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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 computationMon, 20 Oct 2008 05:45:54 -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/2008/Oct/20/t12245032151c0ivp3881j8k3j.htm/, Retrieved Sun, 19 May 2024 13:35:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17202, Retrieved Sun, 19 May 2024 13:35:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Pearson Correlation] [Correlatie tussen...] [2008-10-20 11:45:54] [d8c5724db236abb5950452133b88474d] [Current]
Feedback Forum
2008-10-27 23:41:09 [2b91075c702c6e89854c34747e80ec72] [reply] 
Een negatieve correlatie tussen de reeksen wil zeggen dat als de waarden van de ene reeks stijgen, de waarden van de andere dalen. In dit geval kunnen we dus stellen dat als bijvoorbeeld de waarde van de wisky daalt, dat de waarde van de gezondheidsindex dan gaat stijgen.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
16.42
16.47
16.44
16.44
16.49
16.32
16.47
16.39
16.42
16.39
16.4
16.24
16.42
16.46
16.47
16.37
16.42
16.34
16.41
16.43
16.4
16.35
16.31
16.18
16.29
16.27
16.31
16.28
16.32
16.32
16.37
16.39
16.51
16.5
16.49
16.32
16.37
16.39
16.41
16.39
16.41
16.37
16.4
16.53
16.63
16.64
16.63
16.47
16.46
16.49
16.59
16.58
16.6
16.55
16.57
16.51
16.5
16.49
16.44
16.26
16.33
16.72
16.75
16.74
16.84
16.79
16.66
16.69
16.84
16.86
16.76
16.72
Dataseries Y:
Download CSV
Histogram 
1,2
1,2
1,4
1,5
1,4
1,8
2
2,3
2,6
2,3
2,5
2,3
2,1
2,2
2,2
2,7
3,1
3,2
3,1
3,1
2,8
3
2,8
2,7
3,2
3,1
3
2
1,7
1,2
1,4
1,3
1,3
1,1
0,9
1,2
0,9
1,3
1,4
1,5
1,1
1,6
1,5
1,6
1,7
1,6
1,7
1,6
1,6
1,3
1,1
1,6
1,9
1,6
1,7
1,6
1,4
2,1
1,9
1,7
1,8
2
2,5
2,1
2,1
2,3
2,4
2,4
2,3
1,7
2
2,3

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=17202&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=17202&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17202&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
Mean16.4751.94166666666667
Biased Variance0.02382222222222220.380763888888889
Biased Standard Deviation0.1543444920372030.617060684932113
Covariance-0.00994366197183105
Correlation-0.102956362881800
Determination0.0106000126578490
T-Test-0.865996749103855
p-value (2 sided)0.389450464325440
p-value (1 sided)0.194725232162720
Degrees of Freedom70
Number of Observations72

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 16.475 & 1.94166666666667 \tabularnewline
Biased Variance & 0.0238222222222222 & 0.380763888888889 \tabularnewline
Biased Standard Deviation & 0.154344492037203 & 0.617060684932113 \tabularnewline
Covariance & -0.00994366197183105 \tabularnewline
Correlation & -0.102956362881800 \tabularnewline
Determination & 0.0106000126578490 \tabularnewline
T-Test & -0.865996749103855 \tabularnewline
p-value (2 sided) & 0.389450464325440 \tabularnewline
p-value (1 sided) & 0.194725232162720 \tabularnewline
Degrees of Freedom & 70 \tabularnewline
Number of Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17202&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]16.475[/C][C]1.94166666666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.0238222222222222[/C][C]0.380763888888889[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.154344492037203[/C][C]0.617060684932113[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.00994366197183105[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.102956362881800[/C][/ROW]
[ROW][C]Determination[/C][C]0.0106000126578490[/C][/ROW]
[ROW][C]T-Test[/C][C]-0.865996749103855[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.389450464325440[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.194725232162720[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]70[/C][/ROW]
[ROW][C]Number of Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17202&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17202&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
Mean16.4751.94166666666667
Biased Variance0.02382222222222220.380763888888889
Biased Standard Deviation0.1543444920372030.617060684932113
Covariance-0.00994366197183105
Correlation-0.102956362881800
Determination0.0106000126578490
T-Test-0.865996749103855
p-value (2 sided)0.389450464325440
p-value (1 sided)0.194725232162720
Degrees of Freedom70
Number of Observations72


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')