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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 13:54:49 -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/t1224532560vnqouqntp4nd5rr.htm/, Retrieved Sun, 19 May 2024 14:43:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18019, Retrieved Sun, 19 May 2024 14:43:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126

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] [Reeks 1 productie...] [2008-10-20 19:54:49] [4b953869c7238aca4b6e0cfb0c5cddd6] [Current]
Feedback Forum
2008-10-22 17:26:22 [Romina Machiels] [reply] 
Q10 werd volledig juist beantwoord. Er mocht telkens wel wat meer uitleg zijn waarom de correlatie zo is, wat de reden hiervoor is. Nu is weten we wel of ze sterk of zwak geassociëerd zijn maar we weten niet echt de reden.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97.4
97
105.4
102.7
98.1
104.5
87.4
89.9
109.8
111.7
98.6
96.9
95.1
97
112.7
102.9
97.4
111.4
87.4
96.8
114.1
110.3
103.9
101.6
94.6
95.9
104.7
102.8
98.1
113.9
80.9
95.7
113.2
105.9
108.8
102.3
99
100.7
115.5
100.7
109.9
114.6
85.4
100.5
114.8
116.5
112.9
102
106
105.3
118.8
106.1
109.3
117.2
92.5
104.2
112.5
122.4
113.3
100
110.7
112.8
109.8
117.3
109.1
115.9
95.7
Dataseries Y:
Download CSV
Histogram 
104,2
103,2
112,7
106,4
102,6
110,6
95,2
89
112,5
116,8
107,2
113,6
101,8
102,6
122,7
110,3
110,5
121,6
100,3
100,7
123,4
127,1
124,1
131,2
111,6
114,2
130,1
125,9
119
133,8
107,5
113,5
134,4
126,8
135,6
139,9
129,8
131
153,1
134,1
144,1
155,9
123,3
128,1
144,3
153
149,9
150,9
141
138,9
157,4
142,9
151,7
161
138,5
135,9
151,5
164
159,1
157
142,1
144,8
152,1
154,6
148,7
157,7
146,7

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=18019&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=18019&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18019&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
Mean104.450746268657129.637313432836
Biased Variance78.136827801292376.206816662954
Biased Standard Deviation8.8395038209897319.3960515740435
Covariance121.927623247399
Correlation0.7005352976756
Determination0.490749703289442
T-Test7.91445575968875
p-value (2 sided)4.14150935768021e-11
p-value (1 sided)2.07075467884010e-11
Degrees of Freedom65
Number of Observations67

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 104.450746268657 & 129.637313432836 \tabularnewline
Biased Variance & 78.136827801292 & 376.206816662954 \tabularnewline
Biased Standard Deviation & 8.83950382098973 & 19.3960515740435 \tabularnewline
Covariance & 121.927623247399 \tabularnewline
Correlation & 0.7005352976756 \tabularnewline
Determination & 0.490749703289442 \tabularnewline
T-Test & 7.91445575968875 \tabularnewline
p-value (2 sided) & 4.14150935768021e-11 \tabularnewline
p-value (1 sided) & 2.07075467884010e-11 \tabularnewline
Degrees of Freedom & 65 \tabularnewline
Number of Observations & 67 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18019&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]104.450746268657[/C][C]129.637313432836[/C][/ROW]
[ROW][C]Biased Variance[/C][C]78.136827801292[/C][C]376.206816662954[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]8.83950382098973[/C][C]19.3960515740435[/C][/ROW]
[ROW][C]Covariance[/C][C]121.927623247399[/C][/ROW]
[ROW][C]Correlation[/C][C]0.7005352976756[/C][/ROW]
[ROW][C]Determination[/C][C]0.490749703289442[/C][/ROW]
[ROW][C]T-Test[/C][C]7.91445575968875[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]4.14150935768021e-11[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.07075467884010e-11[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]65[/C][/ROW]
[ROW][C]Number of Observations[/C][C]67[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18019&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18019&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
Mean104.450746268657129.637313432836
Biased Variance78.136827801292376.206816662954
Biased Standard Deviation8.8395038209897319.3960515740435
Covariance121.927623247399
Correlation0.7005352976756
Determination0.490749703289442
T-Test7.91445575968875
p-value (2 sided)4.14150935768021e-11
p-value (1 sided)2.07075467884010e-11
Degrees of Freedom65
Number of Observations67


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')