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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 computationWed, 03 Dec 2008 09:33:26 -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/03/t122832234354g391mxhk9ssk5.htm/, Retrieved Tue, 21 May 2024 05:12:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28778, Retrieved Tue, 21 May 2024 05:12:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Standard Deviation-Mean Plot] [SMP] [2008-12-03 16:33:26] [21d7d81e7693ad6dde5aadefb1046611] [Current]
Feedback Forum
2008-12-14 21:08:03 [Bob Leysen] [reply] 
Op de horizontale as nemen we de gemiddelde waarde weer (mean), op de verticale as noteren we de standaard fout (standard deviation).

Er kan geen duidelijk verband worden waargenomen tussen de 2 variabelen, nl de gemiddelde waarde en standaardfout.

Als we 1 in vermindering brengen met de Beta waarde resulteert dit in de optimale Lamba Coëfficiënt.

We bekomen dus een optimale variantie wanneer zich een transformatie voordoet met 0,4753. Deze transformatie wordt enkel uitgevoerd wanneer zich een verband voordoet tussen standaardfout en gemiddelde waarde. Er werd reeds besloten dat hier géén verband aanwezig is en nemen bijgevolg 0 als Lamba Coëfficiënt.

De p-value heeft betrekking op bètacoëfficiënt. De bètacoëfficiënt van regressierechte is significant verschillend van nul dus bèta is ook de helling van regressierechte die door scatterplot gaat.
2008-12-15 08:41:12 [Davy De Nef] [reply] 
In stap 1 van de opdracht dient er gebruik gemaakt te worden van de Standard Deviation Mean Plot.
Deze zal onze lambda waarde berekenen. In dit geval is die 0,47.
Om deze later toe te passen op de tijdreeks zal deze afgerond worden naar 0,5.

In de grafieken zien we niet echt een overeenkomst tussen de standaardfout en het gemiddelde.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
206010
198112
194519
185705
180173
176142
203401
221902
197378
185001
176356
180449
180144
173666
165688
161570
156145
153730
182698
200765
176512
166618
158644
159585
163095
159044
155511
153745
150569
150605
179612
194690
189917
184128
175335
179566
181140
177876
175041
169292
166070
166972
206348
215706
202108
195411
193111
195198
198770
194163
190420
189733
186029
191531
232571
243477
227247
217859
208679
213188
216234
213586
209465
204045
200237
203666
241476
260307
243324
244460
233575
237217
235243
230354
227184
221678
217142
219452
256446
265845
248624
241114
229245
231805
219277
219313
212610
214771
211142
211457
240048
240636
230580
208795
197922
194596
194581
185686
178106
172608
167302
168053
202300
202388
182516
173476
166444
171297
169701
164182
161914
159612
151001
158114
186530
187069
174330
169362

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'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28778&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28778&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28778&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1192095.66666666713983.870333893745760
2169647.08333333313685.351548002947035
3169651.41666666715989.727574337144121
4187022.7516556.473724937549636
5207805.58333333319141.267249101257448
6225632.66666666720014.544794557160070
7235344.33333333315066.829764469948703
8216762.2514480.885445837046040
9180396.41666666713184.570999731835944

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 192095.666666667 & 13983.8703338937 & 45760 \tabularnewline
2 & 169647.083333333 & 13685.3515480029 & 47035 \tabularnewline
3 & 169651.416666667 & 15989.7275743371 & 44121 \tabularnewline
4 & 187022.75 & 16556.4737249375 & 49636 \tabularnewline
5 & 207805.583333333 & 19141.2672491012 & 57448 \tabularnewline
6 & 225632.666666667 & 20014.5447945571 & 60070 \tabularnewline
7 & 235344.333333333 & 15066.8297644699 & 48703 \tabularnewline
8 & 216762.25 & 14480.8854458370 & 46040 \tabularnewline
9 & 180396.416666667 & 13184.5709997318 & 35944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28778&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]192095.666666667[/C][C]13983.8703338937[/C][C]45760[/C][/ROW]
[ROW][C]2[/C][C]169647.083333333[/C][C]13685.3515480029[/C][C]47035[/C][/ROW]
[ROW][C]3[/C][C]169651.416666667[/C][C]15989.7275743371[/C][C]44121[/C][/ROW]
[ROW][C]4[/C][C]187022.75[/C][C]16556.4737249375[/C][C]49636[/C][/ROW]
[ROW][C]5[/C][C]207805.583333333[/C][C]19141.2672491012[/C][C]57448[/C][/ROW]
[ROW][C]6[/C][C]225632.666666667[/C][C]20014.5447945571[/C][C]60070[/C][/ROW]
[ROW][C]7[/C][C]235344.333333333[/C][C]15066.8297644699[/C][C]48703[/C][/ROW]
[ROW][C]8[/C][C]216762.25[/C][C]14480.8854458370[/C][C]46040[/C][/ROW]
[ROW][C]9[/C][C]180396.416666667[/C][C]13184.5709997318[/C][C]35944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28778&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28778&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
1192095.66666666713983.870333893745760
2169647.08333333313685.351548002947035
3169651.41666666715989.727574337144121
4187022.7516556.473724937549636
5207805.58333333319141.267249101257448
6225632.66666666720014.544794557160070
7235344.33333333315066.829764469948703
8216762.2514480.885445837046040
9180396.41666666713184.570999731835944






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha7307.20469515521
beta0.0427821502456978
S.D.0.0340001443445573
T-STAT1.25829319464482
p-value0.248629400194165

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 7307.20469515521 \tabularnewline
beta & 0.0427821502456978 \tabularnewline
S.D. & 0.0340001443445573 \tabularnewline
T-STAT & 1.25829319464482 \tabularnewline
p-value & 0.248629400194165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28778&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7307.20469515521[/C][/ROW]
[ROW][C]beta[/C][C]0.0427821502456978[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0340001443445573[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.25829319464482[/C][/ROW]
[ROW][C]p-value[/C][C]0.248629400194165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28778&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28778&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)
alpha7307.20469515521
beta0.0427821502456978
S.D.0.0340001443445573
T-STAT1.25829319464482
p-value0.248629400194165






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.26164105218474
beta0.524628428574278
S.D.0.411712026132303
T-STAT1.27426063674344
p-value0.243241490834325
Lambda0.475371571425722

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.26164105218474 \tabularnewline
beta & 0.524628428574278 \tabularnewline
S.D. & 0.411712026132303 \tabularnewline
T-STAT & 1.27426063674344 \tabularnewline
p-value & 0.243241490834325 \tabularnewline
Lambda & 0.475371571425722 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28778&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.26164105218474[/C][/ROW]
[ROW][C]beta[/C][C]0.524628428574278[/C][/ROW]
[ROW][C]S.D.[/C][C]0.411712026132303[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.27426063674344[/C][/ROW]
[ROW][C]p-value[/C][C]0.243241490834325[/C][/ROW]
[ROW][C]Lambda[/C][C]0.475371571425722[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28778&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28778&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)
alpha3.26164105218474
beta0.524628428574278
S.D.0.411712026132303
T-STAT1.27426063674344
p-value0.243241490834325
Lambda0.475371571425722


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')