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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 computationMon, 08 Dec 2008 03:57:18 -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/08/t1228734128wi3cdqdp0ga1gqy.htm/, Retrieved Thu, 16 May 2024 05:49:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30370, Retrieved Thu, 16 May 2024 05:49:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact207

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Correlatie tussen...] [2008-12-08 10:57:18] [b4fc5040f26b33db57f84cfb8d1d2b82] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
108,5000
108,9200
109,2300
109,4100
109,6500
109,9100
110,0100
110,2000
110,4900
110,5700
110,7200
110,9400
111,0900
111,2800
111,4100
111,6200
111,7600
111,8900
112,0400
112,1200
112,3000
112,4700
112,5900
112,7800
112,7300
112,9900
113,1000
113,3300
113,3800
113,6800
113,6500
113,8100
113,8800
114,0200
114,2500
114,2800
114,3800
114,7300
114,9700
115,0500
115,2900
115,3700
115,5400
115,7600
115,9200
116,0200
116,2100
116,2600
116,5100
Dataseries Y:
Download CSV
Histogram 
1627
1791
2034
1997
2169
2028
2253
2218
1855
2187
1852
1570
1851
1954
1828
2251
2277
2085
2282
2266
1878
2267
2069
1746
2299
2360
2214
2825
2355
2333
3016
2155
2172
2150
2533
2058
2160
2259
2498
2695
2799
2945
2930
2318
2540
2570
2669
2450
2842

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30370&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30370&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30370&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'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean112.7961224489802254.69387755102
Biased Variance4.76230537276135118173.396084965
Biased Standard Deviation2.18227069190817343.763575855507
Covariance542.595663265306
Correlation0.708521441115849
Determination0.502002632520879
T-Test6.8831685247361
p-value (2 sided)1.22930867707538e-08
p-value (1 sided)6.1465433853769e-09
Degrees of Freedom47
Number of Observations49

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 112.796122448980 & 2254.69387755102 \tabularnewline
Biased Variance & 4.76230537276135 & 118173.396084965 \tabularnewline
Biased Standard Deviation & 2.18227069190817 & 343.763575855507 \tabularnewline
Covariance & 542.595663265306 \tabularnewline
Correlation & 0.708521441115849 \tabularnewline
Determination & 0.502002632520879 \tabularnewline
T-Test & 6.8831685247361 \tabularnewline
p-value (2 sided) & 1.22930867707538e-08 \tabularnewline
p-value (1 sided) & 6.1465433853769e-09 \tabularnewline
Degrees of Freedom & 47 \tabularnewline
Number of Observations & 49 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30370&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]112.796122448980[/C][C]2254.69387755102[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4.76230537276135[/C][C]118173.396084965[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.18227069190817[/C][C]343.763575855507[/C][/ROW]
[ROW][C]Covariance[/C][C]542.595663265306[/C][/ROW]
[ROW][C]Correlation[/C][C]0.708521441115849[/C][/ROW]
[ROW][C]Determination[/C][C]0.502002632520879[/C][/ROW]
[ROW][C]T-Test[/C][C]6.8831685247361[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.22930867707538e-08[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]6.1465433853769e-09[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]47[/C][/ROW]
[ROW][C]Number of Observations[/C][C]49[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30370&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30370&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
Mean112.7961224489802254.69387755102
Biased Variance4.76230537276135118173.396084965
Biased Standard Deviation2.18227069190817343.763575855507
Covariance542.595663265306
Correlation0.708521441115849
Determination0.502002632520879
T-Test6.8831685247361
p-value (2 sided)1.22930867707538e-08
p-value (1 sided)6.1465433853769e-09
Degrees of Freedom47
Number of Observations49


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')