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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 computationTue, 16 Dec 2008 12:18:46 -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/2008/Dec/16/t12294551942mn5l5hiviizyfe.htm/, Retrieved Wed, 08 May 2024 15:18:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34136, Retrieved Wed, 08 May 2024 15:18:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact274

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Correlation: inve...] [2008-12-16 19:18:46] [e515c0250d6233b5d2604259ab52cebe] [Current]
- RMPD    [Univariate Data Series] [] [2008-12-17 14:56:45] [b98453cac15ba1066b407e146608df68]
-   PD      [Univariate Data Series] [] [2008-12-17 17:54:56] [b98453cac15ba1066b407e146608df68]
-   PD      [Univariate Data Series] [] [2008-12-17 17:58:54] [b98453cac15ba1066b407e146608df68]
- RMPD      [Multiple Regression] [] [2008-12-17 18:39:55] [b98453cac15ba1066b407e146608df68]
- RMP       [Variance Reduction Matrix] [] [2008-12-17 18:54:09] [b98453cac15ba1066b407e146608df68]
- RMP       [(Partial) Autocorrelation Function] [] [2008-12-17 18:57:05] [b98453cac15ba1066b407e146608df68]
- RMP       [(Partial) Autocorrelation Function] [] [2008-12-17 19:00:06] [b98453cac15ba1066b407e146608df68]
- RMP       [Spectral Analysis] [] [2008-12-17 19:10:05] [b98453cac15ba1066b407e146608df68]
- RMP       [Spectral Analysis] [] [2008-12-17 19:11:39] [b98453cac15ba1066b407e146608df68]
- RMP       [Standard Deviation-Mean Plot] [] [2008-12-17 19:22:22] [b98453cac15ba1066b407e146608df68]
-    D        [Standard Deviation-Mean Plot] [SDM van x] [2009-01-29 16:24:54] [44ec60eb6065a3f81a5f756bd5af1faf]
-  MPD        [Standard Deviation-Mean Plot] [Standard Deviatio...] [2009-12-15 19:47:25] [1eab65e90adf64584b8e6f0da23ff414]
-   PD          [Standard Deviation-Mean Plot] [Standard Deviatio...] [2009-12-19 18:05:59] [1eab65e90adf64584b8e6f0da23ff414]
- RMP       [ARIMA Backward Selection] [] [2008-12-17 19:26:06] [b98453cac15ba1066b407e146608df68]
- RMP         [ARIMA Forecasting] [] [2008-12-17 21:12:00] [b98453cac15ba1066b407e146608df68]
- RMPD        [Bivariate Kernel Density Estimation] [] [2008-12-17 21:24:20] [b98453cac15ba1066b407e146608df68]
- RMPD        [Pearson Correlation] [] [2008-12-17 21:26:07] [b98453cac15ba1066b407e146608df68]
- RMPD        [Kendall tau Correlation Matrix] [] [2008-12-17 21:29:30] [b98453cac15ba1066b407e146608df68]
- RMPD        [Cross Correlation Function] [] [2008-12-17 21:31:48] [b98453cac15ba1066b407e146608df68]
- RMPD        [Cross Correlation Function] [] [2008-12-17 21:35:12] [b98453cac15ba1066b407e146608df68]
-   PD      [Univariate Data Series] [] [2008-12-17 19:32:14] [b98453cac15ba1066b407e146608df68]
-  MPD        [Univariate Data Series] [Res1] [2009-12-17 19:22:49] [7d268329e554b8694908ba13e6e6f258]
-   P           [Univariate Data Series] [Res1] [2009-12-18 08:57:34] [7d268329e554b8694908ba13e6e6f258]
- RMP           [Harrell-Davis Quantiles] [HDQ1] [2009-12-18 09:04:05] [7d268329e554b8694908ba13e6e6f258]
-   P             [Harrell-Davis Quantiles] [HDQ1] [2009-12-18 16:08:04] [7d268329e554b8694908ba13e6e6f258]
- RMPD        [] [CT1] [-0001-11-30 00:00:00] [7d268329e554b8694908ba13e6e6f258]
- RMPD        [] [CT1] [-0001-11-30 00:00:00] [7d268329e554b8694908ba13e6e6f258]
- RMPD        [Central Tendency] [CT1] [2009-12-18 08:47:00] [7d268329e554b8694908ba13e6e6f258]
