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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 computationThu, 06 Nov 2008 06:05:34 -0700
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/Nov/06/t122597686947ztjm2zic0kctv.htm/, Retrieved Thu, 31 Jul 2025 10:41:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=22105, Retrieved Thu, 31 Jul 2025 10:41:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact234

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] [Q3 Clothing produ...] [2007-10-20 14:22:11] [b731da8b544846036771bbf9bf2f34ce]
-    D  [Pearson Correlation] [correlatie RNR & ...] [2008-11-06 12:46:25] [5262baed313b307078ce11eb68e9efe6]
-    D    [Pearson Correlation] [correlatie RNR & RCF] [2008-11-06 12:51:16] [5262baed313b307078ce11eb68e9efe6]
-    D        [Pearson Correlation] [correlatie RNR & ...] [2008-11-06 13:05:34] [5bd06487453d0eec7a1bf04bf9f25085] [Current]
-    D          [Pearson Correlation] [correlatie RNR & ...] [2008-11-06 13:09:22] [5262baed313b307078ce11eb68e9efe6]
- RM D          [Star Plot] [Q2: Starplot] [2008-11-06 15:09:04] [5262baed313b307078ce11eb68e9efe6]
- RM D            [Notched Boxplots] [Q3: Taak 2] [2008-11-06 17:15:12] [5262baed313b307078ce11eb68e9efe6]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4,8
-4,2
1,6
5,2
9,2
4,6
10,6
Dataseries Y:
Download CSV
Histogram 
20.8
17.1
22.3
25.1
27.7
24.9
29.5

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'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 & 2 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=22105&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22105&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22105&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean4.5428571428571423.9142857142857
Biased Variance20.568163265306115.2355102040816
Biased Standard Deviation4.535213695660453.90326916879705
Covariance19.3042857142857
Correlation0.934718181651295
Determination0.873698079109504
T-Test5.88112912470809
p-value (2 sided)0.00201871267116260
p-value (1 sided)0.00100935633558130
Degrees of Freedom5
Number of Observations7

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 4.54285714285714 & 23.9142857142857 \tabularnewline
Biased Variance & 20.5681632653061 & 15.2355102040816 \tabularnewline
Biased Standard Deviation & 4.53521369566045 & 3.90326916879705 \tabularnewline
Covariance & 19.3042857142857 \tabularnewline
Correlation & 0.934718181651295 \tabularnewline
Determination & 0.873698079109504 \tabularnewline
T-Test & 5.88112912470809 \tabularnewline
p-value (2 sided) & 0.00201871267116260 \tabularnewline
p-value (1 sided) & 0.00100935633558130 \tabularnewline
Degrees of Freedom & 5 \tabularnewline
Number of Observations & 7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22105&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]4.54285714285714[/C][C]23.9142857142857[/C][/ROW]
[ROW][C]Biased Variance[/C][C]20.5681632653061[/C][C]15.2355102040816[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.53521369566045[/C][C]3.90326916879705[/C][/ROW]
[ROW][C]Covariance[/C][C]19.3042857142857[/C][/ROW]
[ROW][C]Correlation[/C][C]0.934718181651295[/C][/ROW]
[ROW][C]Determination[/C][C]0.873698079109504[/C][/ROW]
[ROW][C]T-Test[/C][C]5.88112912470809[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00201871267116260[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00100935633558130[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]5[/C][/ROW]
[ROW][C]Number of Observations[/C][C]7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22105&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22105&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
Mean4.5428571428571423.9142857142857
Biased Variance20.568163265306115.2355102040816
Biased Standard Deviation4.535213695660453.90326916879705
Covariance19.3042857142857
Correlation0.934718181651295
Determination0.873698079109504
T-Test5.88112912470809
p-value (2 sided)0.00201871267116260
p-value (1 sided)0.00100935633558130
Degrees of Freedom5
Number of Observations7


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')