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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 computationSat, 18 Dec 2010 14:15:15 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/18/t1292681588es6x85pwi9idw5f.htm/, Retrieved Tue, 30 Apr 2024 07:23:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111982, Retrieved Tue, 30 Apr 2024 07:23:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
-  MPD  [Univariate Data Series] [WS8 1] [2010-11-30 15:47:30] [07a238a5afc23eb944f8545182f29d5a]
- RMP     [Classical Decomposition] [WS8 2] [2010-11-30 15:54:02] [07a238a5afc23eb944f8545182f29d5a]
- RMPD      [Univariate Data Series] [Statistiek: Werkl...] [2010-12-12 15:20:09] [07a238a5afc23eb944f8545182f29d5a]
-    D        [Univariate Data Series] [Statistiek: Werkl...] [2010-12-14 09:08:05] [07a238a5afc23eb944f8545182f29d5a]
-               [Univariate Data Series] [Statistiek: Werkl...] [2010-12-14 09:12:36] [07a238a5afc23eb944f8545182f29d5a]
- RMPD            [Univariate Explorative Data Analysis] [Statistiek: U EDA...] [2010-12-17 19:07:44] [07a238a5afc23eb944f8545182f29d5a]
- RMP               [Central Tendency] [Statistiek: centr...] [2010-12-18 09:18:46] [07a238a5afc23eb944f8545182f29d5a]
- RMP                 [Harrell-Davis Quantiles] [Statistiek: betro...] [2010-12-18 10:06:35] [07a238a5afc23eb944f8545182f29d5a]
- RMPD                  [Bivariate Explorative Data Analysis] [statistiek: Bivar...] [2010-12-18 13:22:48] [07a238a5afc23eb944f8545182f29d5a]
- RMPD                    [Pearson Correlation] [statistiek: pears...] [2010-12-18 14:12:28] [07a238a5afc23eb944f8545182f29d5a]
-                             [Pearson Correlation] [statistiek: pears...] [2010-12-18 14:15:15] [67e3c2d70de1dbb070b545ca6c893d5e] [Current]
- RM D                          [Mean versus Median] [Statistiek: mean ...] [2010-12-18 14:31:13] [07a238a5afc23eb944f8545182f29d5a]
- RMPD                          [Bivariate Kernel Density Estimation] [statistiek: kerne...] [2010-12-18 15:29:35] [07a238a5afc23eb944f8545182f29d5a]
- RMPD                          [Trivariate Scatterplots] [Statistiek trivar...] [2010-12-18 16:57:07] [07a238a5afc23eb944f8545182f29d5a]
-   PD                            [Trivariate Scatterplots] [Statistiek: triva...] [2010-12-18 17:03:13] [07a238a5afc23eb944f8545182f29d5a]
- RMPD                            [Multiple Regression] [statistiek Multip...] [2010-12-18 19:03:25] [07a238a5afc23eb944f8545182f29d5a]
-    D                              [Multiple Regression] [statistiek Multip...] [2010-12-18 19:19:51] [07a238a5afc23eb944f8545182f29d5a]
-    D                                [Multiple Regression] [statistiek Multip...] [2010-12-18 19:32:07] [07a238a5afc23eb944f8545182f29d5a]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8.9
8.4
8.1
8.3
8.1
8
8.7
9.2
9
8.9
8.5
8.1
7.5
7.1
6.9
7.1
7
6.7
7
7.3
7.7
8.4
8.4
8.8
9.1
9
8.6
7.9
7.7
7.8
9.2
9.4
9.2
8.7
8.4
8.6
9
9.1
8.7
8.2
7.9
7.9
9.1
9.4
9.4
9.1
9
9.3
9.9
9.8
9.3
8.3
8
8.5
10.4
11.1
10.9
10
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9
9
9
9.8
10
9.8
9.3
9
9
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.7
7.9
7.9
8
7.9
7.6
7.1
6.8
6.5
6.9
8.2
8.7
8.3
7.9
7.5
7.8
8.3
8.4
8.2
7.6
7.2
7.5
8.7
9
8.6
7.9
7.8
8.2
Dataseries Y:
Download CSV
Histogram 
6.5
6.3
5.9
5.5
5.2
4.9
5.4
5.8
5.7
5.6
5.5
5.4
5.4
5.4
5.5
5.8
5.7
5.4
5.6
5.8
6.2
6.8
6.7
6.7
6.4
6.3
6.3
6.4
6.3
6
6.3
6.3
6.6
7.5
7.8
7.9
7.8
7.6
7.5
7.6
7.5
7.3
7.6
7.5
7.6
7.9
7.9
8.1
8.2
8
7.5
6.8
6.5
6.6
7.6
8
8.1
7.7
7.5
7.6
7.8
7.8
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.2
7.9
7.3
6.9
6.6
6.7
6.9
7
7.1
7.2
7.1
6.9
7
6.8
6.4
6.7
6.6
6.4
6.3
6.2
6.5
6.8
6.8
6.4
6.1
5.8
6.1
7.2
7.3
6.9
6.1
5.8
6.2
7.1
7.7
8
7.8
7.4
7.4
7.7
7.8
7.8
8
8.1
8.4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111982&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]3 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=111982&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111982&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean8.606666666666676.93416666666667
Biased Variance0.8176222222222220.740582638888889
Biased Standard Deviation0.9042246525185110.860571112046465
Covariance0.433131652661064
Correlation0.551978969180594
Determination0.304680782417671
T-Test7.19070410986467
p-value (2 sided)6.3697269681029e-11
p-value (1 sided)3.18486348405145e-11
Degrees of Freedom118
Number of Observations120

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 8.60666666666667 & 6.93416666666667 \tabularnewline
Biased Variance & 0.817622222222222 & 0.740582638888889 \tabularnewline
Biased Standard Deviation & 0.904224652518511 & 0.860571112046465 \tabularnewline
Covariance & 0.433131652661064 \tabularnewline
Correlation & 0.551978969180594 \tabularnewline
Determination & 0.304680782417671 \tabularnewline
T-Test & 7.19070410986467 \tabularnewline
p-value (2 sided) & 6.3697269681029e-11 \tabularnewline
p-value (1 sided) & 3.18486348405145e-11 \tabularnewline
Degrees of Freedom & 118 \tabularnewline
Number of Observations & 120 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111982&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]8.60666666666667[/C][C]6.93416666666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.817622222222222[/C][C]0.740582638888889[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.904224652518511[/C][C]0.860571112046465[/C][/ROW]
[ROW][C]Covariance[/C][C]0.433131652661064[/C][/ROW]
[ROW][C]Correlation[/C][C]0.551978969180594[/C][/ROW]
[ROW][C]Determination[/C][C]0.304680782417671[/C][/ROW]
[ROW][C]T-Test[/C][C]7.19070410986467[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]6.3697269681029e-11[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]3.18486348405145e-11[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]118[/C][/ROW]
[ROW][C]Number of Observations[/C][C]120[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111982&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111982&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
Mean8.606666666666676.93416666666667
Biased Variance0.8176222222222220.740582638888889
Biased Standard Deviation0.9042246525185110.860571112046465
Covariance0.433131652661064
Correlation0.551978969180594
Determination0.304680782417671
T-Test7.19070410986467
p-value (2 sided)6.3697269681029e-11
p-value (1 sided)3.18486348405145e-11
Degrees of Freedom118
Number of Observations120


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')