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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 computationSun, 19 Oct 2008 15:11:29 -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/19/t1224450788eb8ie9lkbxnir53.htm/, Retrieved Sun, 19 May 2024 16:38:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17107, Retrieved Sun, 19 May 2024 16:38:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139

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...] [2008-10-19 21:11:29] [5925747fb2a6bb4cfcd8015825ee5e92] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
28
30
32
31
32
34
32
35
29
33
33
34
32
27
26
22
22
23
23
19
15
5
1
11
18
20
21
19
20
19
18
16
16
16
15
11
10
6
1
8
10
9
6
8
14
4
13
13
16
18
16
15
13
19
15
17
17
13
12
13
13
16
17
14
8
8
8
9
5
11
10
14
18
17
14
15
13
17
17
17
17
21
20
11
18
20
18
21
21
20
18
17
17
18
11
15
13
16
16
12
10
8
6
8
10
Dataseries Y:
Download CSV
Histogram 
29
34
34
30
21
23
18
27
20
25
24
23
18
22
22
18
19
18
22
22
20
14
15
14
19
23
23
17
21
17
24
18
17
18
16
15
21
17
11
13
11
13
13
14
18
13
16
13
15
20
17
18
17
20
18
18
21
19
17
20
19
24
21
21
16
18
17
16
11
14
11
20
22
18
17
18
15
19
18
15
16
17
12
16
14
18
17
10
18
16
13
13
13
13
5
8
5
4
4
1
6
4
5
4
11

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=17107&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=17107&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17107&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
Mean16.638095238095216.8190476190476
Biased Variance57.754739229024935.1386848072562
Biased Standard Deviation7.599653888765265.9277892006427
Covariance28.3569597069597
Correlation0.623472268883649
Determination0.388717670066925
T-Test8.09309862402834
p-value (2 sided)1.21569421196455e-12
p-value (1 sided)6.07847105982273e-13
Degrees of Freedom103
Number of Observations105

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 16.6380952380952 & 16.8190476190476 \tabularnewline
Biased Variance & 57.7547392290249 & 35.1386848072562 \tabularnewline
Biased Standard Deviation & 7.59965388876526 & 5.9277892006427 \tabularnewline
Covariance & 28.3569597069597 \tabularnewline
Correlation & 0.623472268883649 \tabularnewline
Determination & 0.388717670066925 \tabularnewline
T-Test & 8.09309862402834 \tabularnewline
p-value (2 sided) & 1.21569421196455e-12 \tabularnewline
p-value (1 sided) & 6.07847105982273e-13 \tabularnewline
Degrees of Freedom & 103 \tabularnewline
Number of Observations & 105 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17107&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]16.6380952380952[/C][C]16.8190476190476[/C][/ROW]
[ROW][C]Biased Variance[/C][C]57.7547392290249[/C][C]35.1386848072562[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]7.59965388876526[/C][C]5.9277892006427[/C][/ROW]
[ROW][C]Covariance[/C][C]28.3569597069597[/C][/ROW]
[ROW][C]Correlation[/C][C]0.623472268883649[/C][/ROW]
[ROW][C]Determination[/C][C]0.388717670066925[/C][/ROW]
[ROW][C]T-Test[/C][C]8.09309862402834[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.21569421196455e-12[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]6.07847105982273e-13[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]103[/C][/ROW]
[ROW][C]Number of Observations[/C][C]105[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17107&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17107&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
Mean16.638095238095216.8190476190476
Biased Variance57.754739229024935.1386848072562
Biased Standard Deviation7.599653888765265.9277892006427
Covariance28.3569597069597
Correlation0.623472268883649
Determination0.388717670066925
T-Test8.09309862402834
p-value (2 sided)1.21569421196455e-12
p-value (1 sided)6.07847105982273e-13
Degrees of Freedom103
Number of Observations105


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')