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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, 23 Oct 2009 06:05:33 -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/23/t12562995631f1lwec38lf17ta.htm/, Retrieved Thu, 02 May 2024 07:03:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49916, Retrieved Thu, 02 May 2024 07:03:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165

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] [WS 4 1 PLOTS] [2009-10-23 11:13:05] [6e4e01d7eb22a9f33d58ebb35753a195]
- RMPD    [Bivariate Explorative Data Analysis] [ws 4 part 2] [2009-10-23 11:56:36] [6e4e01d7eb22a9f33d58ebb35753a195]
- RMP         [Pearson Correlation] [ws 4 2.1 r] [2009-10-23 12:05:33] [2e4ef2c1b76db9b31c0a03b96e94ad77] [Current]
- RMP           [Bivariate Kernel Density Estimation] [ws 4 p2.1] [2009-10-23 16:26:45] [6e4e01d7eb22a9f33d58ebb35753a195]
- RMPD            [Linear Regression Graphical Model Validation] [ws 2.2] [2009-10-23 16:47:44] [6e4e01d7eb22a9f33d58ebb35753a195]
-    D              [Linear Regression Graphical Model Validation] [ws 2.2] [2009-10-23 16:51:23] [6e4e01d7eb22a9f33d58ebb35753a195]
-  M D          [Pearson Correlation] [WS 4 Part 2 r] [2009-11-02 00:36:23] [9717cb857c153ca3061376906953b329]
-  M D          [Pearson Correlation] [WS 4 Part 2 r] [2009-11-02 01:10:27] [9717cb857c153ca3061376906953b329]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100,30
98,50
95,10
93,10
92,20
89,00
86,40
84,50
82,70
80,80
81,80
81,80
82,90
83,80
86,20
86,10
86,20
88,80
89,60
87,80
88,30
88,60
91,00
91,50
95,40
98,70
99,90
98,60
100,30
100,20
100,40
101,40
103,00
109,10
111,40
114,10
121,80
127,60
129,90
128,00
123,50
124,00
127,40
127,60
128,40
131,40
135,10
134,00
144,50
147,30
150,90
148,70
141,40
138,90
139,80
145,60
147,90
148,50
151,10
157,50
Dataseries Y:
Download CSV
Histogram 
103,63
103,64
103,66
103,77
103,88
103,91
103,91
103,92
104,05
104,23
104,30
104,31
104,31
104,34
104,55
104,65
104,73
104,75
104,75
104,76
104,94
105,29
105,38
105,43
105,43
105,42
105,52
105,69
105,72
105,74
105,74
105,74
105,95
106,17
106,34
106,37
106,37
106,36
106,44
106,29
106,23
106,23
106,23
106,23
106,34
106,44
106,44
106,48
106,50
106,57
106,40
106,37
106,25
106,21
106,21
106,24
106,19
106,08
106,13
106,09

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=49916&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=49916&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49916&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
Mean110.838333333333105.437333333333
Biased Variance561.8903638888890.920276222222223
Biased Standard Deviation23.70422670936320.959310284643203
Covariance18.5148327683616
Correlation0.800637011015123
Determination0.64101962340723
T-Test10.1768718246771
p-value (2 sided)1.62092561595273e-14
p-value (1 sided)8.10462807976364e-15
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 110.838333333333 & 105.437333333333 \tabularnewline
Biased Variance & 561.890363888889 & 0.920276222222223 \tabularnewline
Biased Standard Deviation & 23.7042267093632 & 0.959310284643203 \tabularnewline
Covariance & 18.5148327683616 \tabularnewline
Correlation & 0.800637011015123 \tabularnewline
Determination & 0.64101962340723 \tabularnewline
T-Test & 10.1768718246771 \tabularnewline
p-value (2 sided) & 1.62092561595273e-14 \tabularnewline
p-value (1 sided) & 8.10462807976364e-15 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49916&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]110.838333333333[/C][C]105.437333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]561.890363888889[/C][C]0.920276222222223[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]23.7042267093632[/C][C]0.959310284643203[/C][/ROW]
[ROW][C]Covariance[/C][C]18.5148327683616[/C][/ROW]
[ROW][C]Correlation[/C][C]0.800637011015123[/C][/ROW]
[ROW][C]Determination[/C][C]0.64101962340723[/C][/ROW]
[ROW][C]T-Test[/C][C]10.1768718246771[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.62092561595273e-14[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]8.10462807976364e-15[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49916&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49916&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
Mean110.838333333333105.437333333333
Biased Variance561.8903638888890.920276222222223
Biased Standard Deviation23.70422670936320.959310284643203
Covariance18.5148327683616
Correlation0.800637011015123
Determination0.64101962340723
T-Test10.1768718246771
p-value (2 sided)1.62092561595273e-14
p-value (1 sided)8.10462807976364e-15
Degrees of Freedom58
Number of Observations60


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')