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Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Tue, 01 Feb 2011 14:05:45 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Feb/01/t1296569594uf8ou7cdd81n0kw.htm/, Retrieved Wed, 08 May 2024 19:05:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=118005, Retrieved Wed, 08 May 2024 19:05:15 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

256

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Spectral Analysis] [ws9 tim damen cp] [2010-12-05 13:13:38] [74be16979710d4c4e7c6647856088456]
- RMPD      [Standard Deviation-Mean Plot] [w] [2011-02-01 14:05:45] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=118005&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=118005&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=118005&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.org

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	368.833333333333	40.4336343639647	93
2	454.333333333333	45.0481224174031	98
3	534.916666666667	38.1705701325304	90
4	589.5	32.5813666770664	86
5	595.083333333333	31.1578337831853	90
6	557.333333333333	29.7972949758663	113
7	516.75	22.1897806126235	62
8	500.833333333333	19.8898481795629	65
9	459.416666666667	21.0517040266161	70
10	419.25	19.7489930698435	62
11	402.75	24.0156199170457	63
12	429.416666666667	27.9755033534481	70
13	472.75	32.1760074363718	85
14	549.833333333333	39.1589612020575	89
15	570.666666666667	15.7441667889663	40
16	606.666666666667	10.1742396037813	27
17	574	17.949423895541	45
18	619.666666666667	9.31600122305052	23
19	580.5	27.4938009541986	76
20	596	15.4331402566625	41
21	556.666666666667	16.0075739649212	42
22	583.5	16.8927095625195	44
23	533	21.5237712140026	56
24	549.166666666667	23.3114616106379	62
25	498.166666666667	19.8211701944862	52
26	517.166666666667	22.5018517756502	60
27	462.333333333333	20.3395420227932	54
28	486.5	21.7986655137836	61
29	447.5	13.2218826881115	36
30	492	18.2507783146612	42
31	465.5	8.95950485644867	21
32	517.5	5.90069333368392	16
33	510.5	6.31736423748789	18
34	565.666666666667	12.2943692457773	33
35	576.666666666667	29.105867366418	76
36	596.25	21.9757097310148	62
37	588.333333333333	22.7129651934482	69
38	532.583333333333	21.8318296960834	66
39	504.916666666667	19.5794806010287	65
40	554.666666666667	25.5354774002877	73
41	567.25	22.017038856304	67

