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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 computationWed, 08 Dec 2010 18:08:20 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/08/t1291831642oy1z16wtutrh6b2.htm/, Retrieved Fri, 03 May 2024 03:56:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107058, Retrieved Fri, 03 May 2024 03:56:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Voorspelling Fina...] [2010-12-08 18:08:20] [c6b3e187a4a1689d42fffda4bc860ab5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9.769
9.321
9.939
9.336
10.195
9.464
10.010
10.213
9.563
9.890
9.305
9.391
9.928
8.686
9.843
9.627
10.074
9.503
10.119
10.000
9.313
9.866
9.172
9.241
9.659
8.904
9.755
9.080
9.435
8.971
10.063
9.793
9.454
9.759
8.820
9.403
9.676
8.642
9.402
9.610
9.294
9.448
10.319
9.548
9.801
9.596
8.923
9.746
9.829
9.125
9.782
9.441
9.162
9.915
10.444
10.209
9.985
9.842
9.429
10.132
9.849
9.172
10.313
9.819
9.955
10.048
10.082
10.541
10.208
10.233
9.439
9.963
10.158
9.225
10.474
9.757
10.490
10.281
10.444
10.640
10.695
10.786
9.832
9.747
10.411
9.511
10.402
9.701
10.540
10.112
10.915
11.183
10.384
10.834
9.886
10.216
Dataseries Y:
Download CSV
Histogram 
-4
-8
-1
-2
-2
-1
1
2
2
-1
1
-1
-8
1
2
-2
-2
-2
-2
-6
-4
-5
-2
-1
-5
-9
-8
-14
-10
-11
-11
-11
-5
-2
-3
-6
-6
-7
-6
-2
-2
-4
0
-6
-4
-3
-1
-3
-6
-6
-15
-5
-11
-13
-10
-9
-11
-18
-13
-9
-8
-4
-3
-3
-3
-1
0
1
0
2
1
-1
-8
-18
-14
-4
0
4
4
3
3
7
8
13
15
14
14
10
16
13
15
13
12
13
11
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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107058&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107058&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107058&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean9.81677083333333-1.83333333333333
Biased Variance0.26028892664930558.8680555555556
Biased Standard Deviation0.5101851885828377.67255208881345
Covariance1.7371649122807
Correlation0.439162985926685
Determination0.192864128208041
T-Test4.73932325282986
p-value (2 sided)7.60053087534018e-06
p-value (1 sided)3.80026543767009e-06
Degrees of Freedom94
Number of Observations96

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 9.81677083333333 & -1.83333333333333 \tabularnewline
Biased Variance & 0.260288926649305 & 58.8680555555556 \tabularnewline
Biased Standard Deviation & 0.510185188582837 & 7.67255208881345 \tabularnewline
Covariance & 1.7371649122807 \tabularnewline
Correlation & 0.439162985926685 \tabularnewline
Determination & 0.192864128208041 \tabularnewline
T-Test & 4.73932325282986 \tabularnewline
p-value (2 sided) & 7.60053087534018e-06 \tabularnewline
p-value (1 sided) & 3.80026543767009e-06 \tabularnewline
Degrees of Freedom & 94 \tabularnewline
Number of Observations & 96 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107058&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]9.81677083333333[/C][C]-1.83333333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.260288926649305[/C][C]58.8680555555556[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.510185188582837[/C][C]7.67255208881345[/C][/ROW]
[ROW][C]Covariance[/C][C]1.7371649122807[/C][/ROW]
[ROW][C]Correlation[/C][C]0.439162985926685[/C][/ROW]
[ROW][C]Determination[/C][C]0.192864128208041[/C][/ROW]
[ROW][C]T-Test[/C][C]4.73932325282986[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]7.60053087534018e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]3.80026543767009e-06[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]94[/C][/ROW]
[ROW][C]Number of Observations[/C][C]96[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107058&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107058&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
Mean9.81677083333333-1.83333333333333
Biased Variance0.26028892664930558.8680555555556
Biased Standard Deviation0.5101851885828377.67255208881345
Covariance1.7371649122807
Correlation0.439162985926685
Determination0.192864128208041
T-Test4.73932325282986
p-value (2 sided)7.60053087534018e-06
p-value (1 sided)3.80026543767009e-06
Degrees of Freedom94
Number of Observations96


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')