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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 computationFri, 23 Dec 2011 05:07:06 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t1324635007nv6hrz10aig981h.htm/, Retrieved Mon, 29 Apr 2024 22:37:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160231, Retrieved Mon, 29 Apr 2024 22:37:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80

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 Standard de...] [2011-12-20 16:36:34] [abc1cbe561c2c4615f632bb3153b1275]
- R  D    [Standard Deviation-Mean Plot] [StandardDeviation...] [2011-12-23 10:07:06] [8aedcf735e397266388b06f47fe45218] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
274371
277686
282917
286692
285378
262433
266730
271980
277799
282329
285775
283495
279998
287224
296369
300653
302686
277891
277537
285383
292213
298522
300431
297584
286445
288576
293299
295881
292710
271993
267430
273963
273046
268347
264319
255765
246263
245098
246969
248333
247934
226839
225554
237085
237080
245039
248541
247105
243422
250643
254663
260993
258556
235372
246057
253353
255198
264176
269034
265861
269826
278506
292300
290726
289802
271311
274352
275216
276836
280408
280190
282656
281477
288186
292300
291186
287259
264993
267140
270150
275037
277103
277128
277915
276687
283042
286602
285351
277267
254868
254844
258863
264777
267366
267413
262813
258113
267037
269645
270349
264579
236997
236089
240541
241572
244576
244752
240337
238545
242621
241878
242081
237041
209673
210705
214912
218444
220115
220206
216713
216228
229261
230579
225780
213768
191395
195186
198088
200290
205010
208155
203496
205348

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'AstonUniversity' @ aston.wessa.net

\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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160231&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160231&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160231&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'AstonUniversity' @ aston.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1278132.0833333337875.3505140848824259
2291374.259376.8777428601225149
3277647.83333333313195.209308569940116
42418208280.1178515987122987
5254777.3333333339854.4600916016633662
6280177.4166666677479.2680057285822474
7279156.1666666679160.1353784491227307
8269991.08333333311497.728727949531758
9251215.58333333313565.786291980934260
10226077.83333333313146.627495869532948
11209769.66666666713376.456707985339184

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 278132.083333333 & 7875.35051408488 & 24259 \tabularnewline
2 & 291374.25 & 9376.87774286012 & 25149 \tabularnewline
3 & 277647.833333333 & 13195.2093085699 & 40116 \tabularnewline
4 & 241820 & 8280.11785159871 & 22987 \tabularnewline
5 & 254777.333333333 & 9854.46009160166 & 33662 \tabularnewline
6 & 280177.416666667 & 7479.26800572858 & 22474 \tabularnewline
7 & 279156.166666667 & 9160.13537844912 & 27307 \tabularnewline
8 & 269991.083333333 & 11497.7287279495 & 31758 \tabularnewline
9 & 251215.583333333 & 13565.7862919809 & 34260 \tabularnewline
10 & 226077.833333333 & 13146.6274958695 & 32948 \tabularnewline
11 & 209769.666666667 & 13376.4567079853 & 39184 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160231&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]278132.083333333[/C][C]7875.35051408488[/C][C]24259[/C][/ROW]
[ROW][C]2[/C][C]291374.25[/C][C]9376.87774286012[/C][C]25149[/C][/ROW]
[ROW][C]3[/C][C]277647.833333333[/C][C]13195.2093085699[/C][C]40116[/C][/ROW]
[ROW][C]4[/C][C]241820[/C][C]8280.11785159871[/C][C]22987[/C][/ROW]
[ROW][C]5[/C][C]254777.333333333[/C][C]9854.46009160166[/C][C]33662[/C][/ROW]
[ROW][C]6[/C][C]280177.416666667[/C][C]7479.26800572858[/C][C]22474[/C][/ROW]
[ROW][C]7[/C][C]279156.166666667[/C][C]9160.13537844912[/C][C]27307[/C][/ROW]
[ROW][C]8[/C][C]269991.083333333[/C][C]11497.7287279495[/C][C]31758[/C][/ROW]
[ROW][C]9[/C][C]251215.583333333[/C][C]13565.7862919809[/C][C]34260[/C][/ROW]
[ROW][C]10[/C][C]226077.833333333[/C][C]13146.6274958695[/C][C]32948[/C][/ROW]
[ROW][C]11[/C][C]209769.666666667[/C][C]13376.4567079853[/C][C]39184[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160231&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160231&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
1278132.0833333337875.3505140848824259
2291374.259376.8777428601225149
3277647.83333333313195.209308569940116
42418208280.1178515987122987
5254777.3333333339854.4600916016633662
6280177.4166666677479.2680057285822474
7279156.1666666679160.1353784491227307
8269991.08333333311497.728727949531758
9251215.58333333313565.786291980934260
10226077.83333333313146.627495869532948
11209769.66666666713376.456707985339184






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha23581.5321969
beta-0.0498538090581506
S.D.0.026185824456831
T-STAT-1.90384721857193
p-value0.0893367404320133

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 23581.5321969 \tabularnewline
beta & -0.0498538090581506 \tabularnewline
S.D. & 0.026185824456831 \tabularnewline
T-STAT & -1.90384721857193 \tabularnewline
p-value & 0.0893367404320133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160231&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]23581.5321969[/C][/ROW]
[ROW][C]beta[/C][C]-0.0498538090581506[/C][/ROW]
[ROW][C]S.D.[/C][C]0.026185824456831[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.90384721857193[/C][/ROW]
[ROW][C]p-value[/C][C]0.0893367404320133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160231&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160231&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)
alpha23581.5321969
beta-0.0498538090581506
S.D.0.026185824456831
T-STAT-1.90384721857193
p-value0.0893367404320133






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha23.719211987932
beta-1.16115268248851
S.D.0.630845247371322
T-STAT-1.8406299917879
p-value0.0988126038270665
Lambda2.16115268248851

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 23.719211987932 \tabularnewline
beta & -1.16115268248851 \tabularnewline
S.D. & 0.630845247371322 \tabularnewline
T-STAT & -1.8406299917879 \tabularnewline
p-value & 0.0988126038270665 \tabularnewline
Lambda & 2.16115268248851 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160231&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]23.719211987932[/C][/ROW]
[ROW][C]beta[/C][C]-1.16115268248851[/C][/ROW]
[ROW][C]S.D.[/C][C]0.630845247371322[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.8406299917879[/C][/ROW]
[ROW][C]p-value[/C][C]0.0988126038270665[/C][/ROW]
[ROW][C]Lambda[/C][C]2.16115268248851[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160231&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160231&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)
alpha23.719211987932
beta-1.16115268248851
S.D.0.630845247371322
T-STAT-1.8406299917879
p-value0.0988126038270665
Lambda2.16115268248851


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')