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 368.833333333333 & 40.4336343639647 & 93 \tabularnewline
2 & 454.333333333333 & 45.0481224174031 & 98 \tabularnewline
3 & 534.916666666667 & 38.1705701325304 & 90 \tabularnewline
4 & 589.5 & 32.5813666770664 & 86 \tabularnewline
5 & 595.083333333333 & 31.1578337831853 & 90 \tabularnewline
6 & 557.333333333333 & 29.7972949758663 & 113 \tabularnewline
7 & 516.75 & 22.1897806126235 & 62 \tabularnewline
8 & 500.833333333333 & 19.8898481795629 & 65 \tabularnewline
9 & 459.416666666667 & 21.0517040266161 & 70 \tabularnewline
10 & 419.25 & 19.7489930698435 & 62 \tabularnewline
11 & 402.75 & 24.0156199170457 & 63 \tabularnewline
12 & 429.416666666667 & 27.9755033534481 & 70 \tabularnewline
13 & 472.75 & 32.1760074363718 & 85 \tabularnewline
14 & 549.833333333333 & 39.1589612020575 & 89 \tabularnewline
15 & 570.666666666667 & 15.7441667889663 & 40 \tabularnewline
16 & 606.666666666667 & 10.1742396037813 & 27 \tabularnewline
17 & 574 & 17.949423895541 & 45 \tabularnewline
18 & 619.666666666667 & 9.31600122305052 & 23 \tabularnewline
19 & 580.5 & 27.4938009541986 & 76 \tabularnewline
20 & 596 & 15.4331402566625 & 41 \tabularnewline
21 & 556.666666666667 & 16.0075739649212 & 42 \tabularnewline
22 & 583.5 & 16.8927095625195 & 44 \tabularnewline
23 & 533 & 21.5237712140026 & 56 \tabularnewline
24 & 549.166666666667 & 23.3114616106379 & 62 \tabularnewline
25 & 498.166666666667 & 19.8211701944862 & 52 \tabularnewline
26 & 517.166666666667 & 22.5018517756502 & 60 \tabularnewline
27 & 462.333333333333 & 20.3395420227932 & 54 \tabularnewline
28 & 486.5 & 21.7986655137836 & 61 \tabularnewline
29 & 447.5 & 13.2218826881115 & 36 \tabularnewline
30 & 492 & 18.2507783146612 & 42 \tabularnewline
31 & 465.5 & 8.95950485644867 & 21 \tabularnewline
32 & 517.5 & 5.90069333368392 & 16 \tabularnewline
33 & 510.5 & 6.31736423748789 & 18 \tabularnewline
34 & 565.666666666667 & 12.2943692457773 & 33 \tabularnewline
35 & 576.666666666667 & 29.105867366418 & 76 \tabularnewline
36 & 596.25 & 21.9757097310148 & 62 \tabularnewline
37 & 588.333333333333 & 22.7129651934482 & 69 \tabularnewline
38 & 532.583333333333 & 21.8318296960834 & 66 \tabularnewline
39 & 504.916666666667 & 19.5794806010287 & 65 \tabularnewline
40 & 554.666666666667 & 25.5354774002877 & 73 \tabularnewline
41 & 567.25 & 22.017038856304 & 67 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=118005&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]368.833333333333[/C][C]40.4336343639647[/C][C]93[/C][/ROW]
[ROW][C]2[/C][C]454.333333333333[/C][C]45.0481224174031[/C][C]98[/C][/ROW]
[ROW][C]3[/C][C]534.916666666667[/C][C]38.1705701325304[/C][C]90[/C][/ROW]
[ROW][C]4[/C][C]589.5[/C][C]32.5813666770664[/C][C]86[/C][/ROW]
[ROW][C]5[/C][C]595.083333333333[/C][C]31.1578337831853[/C][C]90[/C][/ROW]
[ROW][C]6[/C][C]557.333333333333[/C][C]29.7972949758663[/C][C]113[/C][/ROW]
[ROW][C]7[/C][C]516.75[/C][C]22.1897806126235[/C][C]62[/C][/ROW]
[ROW][C]8[/C][C]500.833333333333[/C][C]19.8898481795629[/C][C]65[/C][/ROW]
[ROW][C]9[/C][C]459.416666666667[/C][C]21.0517040266161[/C][C]70[/C][/ROW]
[ROW][C]10[/C][C]419.25[/C][C]19.7489930698435[/C][C]62[/C][/ROW]
[ROW][C]11[/C][C]402.75[/C][C]24.0156199170457[/C][C]63[/C][/ROW]
[ROW][C]12[/C][C]429.416666666667[/C][C]27.9755033534481[/C][C]70[/C][/ROW]
[ROW][C]13[/C][C]472.75[/C][C]32.1760074363718[/C][C]85[/C][/ROW]
[ROW][C]14[/C][C]549.833333333333[/C][C]39.1589612020575[/C][C]89[/C][/ROW]
[ROW][C]15[/C][C]570.666666666667[/C][C]15.7441667889663[/C][C]40[/C][/ROW]
[ROW][C]16[/C][C]606.666666666667[/C][C]10.1742396037813[/C][C]27[/C][/ROW]
[ROW][C]17[/C][C]574[/C][C]17.949423895541[/C][C]45[/C][/ROW]
[ROW][C]18[/C][C]619.666666666667[/C][C]9.31600122305052[/C][C]23[/C][/ROW]
[ROW][C]19[/C][C]580.5[/C][C]27.4938009541986[/C][C]76[/C][/ROW]
[ROW][C]20[/C][C]596[/C][C]15.4331402566625[/C][C]41[/C][/ROW]
[ROW][C]21[/C][C]556.666666666667[/C][C]16.0075739649212[/C][C]42[/C][/ROW]
[ROW][C]22[/C][C]583.5[/C][C]16.8927095625195[/C][C]44[/C][/ROW]
[ROW][C]23[/C][C]533[/C][C]21.5237712140026[/C][C]56[/C][/ROW]
[ROW][C]24[/C][C]549.166666666667[/C][C]23.3114616106379[/C][C]62[/C][/ROW]
[ROW][C]25[/C][C]498.166666666667[/C][C]19.8211701944862[/C][C]52[/C][/ROW]
[ROW][C]26[/C][C]517.166666666667[/C][C]22.5018517756502[/C][C]60[/C][/ROW]
[ROW][C]27[/C][C]462.333333333333[/C][C]20.3395420227932[/C][C]54[/C][/ROW]
[ROW][C]28[/C][C]486.5[/C][C]21.7986655137836[/C][C]61[/C][/ROW]
[ROW][C]29[/C][C]447.5[/C][C]13.2218826881115[/C][C]36[/C][/ROW]
[ROW][C]30[/C][C]492[/C][C]18.2507783146612[/C][C]42[/C][/ROW]
[ROW][C]31[/C][C]465.5[/C][C]8.95950485644867[/C][C]21[/C][/ROW]
[ROW][C]32[/C][C]517.5[/C][C]5.90069333368392[/C][C]16[/C][/ROW]
[ROW][C]33[/C][C]510.5[/C][C]6.31736423748789[/C][C]18[/C][/ROW]
[ROW][C]34[/C][C]565.666666666667[/C][C]12.2943692457773[/C][C]33[/C][/ROW]
[ROW][C]35[/C][C]576.666666666667[/C][C]29.105867366418[/C][C]76[/C][/ROW]
[ROW][C]36[/C][C]596.25[/C][C]21.9757097310148[/C][C]62[/C][/ROW]
[ROW][C]37[/C][C]588.333333333333[/C][C]22.7129651934482[/C][C]69[/C][/ROW]
[ROW][C]38[/C][C]532.583333333333[/C][C]21.8318296960834[/C][C]66[/C][/ROW]
[ROW][C]39[/C][C]504.916666666667[/C][C]19.5794806010287[/C][C]65[/C][/ROW]
[ROW][C]40[/C][C]554.666666666667[/C][C]25.5354774002877[/C][C]73[/C][/ROW]
[ROW][C]41[/C][C]567.25[/C][C]22.017038856304[/C][C]67[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=118005&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=118005&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	368.833333333333	40.4336343639647	93
2	454.333333333333	45.0481224174031	98
3	534.916666666667	38.1705701325304	90
4	589.5	32.5813666770664	86
5	595.083333333333	31.1578337831853	90
6	557.333333333333	29.7972949758663	113
7	516.75	22.1897806126235	62
8	500.833333333333	19.8898481795629	65
9	459.416666666667	21.0517040266161	70
10	419.25	19.7489930698435	62
11	402.75	24.0156199170457	63
12	429.416666666667	27.9755033534481	70
13	472.75	32.1760074363718	85
14	549.833333333333	39.1589612020575	89
15	570.666666666667	15.7441667889663	40
16	606.666666666667	10.1742396037813	27
17	574	17.949423895541	45
18	619.666666666667	9.31600122305052	23
19	580.5	27.4938009541986	76
20	596	15.4331402566625	41
21	556.666666666667	16.0075739649212	42
22	583.5	16.8927095625195	44
23	533	21.5237712140026	56
24	549.166666666667	23.3114616106379	62
25	498.166666666667	19.8211701944862	52
26	517.166666666667	22.5018517756502	60
27	462.333333333333	20.3395420227932	54
28	486.5	21.7986655137836	61
29	447.5	13.2218826881115	36
30	492	18.2507783146612	42
31	465.5	8.95950485644867	21
32	517.5	5.90069333368392	16
33	510.5	6.31736423748789	18
34	565.666666666667	12.2943692457773	33
35	576.666666666667	29.105867366418	76
36	596.25	21.9757097310148	62
37	588.333333333333	22.7129651934482	69
38	532.583333333333	21.8318296960834	66
39	504.916666666667	19.5794806010287	65
40	554.666666666667	25.5354774002877	73
41	567.25	22.017038856304	67

