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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 computationTue, 26 Apr 2016 10:29:30 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/26/t1461662988uxoeat9x9ld89ju.htm/, Retrieved Fri, 03 May 2024 22:36:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294828, Retrieved Fri, 03 May 2024 22:36:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110

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] [Opgave 8- boekenv...] [2016-04-26 09:29:30] [b1d105767b629000b6b6bd83f6a3d689] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
283411
234585
207695
204000
220791
222335
303510
201602
218279
207253
217639
231043
302988
221415
213989
190507
199397
201077
261048
241508
194637
240044
253534
269220
270820
354121
315233
297098
258289
276246
246652
242945
210838
246343
234636
229011
238756
283696
226656
229790
219831
232331
315447
251031
297019
208424
311626
352320
375214
419501
664867
483142
312717
228228
230978
218033
225566
207708
241861
208381
209071
214514
195868
190208
187651
215934
213012
236845
154595
193485
231875
192259
191609
212911
238596
203033
258272
314681
289789
297541
239578
207798
254091
242544
218067
217463
229438
216485
238410
223108
221267
224802
233630
235134
309660
253229
293530
273323
297578
341589
389911
398685
629637
522502
358941
252783
236585
224995
225721
223338
228952
212759
200270
211925
191206
200511
205944
289288
186209
197515
182038
181606
223337
201213
220700
194043
224593
249907
238613
266200
274197
288601
242662
232105
267842
219037
198404
203910
209685
214274
215376
217711
224819
217142
221445
213483
282063
236194
297296
255885
264502
311580
416595
356762
537286
532855

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294828&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294828&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294828&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1229345.2531915.4283440841101908
223244734978.0749483288112481
326518640477.8440608956143283
4263910.58333333346325.3452608599143896
5318016.333333333143127.241926599457159
6202943.08333333322187.648760918382250
7245870.2539281.8708338153123072
8235057.7525799.793974247993175
9351671.583333333121277.559823031404642
10214469.83333333327167.2406630196103079
1122875435769.1911007224106995
12221913.91666666718655.728140358769438
13327162.166666667112769.147165859323803

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 229345.25 & 31915.4283440841 & 101908 \tabularnewline
2 & 232447 & 34978.0749483288 & 112481 \tabularnewline
3 & 265186 & 40477.8440608956 & 143283 \tabularnewline
4 & 263910.583333333 & 46325.3452608599 & 143896 \tabularnewline
5 & 318016.333333333 & 143127.241926599 & 457159 \tabularnewline
6 & 202943.083333333 & 22187.6487609183 & 82250 \tabularnewline
7 & 245870.25 & 39281.8708338153 & 123072 \tabularnewline
8 & 235057.75 & 25799.7939742479 & 93175 \tabularnewline
9 & 351671.583333333 & 121277.559823031 & 404642 \tabularnewline
10 & 214469.833333333 & 27167.2406630196 & 103079 \tabularnewline
11 & 228754 & 35769.1911007224 & 106995 \tabularnewline
12 & 221913.916666667 & 18655.7281403587 & 69438 \tabularnewline
13 & 327162.166666667 & 112769.147165859 & 323803 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294828&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]229345.25[/C][C]31915.4283440841[/C][C]101908[/C][/ROW]
[ROW][C]2[/C][C]232447[/C][C]34978.0749483288[/C][C]112481[/C][/ROW]
[ROW][C]3[/C][C]265186[/C][C]40477.8440608956[/C][C]143283[/C][/ROW]
[ROW][C]4[/C][C]263910.583333333[/C][C]46325.3452608599[/C][C]143896[/C][/ROW]
[ROW][C]5[/C][C]318016.333333333[/C][C]143127.241926599[/C][C]457159[/C][/ROW]
[ROW][C]6[/C][C]202943.083333333[/C][C]22187.6487609183[/C][C]82250[/C][/ROW]
[ROW][C]7[/C][C]245870.25[/C][C]39281.8708338153[/C][C]123072[/C][/ROW]
[ROW][C]8[/C][C]235057.75[/C][C]25799.7939742479[/C][C]93175[/C][/ROW]
[ROW][C]9[/C][C]351671.583333333[/C][C]121277.559823031[/C][C]404642[/C][/ROW]
[ROW][C]10[/C][C]214469.833333333[/C][C]27167.2406630196[/C][C]103079[/C][/ROW]
[ROW][C]11[/C][C]228754[/C][C]35769.1911007224[/C][C]106995[/C][/ROW]
[ROW][C]12[/C][C]221913.916666667[/C][C]18655.7281403587[/C][C]69438[/C][/ROW]
[ROW][C]13[/C][C]327162.166666667[/C][C]112769.147165859[/C][C]323803[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294828&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294828&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
1229345.2531915.4283440841101908
223244734978.0749483288112481
326518640477.8440608956143283
4263910.58333333346325.3452608599143896
5318016.333333333143127.241926599457159
6202943.08333333322187.648760918382250
7245870.2539281.8708338153123072
8235057.7525799.793974247993175
9351671.583333333121277.559823031404642
10214469.83333333327167.2406630196103079
1122875435769.1911007224106995
12221913.91666666718655.728140358769438
13327162.166666667112769.147165859323803






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-161981.600551284
beta0.840786637877986
S.D.0.0952259636862215
T-STAT8.82938439613441
p-value2.52685321553722e-06

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -161981.600551284 \tabularnewline
beta & 0.840786637877986 \tabularnewline
S.D. & 0.0952259636862215 \tabularnewline
T-STAT & 8.82938439613441 \tabularnewline
p-value & 2.52685321553722e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294828&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-161981.600551284[/C][/ROW]
[ROW][C]beta[/C][C]0.840786637877986[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0952259636862215[/C][/ROW]
[ROW][C]T-STAT[/C][C]8.82938439613441[/C][/ROW]
[ROW][C]p-value[/C][C]2.52685321553722e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294828&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294828&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)
alpha-161981.600551284
beta0.840786637877986
S.D.0.0952259636862215
T-STAT8.82938439613441
p-value2.52685321553722e-06






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-34.6694612789989
beta3.64401672728036
S.D.0.356183226643405
T-STAT10.2307364712842
p-value5.8833024594946e-07
Lambda-2.64401672728036

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -34.6694612789989 \tabularnewline
beta & 3.64401672728036 \tabularnewline
S.D. & 0.356183226643405 \tabularnewline
T-STAT & 10.2307364712842 \tabularnewline
p-value & 5.8833024594946e-07 \tabularnewline
Lambda & -2.64401672728036 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294828&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-34.6694612789989[/C][/ROW]
[ROW][C]beta[/C][C]3.64401672728036[/C][/ROW]
[ROW][C]S.D.[/C][C]0.356183226643405[/C][/ROW]
[ROW][C]T-STAT[/C][C]10.2307364712842[/C][/ROW]
[ROW][C]p-value[/C][C]5.8833024594946e-07[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.64401672728036[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294828&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294828&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-34.6694612789989
beta3.64401672728036
S.D.0.356183226643405
T-STAT10.2307364712842
p-value5.8833024594946e-07
Lambda-2.64401672728036


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')