- RMPD      [Central Tendency] [] [2008-12-17 19:33:25] [b98453cac15ba1066b407e146608df68]
- RMPD      [Harrell-Davis Quantiles] [] [2008-12-17 19:35:33] [b98453cac15ba1066b407e146608df68]
- RMPD      [Testing Mean with unknown Variance - Critical Value] [] [2008-12-17 19:51:11] [b98453cac15ba1066b407e146608df68]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101.3
91.5
152.6
86.6
86.6
98.5
86.7
89.1
111
92.6
85.1
116.1
98.3
97.7
177.9
94.2
83.8
109.5
102.3
102.5
116.4
85.3
88.2
104.7
99.4
113.8
166.6
89.2
93.2
115
97.2
112.5
121.8
100.2
93.8
113.6
110.7
127.6
185.9
105.9
108
125.2
106.2
123.3
145.2
114.3
108.4
120.9
126.3
141.3
208.2
131.6
119.8
122.5
137.6
141
154.1
127
106.1
129.9
Dataseries Y:
Download CSV
Histogram 
124.1
110.7
128.1
108.9
111.2
131.9
120.5
115.4
130.8
112.6
111.1
129.5
131.8
127.7
142.6
115.8
119.5
139.8
130.6
126.2
141.7
118.9
120.3
141.2
138.9
141.3
153.7
131
136.5
160.1
139.8
143.8
155.8
131
131.8
151.7
153.8
152.9
156.1
147.2
145.7
165.3
147.4
154.4
165.3
145.2
139.7
158.4
169.1
162.1
166.2
157.2
161.4
169
171.8
161.4
175.7
164.7
146.1
173

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34136&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34136&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34136&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean115.03141.923333333333
Biased Variance660.115766666667332.484455555555
Biased Standard Deviation25.692718164232218.2341562885579
Covariance325.161491525424
Correlation0.68250233639836
Determination0.46580943918922
T-Test7.11164442696358
p-value (2 sided)1.90322757553929e-09
p-value (1 sided)9.51613787769645e-10
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 115.03 & 141.923333333333 \tabularnewline
Biased Variance & 660.115766666667 & 332.484455555555 \tabularnewline
Biased Standard Deviation & 25.6927181642322 & 18.2341562885579 \tabularnewline
Covariance & 325.161491525424 \tabularnewline
Correlation & 0.68250233639836 \tabularnewline
Determination & 0.46580943918922 \tabularnewline
T-Test & 7.11164442696358 \tabularnewline
p-value (2 sided) & 1.90322757553929e-09 \tabularnewline
p-value (1 sided) & 9.51613787769645e-10 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34136&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]115.03[/C][C]141.923333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]660.115766666667[/C][C]332.484455555555[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]25.6927181642322[/C][C]18.2341562885579[/C][/ROW]
[ROW][C]Covariance[/C][C]325.161491525424[/C][/ROW]
[ROW][C]Correlation[/C][C]0.68250233639836[/C][/ROW]
[ROW][C]Determination[/C][C]0.46580943918922[/C][/ROW]
[ROW][C]T-Test[/C][C]7.11164442696358[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.90322757553929e-09[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]9.51613787769645e-10[/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=34136&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34136&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
Mean115.03141.923333333333
Biased Variance660.115766666667332.484455555555
Biased Standard Deviation25.692718164232218.2341562885579
Covariance325.161491525424
Correlation0.68250233639836
Determination0.46580943918922
T-Test7.11164442696358
p-value (2 sided)1.90322757553929e-09
p-value (1 sided)9.51613787769645e-10
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')