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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 computationWed, 28 Oct 2009 13:43:02 -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/28/t12567590208mugvghjg0a58g1.htm/, Retrieved Mon, 06 May 2024 09:59:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51782, Retrieved Mon, 06 May 2024 09:59:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129

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] [Reproduce: part 1] [2009-10-27 19:04:39] [f924a0adda9c1905a1ba8f1c751261ff]
- RMP     [Bivariate Explorative Data Analysis] [Bivariate EDA: Pa...] [2009-10-27 21:03:03] [f924a0adda9c1905a1ba8f1c751261ff]
-    D      [Bivariate Explorative Data Analysis] [Bivariate EDA: Pa...] [2009-10-27 22:45:19] [f924a0adda9c1905a1ba8f1c751261ff]
- RMPD        [Pearson Correlation] [Pearson Correlati...] [2009-10-27 23:31:21] [f924a0adda9c1905a1ba8f1c751261ff]
-   PD            [Pearson Correlation] [WS4-2-Pear^2] [2009-10-28 19:43:02] [30970b478e356ce7f8c2e9fca280b230] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9370,24
13018,81
12166,09
10795,21
10322,56
8949,16
9196,81
10962,09
10567,84
9623,61
12973,21
6544,81
9158,49
12814,24
11214,81
11837,44
10465,29
9801
10140,49
13340,25
10140,49
12078,01
13133,16
7293,16
10100,25
13179,04
13572,25
12746,41
10404
11236
11088,09
14113,44
11257,21
11946,49
13735,84
8556,25
10857,64
12656,25
14981,76
12836,89
10000
12254,49
12723,84
12056,04
13759,29
11902,81
13432,81
9216
9960,04
13642,24
13386,49
9880,36
8892,49
8281
8686,24
10629,61
8854,81
8427,24
10547,29
Dataseries Y:
Download CSV
Histogram 
39120
33702
25094
51442
45594
52518
48564
41745
49585
32747
33379
35645
37034
35681
20972
58552
54955
65540
51570
51145
46641
35704
33253
35193
41668
34865
21210
56126
49231
59723
48103
47472
50497
40059
34149
36860
46356
36577
23872
57276
56389
57657
62300
48929
51168
39636
33213
38127
43291
30600
21956
48033
46148
50736
48114
38390
44112
36287
30333

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'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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51782&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51782&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51782&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean11113.697796610242793.8644067797
Biased Variance3497858.84296633111411205.608733
Biased Standard Deviation1870.2563575527110555.1506672682
Covariance-3824274.20478667
Correlation-0.190440551024791
Determination0.036267603474626
T-Test-1.46459864521547
p-value (2 sided)0.148524470807114
p-value (1 sided)0.0742622354035571
Degrees of Freedom57
Number of Observations59

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 11113.6977966102 & 42793.8644067797 \tabularnewline
Biased Variance & 3497858.84296633 & 111411205.608733 \tabularnewline
Biased Standard Deviation & 1870.25635755271 & 10555.1506672682 \tabularnewline
Covariance & -3824274.20478667 \tabularnewline
Correlation & -0.190440551024791 \tabularnewline
Determination & 0.036267603474626 \tabularnewline
T-Test & -1.46459864521547 \tabularnewline
p-value (2 sided) & 0.148524470807114 \tabularnewline
p-value (1 sided) & 0.0742622354035571 \tabularnewline
Degrees of Freedom & 57 \tabularnewline
Number of Observations & 59 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51782&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]11113.6977966102[/C][C]42793.8644067797[/C][/ROW]
[ROW][C]Biased Variance[/C][C]3497858.84296633[/C][C]111411205.608733[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1870.25635755271[/C][C]10555.1506672682[/C][/ROW]
[ROW][C]Covariance[/C][C]-3824274.20478667[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.190440551024791[/C][/ROW]
[ROW][C]Determination[/C][C]0.036267603474626[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.46459864521547[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.148524470807114[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0742622354035571[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]57[/C][/ROW]
[ROW][C]Number of Observations[/C][C]59[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51782&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51782&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
Mean11113.697796610242793.8644067797
Biased Variance3497858.84296633111411205.608733
Biased Standard Deviation1870.2563575527110555.1506672682
Covariance-3824274.20478667
Correlation-0.190440551024791
Determination0.036267603474626
T-Test-1.46459864521547
p-value (2 sided)0.148524470807114
p-value (1 sided)0.0742622354035571
Degrees of Freedom57
Number of Observations59


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0 ; par2 = 36 ;
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')