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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 computationThu, 24 Nov 2011 17:53:50 -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/24/t1322175279fkhdht1evs4dew5.htm/, Retrieved Sat, 20 Apr 2024 12:16:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147231, Retrieved Sat, 20 Apr 2024 12:16:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Brent/DJ] [2011-11-24 22:53:50] [0956ee981dded61b2e7128dae94e5715] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10539.51
10723.78
10682.06
10283.19
10377.18
10486.64
10545.38
10554.27
10532.54
10324.31
10695.25
10827.81
10872.48
10971.19
11145.65
11234.68
11333.88
10997.97
11036.89
11257.35
11533.59
11963.12
12185.15
12377.62
12512.89
12631.48
12268.53
12754.8
13407.75
13480.21
13673.28
13239.71
13557.69
13901.28
13200.58
13406.97
12538.12
12419.57
12193.88
12656.63
12812.48
12056.67
11322.38
11530.75
11114.08
9181.73
8614.55
8595.56
8396.2
7690.5
7235.47
7992.12
8398.37
8593
8679.75
9374.63
9634.97
9857.34
10238.83
10433.44
10471.24
Dataseries Y:
Download CSV
Histogram 
44,23
45,85
53,38
53,26
51,8
55,3
57,81
63,96
63,77
59,15
56,12
57,42
63,52
61,71
63,01
68,18
72,03
69,75
74,41
74,33
64,24
60,03
59,44
62,5
55,04
58,34
61,92
67,65
67,68
70,3
75,26
71,44
76,36
81,71
92,6
90,6
92,23
94,09
102,79
109,65
124,05
132,69
135,81
116,07
101,42
75,73
55,48
43,8
45,29
44,01
47,48
51,07
57,84
69,04
65,61
72,87
68,41
73,25
77,43
75,28
77,33

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 0 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147231&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147231&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147231&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 time0 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean11041.785573770571.0298360655738
Biased Variance2636081.3074509434.175988497716
Biased Standard Deviation1623.601338830120.8368900869999
Covariance15672.4053842623
Correlation0.45566405470242
Determination0.20762973074785
T-Test3.93193826380222
p-value (2 sided)0.000224116552844267
p-value (1 sided)0.000112058276422133
Degrees of Freedom59
Number of Observations61

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 11041.7855737705 & 71.0298360655738 \tabularnewline
Biased Variance & 2636081.3074509 & 434.175988497716 \tabularnewline
Biased Standard Deviation & 1623.6013388301 & 20.8368900869999 \tabularnewline
Covariance & 15672.4053842623 \tabularnewline
Correlation & 0.45566405470242 \tabularnewline
Determination & 0.20762973074785 \tabularnewline
T-Test & 3.93193826380222 \tabularnewline
p-value (2 sided) & 0.000224116552844267 \tabularnewline
p-value (1 sided) & 0.000112058276422133 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147231&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]11041.7855737705[/C][C]71.0298360655738[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2636081.3074509[/C][C]434.175988497716[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1623.6013388301[/C][C]20.8368900869999[/C][/ROW]
[ROW][C]Covariance[/C][C]15672.4053842623[/C][/ROW]
[ROW][C]Correlation[/C][C]0.45566405470242[/C][/ROW]
[ROW][C]Determination[/C][C]0.20762973074785[/C][/ROW]
[ROW][C]T-Test[/C][C]3.93193826380222[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000224116552844267[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000112058276422133[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]59[/C][/ROW]
[ROW][C]Number of Observations[/C][C]61[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147231&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147231&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
Mean11041.785573770571.0298360655738
Biased Variance2636081.3074509434.175988497716
Biased Standard Deviation1623.601338830120.8368900869999
Covariance15672.4053842623
Correlation0.45566405470242
Determination0.20762973074785
T-Test3.93193826380222
p-value (2 sided)0.000224116552844267
p-value (1 sided)0.000112058276422133
Degrees of Freedom59
Number of Observations61


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')