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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 computationSun, 21 Dec 2008 08:40:31 -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/Dec/21/t1229874146s79t183a46xfhx2.htm/, Retrieved Sun, 19 May 2024 08:47:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35635, Retrieved Sun, 19 May 2024 08:47:32 +0000
QR Codes:

Original text written by user:2000-2007
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Paper - Correlation] [2008-12-21 15:40:31] [821c4b3d195be8e737cf8c9dc649d3cf] [Current]
- RMP     [Bivariate Kernel Density Estimation] [Paper - Density plot] [2008-12-21 15:59:20] [3a9fc6d5b5e0e816787b7dbace57e7cd]
-    D    [Pearson Correlation] [Paper - Correlation] [2008-12-21 16:04:50] [3a9fc6d5b5e0e816787b7dbace57e7cd]
- RMP       [Bivariate Kernel Density Estimation] [Paper - Density plot] [2008-12-21 16:07:53] [3a9fc6d5b5e0e816787b7dbace57e7cd]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
31.58
27.88
27.32
28.89
28.05
28.73
32.00
34.53
33.47
34.09
35.47
34.59
34.32
32.78
28.38
29.18
28.62
28.20
29.33
29.72
26.29
26.82
27.64
27.10
27.05
26.02
25.76
25.94
24.97
21.74
18.16
16.95
16.46
16.44
18.20
16.44
15.70
13.94
12.23
14.75
14.62
15.04
15.50
16.10
15.44
15.14
15.42
15.69
17.57
18.42
17.96
18.39
17.63
17.95
17.79
17.73
18.99
19.83
20.23
20.24
21.12
21.25
21.80
21.84
22.21
22.64
23.54
23.78
23.65
23.93
24.77
26.26
27.69
29.54
29.31
29.26
28.69
26.16
27.12
29.40
30.99
32.96
32.20
31.67
32.49
33.66
32.44
34.38
32.36
30.73
30.31
27.26
25.05
22.33
18.26
18.30
Dataseries Y:
Download CSV
Histogram 
3030.29
2803.47
2767.63
2882.6
2863.36
2897.06
3012.61
3142.95
3032.93
3045.78
3110.52
3013.24
2987.1
2995.55
2833.18
2848.96
2794.83
2845.26
2915.02
2892.63
2604.42
2641.65
2659.81
2638.53
2720.25
2745.88
2735.7
2811.7
2799.43
2555.28
2304.98
2214.95
2065.81
1940.49
2042
1995.37
1946.81
1765.9
1635.25
1833.42
1910.43
1959.67
1969.6
2061.41
2093.48
2120.88
2174.56
2196.72
2350.44
2440.25
2408.64
2472.81
2407.6
2454.62
2448.05
2497.84
2645.64
2756.76
2849.27
2921.44
2981.85
3080.58
3106.22
3119.31
3061.26
3097.31
3161.69
3257.16
3277.01
3295.32
3363.99
3494.17
3667.03
3813.06
3917.96
3895.51
3801.06
3570.12
3701.61
3862.27
3970.1
4138.52
4199.75
4290.89
4443.91
4502.64
4356.98
4591.27
4696.96
4621.4
4562.84
4202.52
4296.49
4435.23
4105.18
4116.68

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=35635&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=35635&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35635&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
Mean24.48708333333333026.75583333333
Biased Variance39.6756373263889597362.634299306
Biased Standard Deviation6.29886000212649772.892382094238
Covariance3334.73660877193
Correlation0.677848948763485
Determination0.459479197339762
T-Test8.93903519424997
p-value (2 sided)3.30846461338297e-14
p-value (1 sided)1.65423230669148e-14
Degrees of Freedom94
Number of Observations96

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 24.4870833333333 & 3026.75583333333 \tabularnewline
Biased Variance & 39.6756373263889 & 597362.634299306 \tabularnewline
Biased Standard Deviation & 6.29886000212649 & 772.892382094238 \tabularnewline
Covariance & 3334.73660877193 \tabularnewline
Correlation & 0.677848948763485 \tabularnewline
Determination & 0.459479197339762 \tabularnewline
T-Test & 8.93903519424997 \tabularnewline
p-value (2 sided) & 3.30846461338297e-14 \tabularnewline
p-value (1 sided) & 1.65423230669148e-14 \tabularnewline
Degrees of Freedom & 94 \tabularnewline
Number of Observations & 96 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35635&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]24.4870833333333[/C][C]3026.75583333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]39.6756373263889[/C][C]597362.634299306[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]6.29886000212649[/C][C]772.892382094238[/C][/ROW]
[ROW][C]Covariance[/C][C]3334.73660877193[/C][/ROW]
[ROW][C]Correlation[/C][C]0.677848948763485[/C][/ROW]
[ROW][C]Determination[/C][C]0.459479197339762[/C][/ROW]
[ROW][C]T-Test[/C][C]8.93903519424997[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]3.30846461338297e-14[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.65423230669148e-14[/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=35635&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35635&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
Mean24.48708333333333026.75583333333
Biased Variance39.6756373263889597362.634299306
Biased Standard Deviation6.29886000212649772.892382094238
Covariance3334.73660877193
Correlation0.677848948763485
Determination0.459479197339762
T-Test8.93903519424997
p-value (2 sided)3.30846461338297e-14
p-value (1 sided)1.65423230669148e-14
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')