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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, 20 Oct 2008 14:31:45 -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/t1224534760zc0473vm04xek1b.htm/, Retrieved Fri, 17 May 2024 04:24:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18095, Retrieved Fri, 17 May 2024 04:24:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [investigating Ass...] [2007-10-22 22:15:01] [8cd6641b921d30ebe00b648d1481bba0]
-    D    [Pearson Correlation] [Relatie Totaal/Wa...] [2008-10-20 20:31:45] [7ed4ec9f8cdf7df79ef87b9dc09dff20] [Current]
F R  D      [Pearson Correlation] [correlatie Totaal...] [2008-10-20 22:18:38] [84dda5145c389bd11bcc662bd33fe4ba]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15370,6
14956,9
15469,7
15101,8
11703,7
16283,6
16726,5
14968,9
14861
14583,3
15305,8
17903,9
16379,4
15420,3
17870,5
15912,8
13866,5
17823,2
17872
17422
16704,5
15991,2
16583,6
19123,5
17838,7
17209,4
18586,5
16258,1
15141,6
19202,1
17746,5
19090,1
18040,3
17515,5
17751,8
21072,4
17170
19439,5
19795,4
17574,9
16165,4
19464,6
19932,1
19961,2
17343,4
18924,2
18574,1
21350,6
18594,6
19823,1
20844,4
19640,2
17735,4
19813,6
22238,5
20682,2
17818,6
21872,1
22117
21865,9
Dataseries Y:
Download CSV
Histogram 
2435,2
2273,3
2454,7
2328,8
1897
2608,1
2712,3
2322
2282,6
2241,1
2417,2
2829
2600,6
2321
2768,5
2457,3
2142,7
2764,4
2788,9
2679,5
2536,5
2682,7
2699,6
3097,8
3015,2
2878
3010,9
2612,3
2419,3
3096,5
3013
3397,4
3423,1
3298,7
3065,7
3918,3
3154,4
3334,7
3461,6
3018,5
2832
3301,3
3342,8
3464,4
3016,6
3201,3
3135,3
3549,8
3247,2
3441,8
3535,6
3384,7
2996,6
3402,8
3900,2
3776,4
3197,5
4022,4
3845,1
3818,6

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'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18095&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18095&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18095&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean17806.65333333332981.18
Biased Variance4961000.60115555249193.498933333
Biased Standard Deviation2227.33037539462499.192847438075
Covariance1084071.59955932
Correlation0.95875078896063
Determination0.91920307533263
T-Test25.6875281852304
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 17806.6533333333 & 2981.18 \tabularnewline
Biased Variance & 4961000.60115555 & 249193.498933333 \tabularnewline
Biased Standard Deviation & 2227.33037539462 & 499.192847438075 \tabularnewline
Covariance & 1084071.59955932 \tabularnewline
Correlation & 0.95875078896063 \tabularnewline
Determination & 0.91920307533263 \tabularnewline
T-Test & 25.6875281852304 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18095&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]17806.6533333333[/C][C]2981.18[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4961000.60115555[/C][C]249193.498933333[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2227.33037539462[/C][C]499.192847438075[/C][/ROW]
[ROW][C]Covariance[/C][C]1084071.59955932[/C][/ROW]
[ROW][C]Correlation[/C][C]0.95875078896063[/C][/ROW]
[ROW][C]Determination[/C][C]0.91920307533263[/C][/ROW]
[ROW][C]T-Test[/C][C]25.6875281852304[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/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=18095&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18095&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
Mean17806.65333333332981.18
Biased Variance4961000.60115555249193.498933333
Biased Standard Deviation2227.33037539462499.192847438075
Covariance1084071.59955932
Correlation0.95875078896063
Determination0.91920307533263
T-Test25.6875281852304
p-value (2 sided)0
p-value (1 sided)0
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')