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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 computationWed, 29 Dec 2010 15:56:53 +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/29/t1293638107sv11zww2mlvtcdc.htm/, Retrieved Fri, 03 May 2024 08:22:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116926, Retrieved Fri, 03 May 2024 08:22:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98

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] [Paper] [2010-12-29 15:56:53] [d5e0edb7e0239841e94676417b2a1e2e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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
203555
195770

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' @ www.wessa.org

\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' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116926&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' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116926&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116926&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' @ www.wessa.org






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1235344.33333333315066.829764469948703
2216762.2514480.88544583746040
3180396.41666666713184.570999731835944
4168889.91666666711090.917434454136068
5202808.2515307.616162165240894

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 235344.333333333 & 15066.8297644699 & 48703 \tabularnewline
2 & 216762.25 & 14480.885445837 & 46040 \tabularnewline
3 & 180396.416666667 & 13184.5709997318 & 35944 \tabularnewline
4 & 168889.916666667 & 11090.9174344541 & 36068 \tabularnewline
5 & 202808.25 & 15307.6161621652 & 40894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116926&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]235344.333333333[/C][C]15066.8297644699[/C][C]48703[/C][/ROW]
[ROW][C]2[/C][C]216762.25[/C][C]14480.885445837[/C][C]46040[/C][/ROW]
[ROW][C]3[/C][C]180396.416666667[/C][C]13184.5709997318[/C][C]35944[/C][/ROW]
[ROW][C]4[/C][C]168889.916666667[/C][C]11090.9174344541[/C][C]36068[/C][/ROW]
[ROW][C]5[/C][C]202808.25[/C][C]15307.6161621652[/C][C]40894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116926&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116926&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
1235344.33333333315066.829764469948703
2216762.2514480.88544583746040
3180396.41666666713184.570999731835944
4168889.91666666711090.917434454136068
5202808.2515307.616162165240894






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2926.83892111905
beta0.054268633626426
S.D.0.0202588810487484
T-STAT2.6787577011702
p-value0.0751282414467939

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2926.83892111905 \tabularnewline
beta & 0.054268633626426 \tabularnewline
S.D. & 0.0202588810487484 \tabularnewline
T-STAT & 2.6787577011702 \tabularnewline
p-value & 0.0751282414467939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116926&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2926.83892111905[/C][/ROW]
[ROW][C]beta[/C][C]0.054268633626426[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0202588810487484[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.6787577011702[/C][/ROW]
[ROW][C]p-value[/C][C]0.0751282414467939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116926&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116926&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)
alpha2926.83892111905
beta0.054268633626426
S.D.0.0202588810487484
T-STAT2.6787577011702
p-value0.0751282414467939






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.79625492960034
beta0.845999400807817
S.D.0.293814759269813
T-STAT2.87936318417186
p-value0.0635620626146514
Lambda0.154000599192183

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.79625492960034 \tabularnewline
beta & 0.845999400807817 \tabularnewline
S.D. & 0.293814759269813 \tabularnewline
T-STAT & 2.87936318417186 \tabularnewline
p-value & 0.0635620626146514 \tabularnewline
Lambda & 0.154000599192183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116926&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.79625492960034[/C][/ROW]
[ROW][C]beta[/C][C]0.845999400807817[/C][/ROW]
[ROW][C]S.D.[/C][C]0.293814759269813[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.87936318417186[/C][/ROW]
[ROW][C]p-value[/C][C]0.0635620626146514[/C][/ROW]
[ROW][C]Lambda[/C][C]0.154000599192183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116926&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116926&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-0.79625492960034
beta0.845999400807817
S.D.0.293814759269813
T-STAT2.87936318417186
p-value0.0635620626146514
Lambda0.154000599192183


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 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')