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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, 27 Jan 2009 09:39:47 -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/2009/Jan/27/t1233074485852c5bbt8wc7dn8.htm/, Retrieved Mon, 06 May 2024 09:30:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36988, Retrieved Mon, 06 May 2024 09:30:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact221

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] [2MAR03A_Robbe Ley...] [2009-01-08 11:29:09] [73702d50a449ca9a9e8052b5a190ceb8]
-   P     [Standard Deviation-Mean Plot] [Robbe Leys_2MAR03...] [2009-01-27 16:39:47] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
284.4
212.8
226.9
308.4
262
227.9
236.1
320.4
271.9
232.8
237
313.4
261.4
226.8
249.9
314.3
286.1
226.5
260.4
311.4
294.7
232.6
257.2
339.2
279.1
249.8
269.8
345.7
293.8
254.7
277.5
363.4
313.4
272.8
300.1
369.5
330.8
287.8
305.9
386.1
335.2
288
308.3
402.3
352.8
316.1
324.9
404.8
393
318.9
327
442.3
383.1
331.6
361.4
445.9
386.6
357.2
373.6
466.2
409.6
369.8
378.6
487
419.2
376.7
392.8
506.1
458.4
387.4
426.9
565
464.8
444.5
449.5
556.1
499.6
451.9
434.9
553.8
510
432.9
453.2
547.6
485.8
452.6
456.6
565.7
514.8
464.3
430.9
588.3
503.1
442.6
448
554.5
504.5
427.3
473.1
526.2
547.5
440.2
468.7
574.5
492.6
432.6
479.8
575.7
474.6
405.3
434.6
535.1
452.6
429.5
417.2
551.8
464
416.6
422.9
553.6
458.6
427.6
429.2
534.2
481.7
416
440.2
538.7
473.8
439.9
446.8
597.5
467.2
439.4
447.4
568.5
485.9
442.1
430.5
600
464.5
423.6
437
574
443
410
420
532
432
420
411
512

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36988&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36988&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36988&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1258.12545.63371377976395.6
2261.641.807256148504592.5
3263.77537.438872401110980.6
4263.137.041688226465487.5
5271.136.298484816862584.9
6280.92546.4898107115957106.6
7286.141.571384388783695.9
8297.3546.8623871920043108.7
9313.9540.707288454689996.7
10327.6542.768407343115698.3
11333.4549.8049863634824114.3
12349.6539.95668488083988.7
13370.358.3556338325615123.4
14380.548.442199234414114.3
15395.948.3858105922249109
16411.2553.3070039175591117.2
17423.757.6594022399354129.4
18459.42576.141551293189177.6
19478.72552.3012029817033111.6
20485.0553.3922903298469118.9
21485.92552.4912294261305114.7
22490.17552.4796071504605113.1
23499.57568.4702064161243157.4
24487.0552.6238539067598111.9
25482.77542.929350876372198.9
26507.72563.570243300882134.3
27495.17559.5620894529398143.1
28462.456.1764482085984129.8
29462.77561.1372431501454134.6
30464.27563.150158352929137
31462.449.9431677008978106.6
32469.1553.7206664143326122.7
33489.573.4709466387905157.6
34480.62559.737334780409129.1
35489.62577.3539645611867169.5
36474.77568.3057037637902150.4
37451.2555.5780232346084122
38443.7546.3060471212994101

