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*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Thu, 27 Nov 2008 04:41:09 -0700

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/2008/Nov/27/t1227786343hdjjb5ysowfvtwq.htm/, Retrieved Sun, 19 May 2024 04:28:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25761, Retrieved Sun, 19 May 2024 04:28:09 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

195

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

F       [Standard Deviation-Mean Plot] [Opdracht Non stat...] [2008-11-27 11:41:09] [e1dd70d3b1099218056e8ae5041dcc2f] [Current]

Feedback Forum

2008-12-04 12:54:30 [Steven Vercammen] [reply] 
De seasonal periods moeten op 12 gezet worden. 
Dit is wat er in de theorie te vinden is over de Standard Deviation-Mean Plot:  
 
1)“The SMP is often used to identify the quasi-optimal Box-Cox transformation parameter that induces stationarity of the variance. “  
 
2)To achieve a constant variance over time a variance stabilizing transformation has to be applied to the measurements. The range of variance stabilizing transformations that can be used is very wide. However for most of the practical situations the power transformation has been found of considerable value. This transformation is given by : G(Zt)= Zt ^ lambda when lambda is not 0 and ln Zt when lambda is 0.  
 
De optimale lambda om een transformatie uit te voeren blijkt hier -0.3 te zijn. Wanneer deze transformatie wordt toegepast zal de variantie stationair worden. 
 
2008-12-06 10:44:36 [Maarten Van Gucht] [reply] 
Zoals de student hiervoor al zei, de seasonal periods moeten op 12 worden gezet, dit wilt zeggen dat we rekenen over 12 maanden tijd. 
de lamba berekenen doen we door de standard deviation plot. deze verdeelt de reeks onder in perioden. in de grafiek zie je punten die de jaren voorstellen. 
x-as = het gemiddelde 
y-as = standard deviation 
 
Door een lambda toe te voegen kan men de tijdreeks transformeren waardoor de spreiding harder naar een diagonaal zal deinen. Een lambda van 1 geeft bijvoorbeeld een perfecte rechte. De bedoeling van deze transformatie is om de tijdreeks stationair proberen te krijgen. Hier voor moet je zien dat de spreiding gelijk loopt door de tijd en hierdoor wordt de trend eruit gehaald. 
de optimale lambda is -0.312592539725757 
We hebben gezien op de run sequence plot dat er sprake was van heteroskedasticiteit : de variantie werd groter naarmate de tijd vordert. De gegevens in de standard deviation mean plot bevestigden dit. Ook de p value (6.19…e-11) is kleiner dan 0.05 wat de heteroskedasticiteit  bevestigt. We gaan de tijdreeks tot de 0.3e macht vereffenen om deze heteroskedastische trend weg te werken.

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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	'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25761&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25761&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25761&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	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	122.75	9.35859676091097	20
2	138	12.8840987267251	27
3	119.25	13.0989821487524	32
4	126.75	13.2256064763272	26
5	153.5	21.4242852856285	45
6	136.25	18.1911150473704	44
7	159	14.7648230602334	33
8	187	14.0712472794703	27
9	164.5	15.6098259652908	38
10	181.25	9.03234926989282	22
11	218.25	25.4607541129480	59
12	191.5	15.1986841535707	37
13	215.75	22.8089894559141	40
14	252	19.6129209111409	43
15	207.25	23.6696007570892	57
16	213.5	21.4864298259778	47
17	273.25	30.7828415409191	68
18	230	22.8910462845192	56
19	252.75	18.0069431053691	36
20	324	41.3360214179675	94
21	275.25	30.6743649757687	75
22	297.75	20.1886932051912	40
23	377.5	43.08518693627	95
24	309.5	34.5301800362137	84
25	330	26.2424592343528	55
26	427.25	52.4491817540242	112
27	348	41.3521462562707	99
28	342	18.4028983224563	44
29	448.5	64.5264803523845	142
30	352.5	39.7534065626247	94
31	376	30.0665927567458	64
32	499.75	65.7488909919146	139
33	409.25	41.4115523334572	101
34	422	28.9597421719646	70
35	558.75	69.0959477827752	150
36	447.75	49.6277811983033	118

