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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 Oct 2008 04:40:26 -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/18/t12243264782y1f2qmuen86lye.htm/, Retrieved Sun, 19 May 2024 15:54:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16565, Retrieved Sun, 19 May 2024 15:54:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149

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] [uitvoer intra ext...] [2008-10-18 10:40:26] [b05bea52879de0a398b42c6968cc24b2] [Current]
Feedback Forum
2008-10-25 11:57:59 [Davy De Nef] [reply] 
De student maakt hier gebruik van de Pearson correlation.
Het resultaat van 0,84 dat de student bekomt, wijst op een positieve correlatie.
Dit is ook duidelijk af te leiden uit de grafiek. Je kan een denkbeeldige stijgende rechte tekenen tussen de punten van de grafiek. Dit wijst ook weer op dezelfde positieve correlatie.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12112
10875,2
9897,3
11672,1
12385,7
11405,6
9830,9
11025,1
10853,8
12252,6
11839,4
11669,1
11601,4
11178,4
9516,4
12102,8
12989
11610,2
10205,5
11356,2
11307,1
12648,6
11947,2
11714,1
12192,5
11268,8
9097,4
12639,8
13040,1
11687,3
11191,7
11391,9
11793,1
13933,2
12778,1
11810,3
13698,4
11956,6
10723,8
13938,9
13979,8
13807,4
12973,9
12509,8
12934,1
14908,3
13772,1
13012,6
14049,9
11816,5
11593,2
14466,2
13615,9
14733,9
13880,7
13527,5
13584
16170,2
13260,6
14741,9
15486,5
13154,5
12621,2
15031,6
15452,4
15428
13105,9
14716,8
14180
16202,2
14392,4
15140,6
15960,1
14351,3
13230,2
15202,1
17157,3
16159,1
13405,7
17224,7
17338,4
17370,6
18817,8
16593,2
17979,5
Dataseries Y:
Download CSV
Histogram 
3532,8
3693,1
2622,9
3130,8
3487,5
3349,7
3044,2
3266
3351,5
3606,8
3419,5
3829,5
3505,1
3845,3
2566,6
3658,5
3954
3460,1
3454,1
3412,8
3418
3349,5
3423,4
3242,8
3277,2
3833
2606,3
3643,8
3686,4
3281,6
3669,3
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3610
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3613
3730,5
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4735,9
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3988
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5148,4
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4682,5
4884,3
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4505,2
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5081,1
4523,1
4412,8
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4778,6
4495,3
4633,5
4360,5
4517,9

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 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16565&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 Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16565&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16565&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 Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean13249.15529411763934.28117647059
Biased Variance4181281.63282491347233.207880969
Biased Standard Deviation2044.81823955698589.264972555614
Covariance1031756.62105322
Correlation0.84619857231465
Determination0.716052023787353
T-Test14.4674485180386
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom83
Number of Observations85

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 13249.1552941176 & 3934.28117647059 \tabularnewline
Biased Variance & 4181281.63282491 & 347233.207880969 \tabularnewline
Biased Standard Deviation & 2044.81823955698 & 589.264972555614 \tabularnewline
Covariance & 1031756.62105322 \tabularnewline
Correlation & 0.84619857231465 \tabularnewline
Determination & 0.716052023787353 \tabularnewline
T-Test & 14.4674485180386 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 83 \tabularnewline
Number of Observations & 85 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16565&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]13249.1552941176[/C][C]3934.28117647059[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4181281.63282491[/C][C]347233.207880969[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2044.81823955698[/C][C]589.264972555614[/C][/ROW]
[ROW][C]Covariance[/C][C]1031756.62105322[/C][/ROW]
[ROW][C]Correlation[/C][C]0.84619857231465[/C][/ROW]
[ROW][C]Determination[/C][C]0.716052023787353[/C][/ROW]
[ROW][C]T-Test[/C][C]14.4674485180386[/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]83[/C][/ROW]
[ROW][C]Number of Observations[/C][C]85[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16565&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16565&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
Mean13249.15529411763934.28117647059
Biased Variance4181281.63282491347233.207880969
Biased Standard Deviation2044.81823955698589.264972555614
Covariance1031756.62105322
Correlation0.84619857231465
Determination0.716052023787353
T-Test14.4674485180386
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom83
Number of Observations85


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')