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 258.125 & 45.633713779763 & 95.6 \tabularnewline
2 & 261.6 & 41.8072561485045 & 92.5 \tabularnewline
3 & 263.775 & 37.4388724011109 & 80.6 \tabularnewline
4 & 263.1 & 37.0416882264654 & 87.5 \tabularnewline
5 & 271.1 & 36.2984848168625 & 84.9 \tabularnewline
6 & 280.925 & 46.4898107115957 & 106.6 \tabularnewline
7 & 286.1 & 41.5713843887836 & 95.9 \tabularnewline
8 & 297.35 & 46.8623871920043 & 108.7 \tabularnewline
9 & 313.95 & 40.7072884546899 & 96.7 \tabularnewline
10 & 327.65 & 42.7684073431156 & 98.3 \tabularnewline
11 & 333.45 & 49.8049863634824 & 114.3 \tabularnewline
12 & 349.65 & 39.956684880839 & 88.7 \tabularnewline
13 & 370.3 & 58.3556338325615 & 123.4 \tabularnewline
14 & 380.5 & 48.442199234414 & 114.3 \tabularnewline
15 & 395.9 & 48.3858105922249 & 109 \tabularnewline
16 & 411.25 & 53.3070039175591 & 117.2 \tabularnewline
17 & 423.7 & 57.6594022399354 & 129.4 \tabularnewline
18 & 459.425 & 76.141551293189 & 177.6 \tabularnewline
19 & 478.725 & 52.3012029817033 & 111.6 \tabularnewline
20 & 485.05 & 53.3922903298469 & 118.9 \tabularnewline
21 & 485.925 & 52.4912294261305 & 114.7 \tabularnewline
22 & 490.175 & 52.4796071504605 & 113.1 \tabularnewline
23 & 499.575 & 68.4702064161243 & 157.4 \tabularnewline
24 & 487.05 & 52.6238539067598 & 111.9 \tabularnewline
25 & 482.775 & 42.9293508763721 & 98.9 \tabularnewline
26 & 507.725 & 63.570243300882 & 134.3 \tabularnewline
27 & 495.175 & 59.5620894529398 & 143.1 \tabularnewline
28 & 462.4 & 56.1764482085984 & 129.8 \tabularnewline
29 & 462.775 & 61.1372431501454 & 134.6 \tabularnewline
30 & 464.275 & 63.150158352929 & 137 \tabularnewline
31 & 462.4 & 49.9431677008978 & 106.6 \tabularnewline
32 & 469.15 & 53.7206664143326 & 122.7 \tabularnewline
33 & 489.5 & 73.4709466387905 & 157.6 \tabularnewline
34 & 480.625 & 59.737334780409 & 129.1 \tabularnewline
35 & 489.625 & 77.3539645611867 & 169.5 \tabularnewline
36 & 474.775 & 68.3057037637902 & 150.4 \tabularnewline
37 & 451.25 & 55.5780232346084 & 122 \tabularnewline
38 & 443.75 & 46.3060471212994 & 101 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36988&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]258.125[/C][C]45.633713779763[/C][C]95.6[/C][/ROW]
[ROW][C]2[/C][C]261.6[/C][C]41.8072561485045[/C][C]92.5[/C][/ROW]
[ROW][C]3[/C][C]263.775[/C][C]37.4388724011109[/C][C]80.6[/C][/ROW]
[ROW][C]4[/C][C]263.1[/C][C]37.0416882264654[/C][C]87.5[/C][/ROW]
[ROW][C]5[/C][C]271.1[/C][C]36.2984848168625[/C][C]84.9[/C][/ROW]
[ROW][C]6[/C][C]280.925[/C][C]46.4898107115957[/C][C]106.6[/C][/ROW]
[ROW][C]7[/C][C]286.1[/C][C]41.5713843887836[/C][C]95.9[/C][/ROW]
[ROW][C]8[/C][C]297.35[/C][C]46.8623871920043[/C][C]108.7[/C][/ROW]
[ROW][C]9[/C][C]313.95[/C][C]40.7072884546899[/C][C]96.7[/C][/ROW]
[ROW][C]10[/C][C]327.65[/C][C]42.7684073431156[/C][C]98.3[/C][/ROW]
[ROW][C]11[/C][C]333.45[/C][C]49.8049863634824[/C][C]114.3[/C][/ROW]
[ROW][C]12[/C][C]349.65[/C][C]39.956684880839[/C][C]88.7[/C][/ROW]
[ROW][C]13[/C][C]370.3[/C][C]58.3556338325615[/C][C]123.4[/C][/ROW]
[ROW][C]14[/C][C]380.5[/C][C]48.442199234414[/C][C]114.3[/C][/ROW]
[ROW][C]15[/C][C]395.9[/C][C]48.3858105922249[/C][C]109[/C][/ROW]
[ROW][C]16[/C][C]411.25[/C][C]53.3070039175591[/C][C]117.2[/C][/ROW]
[ROW][C]17[/C][C]423.7[/C][C]57.6594022399354[/C][C]129.4[/C][/ROW]
[ROW][C]18[/C][C]459.425[/C][C]76.141551293189[/C][C]177.6[/C][/ROW]
[ROW][C]19[/C][C]478.725[/C][C]52.3012029817033[/C][C]111.6[/C][/ROW]
[ROW][C]20[/C][C]485.05[/C][C]53.3922903298469[/C][C]118.9[/C][/ROW]
[ROW][C]21[/C][C]485.925[/C][C]52.4912294261305[/C][C]114.7[/C][/ROW]
[ROW][C]22[/C][C]490.175[/C][C]52.4796071504605[/C][C]113.1[/C][/ROW]
[ROW][C]23[/C][C]499.575[/C][C]68.4702064161243[/C][C]157.4[/C][/ROW]
[ROW][C]24[/C][C]487.05[/C][C]52.6238539067598[/C][C]111.9[/C][/ROW]
[ROW][C]25[/C][C]482.775[/C][C]42.9293508763721[/C][C]98.9[/C][/ROW]
[ROW][C]26[/C][C]507.725[/C][C]63.570243300882[/C][C]134.3[/C][/ROW]
[ROW][C]27[/C][C]495.175[/C][C]59.5620894529398[/C][C]143.1[/C][/ROW]
[ROW][C]28[/C][C]462.4[/C][C]56.1764482085984[/C][C]129.8[/C][/ROW]
[ROW][C]29[/C][C]462.775[/C][C]61.1372431501454[/C][C]134.6[/C][/ROW]
[ROW][C]30[/C][C]464.275[/C][C]63.150158352929[/C][C]137[/C][/ROW]
[ROW][C]31[/C][C]462.4[/C][C]49.9431677008978[/C][C]106.6[/C][/ROW]
[ROW][C]32[/C][C]469.15[/C][C]53.7206664143326[/C][C]122.7[/C][/ROW]
[ROW][C]33[/C][C]489.5[/C][C]73.4709466387905[/C][C]157.6[/C][/ROW]
[ROW][C]34[/C][C]480.625[/C][C]59.737334780409[/C][C]129.1[/C][/ROW]
[ROW][C]35[/C][C]489.625[/C][C]77.3539645611867[/C][C]169.5[/C][/ROW]
[ROW][C]36[/C][C]474.775[/C][C]68.3057037637902[/C][C]150.4[/C][/ROW]
[ROW][C]37[/C][C]451.25[/C][C]55.5780232346084[/C][C]122[/C][/ROW]
[ROW][C]38[/C][C]443.75[/C][C]46.3060471212994[/C][C]101[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36988&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36988&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
1258.12545.63371377976395.6
2261.641.807256148504592.5
3263.77537.438872401110980.6
4263.137.041688226465487.5
5271.136.298484816862584.9
6280.92546.4898107115957106.6
7286.141.571384388783695.9
8297.3546.8623871920043108.7
9313.9540.707288454689996.7
10327.6542.768407343115698.3
11333.4549.8049863634824114.3
12349.6539.95668488083988.7
13370.358.3556338325615123.4
14380.548.442199234414114.3
15395.948.3858105922249109
16411.2553.3070039175591117.2
17423.757.6594022399354129.4
18459.42576.141551293189177.6
19478.72552.3012029817033111.6
20485.0553.3922903298469118.9
21485.92552.4912294261305114.7
22490.17552.4796071504605113.1
23499.57568.4702064161243157.4
24487.0552.6238539067598111.9
25482.77542.929350876372198.9
26507.72563.570243300882134.3
27495.17559.5620894529398143.1
28462.456.1764482085984129.8
29462.77561.1372431501454134.6
30464.27563.150158352929137
31462.449.9431677008978106.6
32469.1553.7206664143326122.7
33489.573.4709466387905157.6
34480.62559.737334780409129.1
35489.62577.3539645611867169.5
36474.77568.3057037637902150.4
37451.2555.5780232346084122
38443.7546.3060471212994101






