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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 16:03:17 -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/21/t1224540484orx6sxxb9lk4sz3.htm/, Retrieved Fri, 17 May 2024 05:03:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18236, Retrieved Fri, 17 May 2024 05:03:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185

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 22:08:56] [8cd6641b921d30ebe00b648d1481bba0]
F    D    [Pearson Correlation] [Pearson België me...] [2008-10-20 22:03:17] [d6e9f26c3644bfc30f06303d9993b878] [Current]
Feedback Forum
2008-10-27 18:04:14 [Evelien Blockx] [reply] 
Ook hier zie je 2 outliers (in de rechterbovenhoek van de grafiek). Deze kunnen ervoor zorgen dat je grafiek helemaal anders wordt. Bovendien is de correlatie hier negatief, dat wil niet zeggen dat er helemaal geen verband is. Een negatieve correlatie duidt op een negatief verband. Als het ene daalt, zal het andere stijgen.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
116.1
102.5
102.0
101.3
100.6
100.9
104.2
108.3
108.9
109.9
106.8
112.7
113.4
101.3
97.8
95.0
93.8
94.5
101.4
105.8
106.6
109.7
108.8
113.4
113.7
103.6
98.2
95.5
94.4
95.9
103.2
104.1
127.6
130.3
133.0
140.4
123.5
116.9
115.9
113.1
112.1
112.4
118.9
117.4
115.6
120.7
114.9
122.0
119.6
114.6
118.4
110.9
111.6
114.6
112.1
117.4
114.8
123.4
118.1
121.9
123.3
Dataseries Y:
Download CSV
Histogram 
100.3
97.6
89.1
99.1
94.9
96.5
92.6
80.8
89.5
101.4
95.9
92.3
91.2
88.3
80.7
89.9
87.2
86.9
82.8
72.6
81.3
91.2
87.3
83.4
81.7
80.2
74.1
80.6
79.0
79.3
71.2
78.1
68.2
81.0
106.9
123.7
73.7
69.2
72.5
75.7
73.5
70.4
65.7
68.1
62.4
64.7
77.7
85.9
61.0
57.4
75.1
75.9
71.8
72.3
67.3
71.5
67.6
74.2
77.6
76.4
74.2

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=18236&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=18236&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18236&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
Mean111.14262295082080.960655737705
Biased Variance100.802117710293148.657796291320
Biased Standard Deviation10.04002578235212.1925303481812
Covariance-10.2897950819672
Correlation-0.0826798096433685
Determination0.00683595092266365
T-Test-0.637257534066917
p-value (2 sided)0.526422322328302
p-value (1 sided)0.263211161164151
Degrees of Freedom59
Number of Observations61

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 111.142622950820 & 80.960655737705 \tabularnewline
Biased Variance & 100.802117710293 & 148.657796291320 \tabularnewline
Biased Standard Deviation & 10.040025782352 & 12.1925303481812 \tabularnewline
Covariance & -10.2897950819672 \tabularnewline
Correlation & -0.0826798096433685 \tabularnewline
Determination & 0.00683595092266365 \tabularnewline
T-Test & -0.637257534066917 \tabularnewline
p-value (2 sided) & 0.526422322328302 \tabularnewline
p-value (1 sided) & 0.263211161164151 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18236&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]111.142622950820[/C][C]80.960655737705[/C][/ROW]
[ROW][C]Biased Variance[/C][C]100.802117710293[/C][C]148.657796291320[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]10.040025782352[/C][C]12.1925303481812[/C][/ROW]
[ROW][C]Covariance[/C][C]-10.2897950819672[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.0826798096433685[/C][/ROW]
[ROW][C]Determination[/C][C]0.00683595092266365[/C][/ROW]
[ROW][C]T-Test[/C][C]-0.637257534066917[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.526422322328302[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.263211161164151[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]59[/C][/ROW]
[ROW][C]Number of Observations[/C][C]61[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18236&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18236&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
Mean111.14262295082080.960655737705
Biased Variance100.802117710293148.657796291320
Biased Standard Deviation10.04002578235212.1925303481812
Covariance-10.2897950819672
Correlation-0.0826798096433685
Determination0.00683595092266365
T-Test-0.637257534066917
p-value (2 sided)0.526422322328302
p-value (1 sided)0.263211161164151
Degrees of Freedom59
Number of Observations61


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')