] [] [2010-11-26 08:45:54] [33c49f0356cf94839cc9a2df1ea19a67] [Current]
-    D      [Pearson Correlation] [] [2010-11-26 12:08:21] [eab273d59b25a7fddba6574425ce83eb]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
825
101
851
1.645
12.952
8.816
3
96
4.942
2.525
311
753
1.433
848
401
145
260
3.213
315
443
914
1.114
268
145
1.909
4.376
3
495
293
1.801
189
799
2.610
10
801
123
662
573
2.086
61
2.199
427
106
254
295
244
79
42
123
1.022
106
192
810
324
75
80
761
1.555
308
55
522
72
399
1.100
31
184
46
376
129
1.260
668
172
Dataseries Y:
Download CSV
Histogram 
1.055
87
892
9.365
11.415
1.219
33
2
13.060
8.642
672
957
1.592
812
882
123
739
1.995
935
636
1.410
619
400
155
1.299
526
2
544
41
2.071
53
3.539
3.605
408
2.177
197
499
1.695
616
26
987
250
195
381
361
383
215
30
446
683
342
251
1.449
255
97
41
552
250
374
14
676
33
2.073
1.491
222
475
87
374
493
324
319
99

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=101706&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=101706&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101706&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
Mean244.785527777778279.641
Biased Variance75445.530050165984870.0095098611
Biased Standard Deviation274.673497174674291.324577593208
Covariance21065.7273406197
Correlation0.259602235839041
Determination0.0673933208526293
T-Test2.24909700793444
p-value (2 sided)0.0276547293608607
p-value (1 sided)0.0138273646804303
Degrees of Freedom70
Number of Observations72

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 244.785527777778 & 279.641 \tabularnewline
Biased Variance & 75445.5300501659 & 84870.0095098611 \tabularnewline
Biased Standard Deviation & 274.673497174674 & 291.324577593208 \tabularnewline
Covariance & 21065.7273406197 \tabularnewline
Correlation & 0.259602235839041 \tabularnewline
Determination & 0.0673933208526293 \tabularnewline
T-Test & 2.24909700793444 \tabularnewline
p-value (2 sided) & 0.0276547293608607 \tabularnewline
p-value (1 sided) & 0.0138273646804303 \tabularnewline
Degrees of Freedom & 70 \tabularnewline
Number of Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101706&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]244.785527777778[/C][C]279.641[/C][/ROW]
[ROW][C]Biased Variance[/C][C]75445.5300501659[/C][C]84870.0095098611[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]274.673497174674[/C][C]291.324577593208[/C][/ROW]
[ROW][C]Covariance[/C][C]21065.7273406197[/C][/ROW]
[ROW][C]Correlation[/C][C]0.259602235839041[/C][/ROW]
[ROW][C]Determination[/C][C]0.0673933208526293[/C][/ROW]
[ROW][C]T-Test[/C][C]2.24909700793444[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0276547293608607[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0138273646804303[/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=101706&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101706&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
Mean244.785527777778279.641
Biased Variance75445.530050165984870.0095098611
Biased Standard Deviation274.673497174674291.324577593208
Covariance21065.7273406197
Correlation0.259602235839041
Determination0.0673933208526293
T-Test2.24909700793444
p-value (2 sided)0.0276547293608607
p-value (1 sided)0.0138273646804303
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')