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha16.6203405754596
beta0.0889587668856259
S.D.0.0142001631330144
T-STAT6.26462992377903
p-value3.08290597677703e-07

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 16.6203405754596 \tabularnewline
beta & 0.0889587668856259 \tabularnewline
S.D. & 0.0142001631330144 \tabularnewline
T-STAT & 6.26462992377903 \tabularnewline
p-value & 3.08290597677703e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36988&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]16.6203405754596[/C][/ROW]
[ROW][C]beta[/C][C]0.0889587668856259[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0142001631330144[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.26462992377903[/C][/ROW]
[ROW][C]p-value[/C][C]3.08290597677703e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36988&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36988&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)
alpha16.6203405754596
beta0.0889587668856259
S.D.0.0142001631330144
T-STAT6.26462992377903
p-value3.08290597677703e-07






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.105959041575507
beta0.642023662158066
S.D.0.0931449867563278
T-STAT6.89273448325924
p-value4.54084145408177e-08
Lambda0.357976337841934

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.105959041575507 \tabularnewline
beta & 0.642023662158066 \tabularnewline
S.D. & 0.0931449867563278 \tabularnewline
T-STAT & 6.89273448325924 \tabularnewline
p-value & 4.54084145408177e-08 \tabularnewline
Lambda & 0.357976337841934 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36988&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.105959041575507[/C][/ROW]
[ROW][C]beta[/C][C]0.642023662158066[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0931449867563278[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.89273448325924[/C][/ROW]
[ROW][C]p-value[/C][C]4.54084145408177e-08[/C][/ROW]
[ROW][C]Lambda[/C][C]0.357976337841934[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36988&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36988&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)
alpha0.105959041575507
beta0.642023662158066
S.D.0.0931449867563278
T-STAT6.89273448325924
p-value4.54084145408177e-08
Lambda0.357976337841934


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')