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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 computationSat, 04 Dec 2010 11:39:39 +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/Dec/04/t1291462692uko3cpg406rptwl.htm/, Retrieved Sun, 05 May 2024 06:32:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105104, Retrieved Sun, 05 May 2024 06:32:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact148

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variability] [CORRECT! spreidin...] [2010-12-04 10:16:50] [4f0d7884a58460e5666de6340c9aadd9]
- RMPD    [Standard Deviation-Mean Plot] [Standard Deviatio...] [2010-12-04 11:39:39] [3ed99328c0a6512dc7383724785cc652] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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
166827
178037
186413
189226
191563
188906
186005
195309
223532
226899
214126
206903
204442
220375
214320
212588
205816
202196
195722
198563
229139
229527
211868

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105104&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105104&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105104&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1169647.08333333313685.351548002947035
2169651.41666666715989.727574337144121
3187022.7516556.473724937549636
4207805.58333333319141.267249101257448
5225632.66666666720014.544794557160070
6235344.33333333315066.829764469948703
7216762.2514480.885445837046040
8180396.41666666713184.570999731835944
9168889.91666666711090.917434454136068
10202808.2515307.616162165240894

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 169647.083333333 & 13685.3515480029 & 47035 \tabularnewline
2 & 169651.416666667 & 15989.7275743371 & 44121 \tabularnewline
3 & 187022.75 & 16556.4737249375 & 49636 \tabularnewline
4 & 207805.583333333 & 19141.2672491012 & 57448 \tabularnewline
5 & 225632.666666667 & 20014.5447945571 & 60070 \tabularnewline
6 & 235344.333333333 & 15066.8297644699 & 48703 \tabularnewline
7 & 216762.25 & 14480.8854458370 & 46040 \tabularnewline
8 & 180396.416666667 & 13184.5709997318 & 35944 \tabularnewline
9 & 168889.916666667 & 11090.9174344541 & 36068 \tabularnewline
10 & 202808.25 & 15307.6161621652 & 40894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105104&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]169647.083333333[/C][C]13685.3515480029[/C][C]47035[/C][/ROW]
[ROW][C]2[/C][C]169651.416666667[/C][C]15989.7275743371[/C][C]44121[/C][/ROW]
[ROW][C]3[/C][C]187022.75[/C][C]16556.4737249375[/C][C]49636[/C][/ROW]
[ROW][C]4[/C][C]207805.583333333[/C][C]19141.2672491012[/C][C]57448[/C][/ROW]
[ROW][C]5[/C][C]225632.666666667[/C][C]20014.5447945571[/C][C]60070[/C][/ROW]
[ROW][C]6[/C][C]235344.333333333[/C][C]15066.8297644699[/C][C]48703[/C][/ROW]
[ROW][C]7[/C][C]216762.25[/C][C]14480.8854458370[/C][C]46040[/C][/ROW]
[ROW][C]8[/C][C]180396.416666667[/C][C]13184.5709997318[/C][C]35944[/C][/ROW]
[ROW][C]9[/C][C]168889.916666667[/C][C]11090.9174344541[/C][C]36068[/C][/ROW]
[ROW][C]10[/C][C]202808.25[/C][C]15307.6161621652[/C][C]40894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105104&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105104&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
1169647.08333333313685.351548002947035
2169651.41666666715989.727574337144121
3187022.7516556.473724937549636
4207805.58333333319141.267249101257448
5225632.66666666720014.544794557160070
6235344.33333333315066.829764469948703
7216762.2514480.885445837046040
8180396.41666666713184.570999731835944
9168889.91666666711090.917434454136068
10202808.2515307.616162165240894






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4054.6560202956
beta0.0580315209102819
S.D.0.0323111383325112
T-STAT1.79602217393533
p-value0.110220968780478

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4054.6560202956 \tabularnewline
beta & 0.0580315209102819 \tabularnewline
S.D. & 0.0323111383325112 \tabularnewline
T-STAT & 1.79602217393533 \tabularnewline
p-value & 0.110220968780478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105104&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4054.6560202956[/C][/ROW]
[ROW][C]beta[/C][C]0.0580315209102819[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0323111383325112[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.79602217393533[/C][/ROW]
[ROW][C]p-value[/C][C]0.110220968780478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105104&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105104&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)
alpha4054.6560202956
beta0.0580315209102819
S.D.0.0323111383325112
T-STAT1.79602217393533
p-value0.110220968780478






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.222660649785404
beta0.772469279741336
S.D.0.408438489482735
T-STAT1.89127445045550
p-value0.0952389031622506
Lambda0.227530720258664

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.222660649785404 \tabularnewline
beta & 0.772469279741336 \tabularnewline
S.D. & 0.408438489482735 \tabularnewline
T-STAT & 1.89127445045550 \tabularnewline
p-value & 0.0952389031622506 \tabularnewline
Lambda & 0.227530720258664 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105104&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.222660649785404[/C][/ROW]
[ROW][C]beta[/C][C]0.772469279741336[/C][/ROW]
[ROW][C]S.D.[/C][C]0.408438489482735[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.89127445045550[/C][/ROW]
[ROW][C]p-value[/C][C]0.0952389031622506[/C][/ROW]
[ROW][C]Lambda[/C][C]0.227530720258664[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105104&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105104&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)
alpha0.222660649785404
beta0.772469279741336
S.D.0.408438489482735
T-STAT1.89127445045550
p-value0.0952389031622506
Lambda0.227530720258664


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')