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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationFri, 14 Dec 2007 06:50:37 -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/2007/Dec/14/t1197639399o023alb4fnxwuj1.htm/, Retrieved Thu, 02 May 2024 18:31:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3884, Retrieved Thu, 02 May 2024 18:31:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Paper_Corr_output1] [2007-12-14 13:50:37] [1ea0754dc57274996703e6220e342fe8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
102,61
102,18
101,64
102
102,18
101,89
102,09
101,6
101,33
101,44
101,49
100,41
101,38
101,4
102,16
104,46
104,75
104,2
106,05
107,54
108,23
108,99
109,51
111,99
111,08
112,95
115,49
114,67
116,85
119,57
119,41
118,46
122,81
121,76
121,37
118,61
116,08
117,84
117,02
119,78
122,58
120,98
118,92
117,81
119,73
117,16
116,03
115,55
115,36
116,09
117,32
120,45
119,86
118,51
118,92
119,11
120,34
121,23
119,43
119,28
120,64
122,24
123,1
120,72
118,34
118,8
119,29
121,47
122,35
121,53
121,72
121,58
121,55
122,02
123,74
125,8
129,29
128,89
130,04
131,57
131,97
134,43
132,63
130,26
129
131,65
134,21
138,63
138,1
140,51
144,36
145,57
148,7
147,86
143,16
141,96
Dataseries Y:
Download CSV
Histogram 
36409
33163
34122
35225
28249
30374
26311
22069
23651
28628
23187
14727
43080
32519
39657
33614
28671
34243
27336
22916
24537
26128
22602
15744
41086
39690
43129
37863
35953
29133
24693
22205
21725
27192
21790
13253
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3884&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3884&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3884&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean119.03760416666726098.1770833333
Biased Variance138.16123071831652962213.1457248
Biased Standard Deviation11.75420055632527277.51421473877
Covariance-35669.3291502193
Correlation-0.412639838377558
Determination0.170271636216257
T-Test-4.39204835861422
p-value (2 sided)2.94325532186392e-05
p-value (1 sided)1.47162766093196e-05
Degrees of Freedom94
Number of Observations96

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 119.037604166667 & 26098.1770833333 \tabularnewline
Biased Variance & 138.161230718316 & 52962213.1457248 \tabularnewline
Biased Standard Deviation & 11.7542005563252 & 7277.51421473877 \tabularnewline
Covariance & -35669.3291502193 \tabularnewline
Correlation & -0.412639838377558 \tabularnewline
Determination & 0.170271636216257 \tabularnewline
T-Test & -4.39204835861422 \tabularnewline
p-value (2 sided) & 2.94325532186392e-05 \tabularnewline
p-value (1 sided) & 1.47162766093196e-05 \tabularnewline
Degrees of Freedom & 94 \tabularnewline
Number of Observations & 96 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3884&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]119.037604166667[/C][C]26098.1770833333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]138.161230718316[/C][C]52962213.1457248[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]11.7542005563252[/C][C]7277.51421473877[/C][/ROW]
[ROW][C]Covariance[/C][C]-35669.3291502193[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.412639838377558[/C][/ROW]
[ROW][C]Determination[/C][C]0.170271636216257[/C][/ROW]
[ROW][C]T-Test[/C][C]-4.39204835861422[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.94325532186392e-05[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.47162766093196e-05[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]94[/C][/ROW]
[ROW][C]Number of Observations[/C][C]96[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3884&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3884&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
Mean119.03760416666726098.1770833333
Biased Variance138.16123071831652962213.1457248
Biased Standard Deviation11.75420055632527277.51421473877
Covariance-35669.3291502193
Correlation-0.412639838377558
Determination0.170271636216257
T-Test-4.39204835861422
p-value (2 sided)2.94325532186392e-05
p-value (1 sided)1.47162766093196e-05
Degrees of Freedom94
Number of Observations96


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')