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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationMon, 14 Apr 2014 15:56:41 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Apr/14/t13975054608ns83bv4qatx587.htm/, Retrieved Fri, 17 May 2024 04:59:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234448, Retrieved Fri, 17 May 2024 04:59:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact194

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
41
44
44
33
33
33
33
36
36
44
44
38
38
42
42
41
41
40
40
38
38
40
40
53
53
52
52
51
51
51
51
53
53
53
53
46
46
41
41
56
56
54
54
Dataseries Y:
Download CSV
Histogram 
10.7
9.4
9.8
15.1
13.5
13.9
13.1
12.5
12.9
15.1
18.1
20.1
16.6
15.1
14.6
13.8
12.7
11.1
10.9
12.5
14.1
13.7
12.4
9.7
10.6
10.5
9.2
8.0
7.4
8.3
10.5
10.3
10.3
10.5
9.5
8.4
9.2
13.7
16.9
15.8
14.1
13.2
12.4

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'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234448&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234448&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234448&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'Gertrude Mary Cox' @ cox.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean44.627906976744212.3302325581395
Biased Variance50.28015143320717.9681557598702
Biased Standard Deviation7.090849838574162.82279219211585
Covariance-9.22895902547065
Correlation-0.450356418418547
Determination0.202820903610781
T-Test-3.22976061247517
p-value (2 sided)0.00244244940636218
p-value (1 sided)0.00122122470318109
Degrees of Freedom41
Number of Observations43

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 44.6279069767442 & 12.3302325581395 \tabularnewline
Biased Variance & 50.2801514332071 & 7.9681557598702 \tabularnewline
Biased Standard Deviation & 7.09084983857416 & 2.82279219211585 \tabularnewline
Covariance & -9.22895902547065 \tabularnewline
Correlation & -0.450356418418547 \tabularnewline
Determination & 0.202820903610781 \tabularnewline
T-Test & -3.22976061247517 \tabularnewline
p-value (2 sided) & 0.00244244940636218 \tabularnewline
p-value (1 sided) & 0.00122122470318109 \tabularnewline
Degrees of Freedom & 41 \tabularnewline
Number of Observations & 43 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234448&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]44.6279069767442[/C][C]12.3302325581395[/C][/ROW]
[ROW][C]Biased Variance[/C][C]50.2801514332071[/C][C]7.9681557598702[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]7.09084983857416[/C][C]2.82279219211585[/C][/ROW]
[ROW][C]Covariance[/C][C]-9.22895902547065[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.450356418418547[/C][/ROW]
[ROW][C]Determination[/C][C]0.202820903610781[/C][/ROW]
[ROW][C]T-Test[/C][C]-3.22976061247517[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00244244940636218[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00122122470318109[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]41[/C][/ROW]
[ROW][C]Number of Observations[/C][C]43[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234448&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234448&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
Mean44.627906976744212.3302325581395
Biased Variance50.28015143320717.9681557598702
Biased Standard Deviation7.090849838574162.82279219211585
Covariance-9.22895902547065
Correlation-0.450356418418547
Determination0.202820903610781
T-Test-3.22976061247517
p-value (2 sided)0.00244244940636218
p-value (1 sided)0.00122122470318109
Degrees of Freedom41
Number of Observations43


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
x <- x[!is.na(y)]
y <- y[!is.na(y)]
y <- y[!is.na(x)]
x <- x[!is.na(x)]
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', na.rm = T)
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')