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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationThu, 04 Dec 2008 04:35:12 -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/04/t1228390584k1ehot8a5m77053.htm/, Retrieved Sun, 19 May 2024 05:35:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28916, Retrieved Sun, 19 May 2024 05:35:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact233

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- RMPD  [Standard Deviation-Mean Plot] [blok 17 Q5 standa...] [2008-12-02 20:05:22] [6173c35e31b784a490c8cd5476f785d4]
-    D    [Standard Deviation-Mean Plot] [blok 17 Q8 standa...] [2008-12-04 11:29:25] [6173c35e31b784a490c8cd5476f785d4]
-    D        [Standard Deviation-Mean Plot] [blok 17 Q8 standa...] [2008-12-04 11:35:12] [1237f4df7e9be807e4c0a07b90c45721] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
98,1
101,1
111,1
93,3
100
108
70,4
75,4
105,5
112,3
102,5
93,5
86,7
95,2
103,8
97
95,5
101
67,5
64
106,7
100,6
101,2
93,1
84,2
85,8
91,8
92,4
80,3
79,7
62,5
57,1
100,8
100,7
86,2
83,2
71,7
77,5
89,8
80,3
78,7
93,8
57,6
60,6
91
85,3
77,4
77,3
68,3
69,9
81,7
75,1
69,9
84
54,3
60
89,9
77
85,3
77,6
69,2
75,5
85,7
72,2
79,9
85,3
52,2
61,2
82,4
85,4
78,2
70,2

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28916&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28916&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28916&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
197.613.070299433170141.9
292.691666666666713.652269763558442.7
383.72513.206136658938043.7
478.416666666666711.178618660260136.2
574.416666666666710.492753632287335.6
674.783333333333310.410818964670933.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 97.6 & 13.0702994331701 & 41.9 \tabularnewline
2 & 92.6916666666667 & 13.6522697635584 & 42.7 \tabularnewline
3 & 83.725 & 13.2061366589380 & 43.7 \tabularnewline
4 & 78.4166666666667 & 11.1786186602601 & 36.2 \tabularnewline
5 & 74.4166666666667 & 10.4927536322873 & 35.6 \tabularnewline
6 & 74.7833333333333 & 10.4108189646709 & 33.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28916&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]97.6[/C][C]13.0702994331701[/C][C]41.9[/C][/ROW]
[ROW][C]2[/C][C]92.6916666666667[/C][C]13.6522697635584[/C][C]42.7[/C][/ROW]
[ROW][C]3[/C][C]83.725[/C][C]13.2061366589380[/C][C]43.7[/C][/ROW]
[ROW][C]4[/C][C]78.4166666666667[/C][C]11.1786186602601[/C][C]36.2[/C][/ROW]
[ROW][C]5[/C][C]74.4166666666667[/C][C]10.4927536322873[/C][C]35.6[/C][/ROW]
[ROW][C]6[/C][C]74.7833333333333[/C][C]10.4108189646709[/C][C]33.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28916&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28916&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:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
197.613.070299433170141.9
292.691666666666713.652269763558442.7
383.72513.206136658938043.7
478.416666666666711.178618660260136.2
574.416666666666710.492753632287335.6
674.783333333333310.410818964670933.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.868825210969511
beta0.133160899422688
S.D.0.0366375074470808
T-STAT3.63455127549344
p-value0.0220707773297733

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.868825210969511 \tabularnewline
beta & 0.133160899422688 \tabularnewline
S.D. & 0.0366375074470808 \tabularnewline
T-STAT & 3.63455127549344 \tabularnewline
p-value & 0.0220707773297733 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28916&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.868825210969511[/C][/ROW]
[ROW][C]beta[/C][C]0.133160899422688[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0366375074470808[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.63455127549344[/C][/ROW]
[ROW][C]p-value[/C][C]0.0220707773297733[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28916&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28916&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.868825210969511
beta0.133160899422688
S.D.0.0366375074470808
T-STAT3.63455127549344
p-value0.0220707773297733






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.80223226781713
beta0.96840038504481
S.D.0.245895750823956
T-STAT3.93825587388094
p-value0.0169846656626195
Lambda0.0315996149551903

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.80223226781713 \tabularnewline
beta & 0.96840038504481 \tabularnewline
S.D. & 0.245895750823956 \tabularnewline
T-STAT & 3.93825587388094 \tabularnewline
p-value & 0.0169846656626195 \tabularnewline
Lambda & 0.0315996149551903 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28916&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.80223226781713[/C][/ROW]
[ROW][C]beta[/C][C]0.96840038504481[/C][/ROW]
[ROW][C]S.D.[/C][C]0.245895750823956[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.93825587388094[/C][/ROW]
[ROW][C]p-value[/C][C]0.0169846656626195[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0315996149551903[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28916&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28916&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.80223226781713
beta0.96840038504481
S.D.0.245895750823956
T-STAT3.93825587388094
p-value0.0169846656626195
Lambda0.0315996149551903


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')