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	37.3811346022443
beta	-0.0289811727144613
S.D.	0.0231649333853542
T-STAT	-1.25107947570375
p-value	0.218358704496817

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 37.3811346022443 \tabularnewline
beta & -0.0289811727144613 \tabularnewline
S.D. & 0.0231649333853542 \tabularnewline
T-STAT & -1.25107947570375 \tabularnewline
p-value & 0.218358704496817 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=118005&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]37.3811346022443[/C][/ROW]
[ROW][C]beta[/C][C]-0.0289811727144613[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0231649333853542[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.25107947570375[/C][/ROW]
[ROW][C]p-value[/C][C]0.218358704496817[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=118005&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=118005&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	37.3811346022443
beta	-0.0289811727144613
S.D.	0.0231649333853542
T-STAT	-1.25107947570375
p-value	0.218358704496817

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	6.91104756361017
beta	-0.624163204575246
S.D.	0.594656482112167
T-STAT	-1.04961977772154
p-value	0.300353953988297
Lambda	1.62416320457525

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 6.91104756361017 \tabularnewline
beta & -0.624163204575246 \tabularnewline
S.D. & 0.594656482112167 \tabularnewline
T-STAT & -1.04961977772154 \tabularnewline
p-value & 0.300353953988297 \tabularnewline
Lambda & 1.62416320457525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=118005&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.91104756361017[/C][/ROW]
[ROW][C]beta[/C][C]-0.624163204575246[/C][/ROW]
[ROW][C]S.D.[/C][C]0.594656482112167[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.04961977772154[/C][/ROW]
[ROW][C]p-value[/C][C]0.300353953988297[/C][/ROW]
[ROW][C]Lambda[/C][C]1.62416320457525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=118005&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=118005&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	6.91104756361017
beta	-0.624163204575246
S.D.	0.594656482112167
T-STAT	-1.04961977772154
p-value	0.300353953988297
Lambda	1.62416320457525

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code