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 122.75 & 9.35859676091097 & 20 \tabularnewline
2 & 138 & 12.8840987267251 & 27 \tabularnewline
3 & 119.25 & 13.0989821487524 & 32 \tabularnewline
4 & 126.75 & 13.2256064763272 & 26 \tabularnewline
5 & 153.5 & 21.4242852856285 & 45 \tabularnewline
6 & 136.25 & 18.1911150473704 & 44 \tabularnewline
7 & 159 & 14.7648230602334 & 33 \tabularnewline
8 & 187 & 14.0712472794703 & 27 \tabularnewline
9 & 164.5 & 15.6098259652908 & 38 \tabularnewline
10 & 181.25 & 9.03234926989282 & 22 \tabularnewline
11 & 218.25 & 25.4607541129480 & 59 \tabularnewline
12 & 191.5 & 15.1986841535707 & 37 \tabularnewline
13 & 215.75 & 22.8089894559141 & 40 \tabularnewline
14 & 252 & 19.6129209111409 & 43 \tabularnewline
15 & 207.25 & 23.6696007570892 & 57 \tabularnewline
16 & 213.5 & 21.4864298259778 & 47 \tabularnewline
17 & 273.25 & 30.7828415409191 & 68 \tabularnewline
18 & 230 & 22.8910462845192 & 56 \tabularnewline
19 & 252.75 & 18.0069431053691 & 36 \tabularnewline
20 & 324 & 41.3360214179675 & 94 \tabularnewline
21 & 275.25 & 30.6743649757687 & 75 \tabularnewline
22 & 297.75 & 20.1886932051912 & 40 \tabularnewline
23 & 377.5 & 43.08518693627 & 95 \tabularnewline
24 & 309.5 & 34.5301800362137 & 84 \tabularnewline
25 & 330 & 26.2424592343528 & 55 \tabularnewline
26 & 427.25 & 52.4491817540242 & 112 \tabularnewline
27 & 348 & 41.3521462562707 & 99 \tabularnewline
28 & 342 & 18.4028983224563 & 44 \tabularnewline
29 & 448.5 & 64.5264803523845 & 142 \tabularnewline
30 & 352.5 & 39.7534065626247 & 94 \tabularnewline
31 & 376 & 30.0665927567458 & 64 \tabularnewline
32 & 499.75 & 65.7488909919146 & 139 \tabularnewline
33 & 409.25 & 41.4115523334572 & 101 \tabularnewline
34 & 422 & 28.9597421719646 & 70 \tabularnewline
35 & 558.75 & 69.0959477827752 & 150 \tabularnewline
36 & 447.75 & 49.6277811983033 & 118 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25761&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]122.75[/C][C]9.35859676091097[/C][C]20[/C][/ROW]
[ROW][C]2[/C][C]138[/C][C]12.8840987267251[/C][C]27[/C][/ROW]
[ROW][C]3[/C][C]119.25[/C][C]13.0989821487524[/C][C]32[/C][/ROW]
[ROW][C]4[/C][C]126.75[/C][C]13.2256064763272[/C][C]26[/C][/ROW]
[ROW][C]5[/C][C]153.5[/C][C]21.4242852856285[/C][C]45[/C][/ROW]
[ROW][C]6[/C][C]136.25[/C][C]18.1911150473704[/C][C]44[/C][/ROW]
[ROW][C]7[/C][C]159[/C][C]14.7648230602334[/C][C]33[/C][/ROW]
[ROW][C]8[/C][C]187[/C][C]14.0712472794703[/C][C]27[/C][/ROW]
[ROW][C]9[/C][C]164.5[/C][C]15.6098259652908[/C][C]38[/C][/ROW]
[ROW][C]10[/C][C]181.25[/C][C]9.03234926989282[/C][C]22[/C][/ROW]
[ROW][C]11[/C][C]218.25[/C][C]25.4607541129480[/C][C]59[/C][/ROW]
[ROW][C]12[/C][C]191.5[/C][C]15.1986841535707[/C][C]37[/C][/ROW]
[ROW][C]13[/C][C]215.75[/C][C]22.8089894559141[/C][C]40[/C][/ROW]
[ROW][C]14[/C][C]252[/C][C]19.6129209111409[/C][C]43[/C][/ROW]
[ROW][C]15[/C][C]207.25[/C][C]23.6696007570892[/C][C]57[/C][/ROW]
[ROW][C]16[/C][C]213.5[/C][C]21.4864298259778[/C][C]47[/C][/ROW]
[ROW][C]17[/C][C]273.25[/C][C]30.7828415409191[/C][C]68[/C][/ROW]
[ROW][C]18[/C][C]230[/C][C]22.8910462845192[/C][C]56[/C][/ROW]
[ROW][C]19[/C][C]252.75[/C][C]18.0069431053691[/C][C]36[/C][/ROW]
[ROW][C]20[/C][C]324[/C][C]41.3360214179675[/C][C]94[/C][/ROW]
[ROW][C]21[/C][C]275.25[/C][C]30.6743649757687[/C][C]75[/C][/ROW]
[ROW][C]22[/C][C]297.75[/C][C]20.1886932051912[/C][C]40[/C][/ROW]
[ROW][C]23[/C][C]377.5[/C][C]43.08518693627[/C][C]95[/C][/ROW]
[ROW][C]24[/C][C]309.5[/C][C]34.5301800362137[/C][C]84[/C][/ROW]
[ROW][C]25[/C][C]330[/C][C]26.2424592343528[/C][C]55[/C][/ROW]
[ROW][C]26[/C][C]427.25[/C][C]52.4491817540242[/C][C]112[/C][/ROW]
[ROW][C]27[/C][C]348[/C][C]41.3521462562707[/C][C]99[/C][/ROW]
[ROW][C]28[/C][C]342[/C][C]18.4028983224563[/C][C]44[/C][/ROW]
[ROW][C]29[/C][C]448.5[/C][C]64.5264803523845[/C][C]142[/C][/ROW]
[ROW][C]30[/C][C]352.5[/C][C]39.7534065626247[/C][C]94[/C][/ROW]
[ROW][C]31[/C][C]376[/C][C]30.0665927567458[/C][C]64[/C][/ROW]
[ROW][C]32[/C][C]499.75[/C][C]65.7488909919146[/C][C]139[/C][/ROW]
[ROW][C]33[/C][C]409.25[/C][C]41.4115523334572[/C][C]101[/C][/ROW]
[ROW][C]34[/C][C]422[/C][C]28.9597421719646[/C][C]70[/C][/ROW]
[ROW][C]35[/C][C]558.75[/C][C]69.0959477827752[/C][C]150[/C][/ROW]
[ROW][C]36[/C][C]447.75[/C][C]49.6277811983033[/C][C]118[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25761&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25761&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	122.75	9.35859676091097	20
2	138	12.8840987267251	27
3	119.25	13.0989821487524	32
4	126.75	13.2256064763272	26
5	153.5	21.4242852856285	45
6	136.25	18.1911150473704	44
7	159	14.7648230602334	33
8	187	14.0712472794703	27
9	164.5	15.6098259652908	38
10	181.25	9.03234926989282	22
11	218.25	25.4607541129480	59
12	191.5	15.1986841535707	37
13	215.75	22.8089894559141	40
14	252	19.6129209111409	43
15	207.25	23.6696007570892	57
16	213.5	21.4864298259778	47
17	273.25	30.7828415409191	68
18	230	22.8910462845192	56
19	252.75	18.0069431053691	36
20	324	41.3360214179675	94
21	275.25	30.6743649757687	75
22	297.75	20.1886932051912	40
23	377.5	43.08518693627	95
24	309.5	34.5301800362137	84
25	330	26.2424592343528	55
26	427.25	52.4491817540242	112
27	348	41.3521462562707	99
28	342	18.4028983224563	44
29	448.5	64.5264803523845	142
30	352.5	39.7534065626247	94
31	376	30.0665927567458	64
32	499.75	65.7488909919146	139
33	409.25	41.4115523334572	101
34	422	28.9597421719646	70
35	558.75	69.0959477827752	150
36	447.75	49.6277811983033	118

