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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationFri, 19 Sep 2014 15:24:51 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Sep/19/t14111369188lculsn4bf20xxq.htm/, Retrieved Mon, 13 May 2024 02:04:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235900, Retrieved Mon, 13 May 2024 02:04:46 +0000
QR Codes:

Original text written by user:X axis is the States' (plus D.C.) percentage for years of majority Democrat votes Y axis is their respective poverty rates
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Democrats vs poverty] [2014-09-19 14:24:51] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
57.89
7.69
32
71.05
38.46
32.35
41.03
100
51.28
57.89
73.68
84.62
33.33
38.46
23.08
25.64
16.22
64.1
63.16
23.08
64.1
46.15
28.21
44.74
59.46
56.41
36.67
19.44
43.24
25.64
51.28
52
48.72
65.79
16.67
28.21
38.46
34.21
33.33
46.15
57.89
13.33
60.53
64.86
27.59
15.38
54.05
50
54.05
35.9
26.67
Dataseries Y:
Download CSV
Histogram 
16.7
10
15.2
15.9
13.2
11.4
9.7
20.7
9.2
11.1
14.4
8.6
9.9
11.5
12.6
11.3
12.5
14.8
18.3
12.6
9.7
10.1
12
8.1
20.1
11.6
13.8
9.5
10.6
5.6
6.8
17.9
14.5
13.1
11.2
12.3
15.6
12
11.2
12.1
15
11.8
15
16.2
9.2
7.6
9.2
10.2
15.4
10.2
10.6

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 Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235900&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235900&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235900&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 Maurice George Kendall' @ kendall.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean43.806666666666712.3098039215686
Biased Variance368.79835555555610.3079430988082
Biased Standard Deviation19.20412339982113.21059855771601
Covariance29.0904733333333
Correlation0.462562180704345
Determination0.213963771017959
T-Test3.65213548223077
p-value (2 sided)0.000631916893063522
p-value (1 sided)0.000315958446531761
Degrees of Freedom49
Number of Observations51

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 43.8066666666667 & 12.3098039215686 \tabularnewline
Biased Variance & 368.798355555556 & 10.3079430988082 \tabularnewline
Biased Standard Deviation & 19.2041233998211 & 3.21059855771601 \tabularnewline
Covariance & 29.0904733333333 \tabularnewline
Correlation & 0.462562180704345 \tabularnewline
Determination & 0.213963771017959 \tabularnewline
T-Test & 3.65213548223077 \tabularnewline
p-value (2 sided) & 0.000631916893063522 \tabularnewline
p-value (1 sided) & 0.000315958446531761 \tabularnewline
Degrees of Freedom & 49 \tabularnewline
Number of Observations & 51 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235900&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]43.8066666666667[/C][C]12.3098039215686[/C][/ROW]
[ROW][C]Biased Variance[/C][C]368.798355555556[/C][C]10.3079430988082[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]19.2041233998211[/C][C]3.21059855771601[/C][/ROW]
[ROW][C]Covariance[/C][C]29.0904733333333[/C][/ROW]
[ROW][C]Correlation[/C][C]0.462562180704345[/C][/ROW]
[ROW][C]Determination[/C][C]0.213963771017959[/C][/ROW]
[ROW][C]T-Test[/C][C]3.65213548223077[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000631916893063522[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000315958446531761[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]49[/C][/ROW]
[ROW][C]Number of Observations[/C][C]51[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235900&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235900&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
Mean43.806666666666712.3098039215686
Biased Variance368.79835555555610.3079430988082
Biased Standard Deviation19.20412339982113.21059855771601
Covariance29.0904733333333
Correlation0.462562180704345
Determination0.213963771017959
T-Test3.65213548223077
p-value (2 sided)0.000631916893063522
p-value (1 sided)0.000315958446531761
Degrees of Freedom49
Number of Observations51






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.4833, p-value = 0.4763
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.3754, p-value = 0.3049
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.271, p-value = 0.6604

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.5163, p-value = 0.1818


\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.4833, p-value = 0.4763
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.3754, p-value = 0.3049
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.271, p-value = 0.6604

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.5163, p-value = 0.1818

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235900&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.4833, p-value = 0.4763
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.3754, p-value = 0.3049
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.271, p-value = 0.6604

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.5163, p-value = 0.1818

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235900&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235900&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.4833, p-value = 0.4763
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.3754, p-value = 0.3049
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.271, p-value = 0.6604

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.5163, p-value = 0.1818


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
x <- x[!is.na(y)]
y <- y[!is.na(y)]
y <- y[!is.na(x)]
x <- x[!is.na(x)]
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, sub=main)
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', na.rm = T)
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')
library(moments)
library(nortest)
jarque.x <- jarque.test(x)
jarque.y <- jarque.test(y)
if(lx>7) {
ad.x <- ad.test(x)
ad.y <- ad.test(y)
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Normality Tests',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.y'),'
',sep=''))
a<-table.row.end(a)
if(lx>7) {
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.y'),'
',sep=''))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
library(car)
bitmap(file='test2.png')
qq.plot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qq.plot(y,main='QQplot of variable y')
dev.off()