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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Module--
Title produced by softwarePearson Correlation
Date of computationTue, 22 Nov 2011 06:02:52 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/22/t1321959784b2yyws60o287qwx.htm/, Retrieved Tue, 16 Apr 2024 11:22:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=146125, Retrieved Tue, 16 Apr 2024 11:22:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Competence to learn] [2010-11-17 07:43:53] [b98453cac15ba1066b407e146608df68]
- RMPD  [Pearson Correlation] [Correlatie belong...] [2010-11-19 18:01:17] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
- RM        [Pearson Correlation] [] [2011-11-22 11:02:52] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
77
63
73
76
90
67
69
70
54
54
76
75
76
80
89
73
74
78
76
69
74
82
77
84
75
54
79
79
69
88
57
69
86
65
66
54
85
79
84
70
54
70
54
69
68
68
71
71
66
67
71
54
76
77
71
69
73
46
66
77
77
70
86
38
66
75
80
64
80
86
54
74
88
85
63
81
81
74
80
80
60
65
62
63
89
76
81
72
84
76
76
78
72
81
72
78
79
52
67
74
73
69
67
76
77
63
84
90
75
76
75
53
87
78
54
58
80
74
56
82
64
67
75
69
72
71
54
68
54
71
53
54
71
69
30
53
68
69
54
66
79
67
74
86
63
69
73
69
71
77
74
82
54
54
80
76
Dataseries Y:
Download CSV
Histogram 
46
37
45
46
55
40
43
43
33
33
47
44
47
49
55
43
46
51
47
42
42
48
45
51
46
33
47
47
42
55
36
42
51
43
40
33
52
49
50
43
33
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33
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40
40
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41
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45
33
46
47
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44
46
30
42
46
46
43
52
11
41
45
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53
35
45
54
53
36
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45
47
49
38
40
46
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54
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53
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51
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46
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31
44
42
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43
41
47
45
37
54
55
45
47
46
37
53
46
33
36
49
44
37
53
40
42
45
40
44
43
33
44
33
43
32
33
43
42
0
32
41
44
33
42
46
44
45
53
38
43
43
42
42
47
44
49
33
33
47
47

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'AstonUniversity' @ aston.wessa.net

\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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146125&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146125&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146125&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'AstonUniversity' @ aston.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean70.891025641025643.1153846153846
Biased Variance111.46889381985551.8584812623274
Biased Standard Deviation10.55788301790927.20128330662858
Covariance72.4578163771712
Correlation0.9469032322957
Determination0.896625731332042
T-Test36.5476733257942
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom154
Number of Observations156

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 70.8910256410256 & 43.1153846153846 \tabularnewline
Biased Variance & 111.468893819855 & 51.8584812623274 \tabularnewline
Biased Standard Deviation & 10.5578830179092 & 7.20128330662858 \tabularnewline
Covariance & 72.4578163771712 \tabularnewline
Correlation & 0.9469032322957 \tabularnewline
Determination & 0.896625731332042 \tabularnewline
T-Test & 36.5476733257942 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 154 \tabularnewline
Number of Observations & 156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146125&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]70.8910256410256[/C][C]43.1153846153846[/C][/ROW]
[ROW][C]Biased Variance[/C][C]111.468893819855[/C][C]51.8584812623274[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]10.5578830179092[/C][C]7.20128330662858[/C][/ROW]
[ROW][C]Covariance[/C][C]72.4578163771712[/C][/ROW]
[ROW][C]Correlation[/C][C]0.9469032322957[/C][/ROW]
[ROW][C]Determination[/C][C]0.896625731332042[/C][/ROW]
[ROW][C]T-Test[/C][C]36.5476733257942[/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]154[/C][/ROW]
[ROW][C]Number of Observations[/C][C]156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146125&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146125&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
Mean70.891025641025643.1153846153846
Biased Variance111.46889381985551.8584812623274
Biased Standard Deviation10.55788301790927.20128330662858
Covariance72.4578163771712
Correlation0.9469032322957
Determination0.896625731332042
T-Test36.5476733257942
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom154
Number of Observations156


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')