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-5.54239894795836
beta	0.122772237859216
S.D.	0.0103647408861152
T-STAT	11.8451815832352
p-value	1.28818972329776e-13

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -5.54239894795836 \tabularnewline
beta & 0.122772237859216 \tabularnewline
S.D. & 0.0103647408861152 \tabularnewline
T-STAT & 11.8451815832352 \tabularnewline
p-value & 1.28818972329776e-13 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25761&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.54239894795836[/C][/ROW]
[ROW][C]beta[/C][C]0.122772237859216[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0103647408861152[/C][/ROW]
[ROW][C]T-STAT[/C][C]11.8451815832352[/C][/ROW]
[ROW][C]p-value[/C][C]1.28818972329776e-13[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25761&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25761&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	-5.54239894795836
beta	0.122772237859216
S.D.	0.0103647408861152
T-STAT	11.8451815832352
p-value	1.28818972329776e-13

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-2.80152129946416
beta	1.08582640187944
S.D.	0.100588602238685
T-STAT	10.7947260197821
p-value	1.58813330658264e-12
Lambda	-0.0858264018794435

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.80152129946416 \tabularnewline
beta & 1.08582640187944 \tabularnewline
S.D. & 0.100588602238685 \tabularnewline
T-STAT & 10.7947260197821 \tabularnewline
p-value & 1.58813330658264e-12 \tabularnewline
Lambda & -0.0858264018794435 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25761&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.80152129946416[/C][/ROW]
[ROW][C]beta[/C][C]1.08582640187944[/C][/ROW]
[ROW][C]S.D.[/C][C]0.100588602238685[/C][/ROW]
[ROW][C]T-STAT[/C][C]10.7947260197821[/C][/ROW]
[ROW][C]p-value[/C][C]1.58813330658264e-12[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0858264018794435[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25761&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25761&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	-2.80152129946416
beta	1.08582640187944
S.D.	0.100588602238685
T-STAT	10.7947260197821
p-value	1.58813330658264e-12
Lambda	-0.0858264018794435

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code