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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationFri, 02 Jul 2010 13:00:21 +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/Jul/02/t12780756508gfy4l66ss26dth.htm/, Retrieved Sat, 04 May 2024 00:59:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77917, Retrieved Sat, 04 May 2024 00:59:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSteffi poppe
Estimated Impact193

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [Tijdreeks2-Stap21] [2010-07-02 13:00:21] [b37bab310ab56201887748d7a7c0dc58] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
59
58
57
55
53
52
53
55
56
56
57
59
68
68
68
70
66
64
72
80
84
82
83
86
99
100
95
98
103
107
114
123
132
137
141
146
156
156
143
143
151
149
156
166
177
180
189
195
205
209
199
191
198
200
208
224
234
243
249
258
274
270
261
258
261
258
264
270
267
287
297
306
322
323
309
303
306
301
316
327
330
342
359
379

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'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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77917&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77917&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77917&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
155.83333333333332.329000305762637
274.258.069302098920122
3116.2518.669980766411751
4163.41666666666717.783845239856152
5218.16666666666722.646827324788567
6272.7515.766045218068548
7326.41666666666723.619938932002278

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 55.8333333333333 & 2.32900030576263 & 7 \tabularnewline
2 & 74.25 & 8.0693020989201 & 22 \tabularnewline
3 & 116.25 & 18.6699807664117 & 51 \tabularnewline
4 & 163.416666666667 & 17.7838452398561 & 52 \tabularnewline
5 & 218.166666666667 & 22.6468273247885 & 67 \tabularnewline
6 & 272.75 & 15.7660452180685 & 48 \tabularnewline
7 & 326.416666666667 & 23.6199389320022 & 78 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77917&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]55.8333333333333[/C][C]2.32900030576263[/C][C]7[/C][/ROW]
[ROW][C]2[/C][C]74.25[/C][C]8.0693020989201[/C][C]22[/C][/ROW]
[ROW][C]3[/C][C]116.25[/C][C]18.6699807664117[/C][C]51[/C][/ROW]
[ROW][C]4[/C][C]163.416666666667[/C][C]17.7838452398561[/C][C]52[/C][/ROW]
[ROW][C]5[/C][C]218.166666666667[/C][C]22.6468273247885[/C][C]67[/C][/ROW]
[ROW][C]6[/C][C]272.75[/C][C]15.7660452180685[/C][C]48[/C][/ROW]
[ROW][C]7[/C][C]326.416666666667[/C][C]23.6199389320022[/C][C]78[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77917&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77917&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
155.83333333333332.329000305762637
274.258.069302098920122
3116.2518.669980766411751
4163.41666666666717.783845239856152
5218.16666666666722.646827324788567
6272.7515.766045218068548
7326.41666666666723.619938932002278






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.22718095901466
beta0.0589158626874354
S.D.0.0215657309018118
T-STAT2.73192051573293
p-value0.0411860138019013

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.22718095901466 \tabularnewline
beta & 0.0589158626874354 \tabularnewline
S.D. & 0.0215657309018118 \tabularnewline
T-STAT & 2.73192051573293 \tabularnewline
p-value & 0.0411860138019013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77917&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.22718095901466[/C][/ROW]
[ROW][C]beta[/C][C]0.0589158626874354[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0215657309018118[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.73192051573293[/C][/ROW]
[ROW][C]p-value[/C][C]0.0411860138019013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77917&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77917&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)
alpha5.22718095901466
beta0.0589158626874354
S.D.0.0215657309018118
T-STAT2.73192051573293
p-value0.0411860138019013






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.66267946139586
beta1.04157422282893
S.D.0.306533158356858
T-STAT3.39791697711332
p-value0.019294629309798
Lambda-0.0415742228289322

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.66267946139586 \tabularnewline
beta & 1.04157422282893 \tabularnewline
S.D. & 0.306533158356858 \tabularnewline
T-STAT & 3.39791697711332 \tabularnewline
p-value & 0.019294629309798 \tabularnewline
Lambda & -0.0415742228289322 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77917&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.66267946139586[/C][/ROW]
[ROW][C]beta[/C][C]1.04157422282893[/C][/ROW]
[ROW][C]S.D.[/C][C]0.306533158356858[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.39791697711332[/C][/ROW]
[ROW][C]p-value[/C][C]0.019294629309798[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0415742228289322[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77917&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77917&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-2.66267946139586
beta1.04157422282893
S.D.0.306533158356858
T-STAT3.39791697711332
p-value0.019294629309798
Lambda-0.0415742228289322


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')