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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

Sun, 07 Dec 2008 07:06:40 -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/Dec/07/t1228659117xvtl5j2yf723qv4.htm/, Retrieved Sun, 19 May 2024 12:02:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29999, Retrieved Sun, 19 May 2024 12:02:33 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

193

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP     [Standard Deviation-Mean Plot] [] [2008-12-07 14:06:40] [d41d8cd98f00b204e9800998ecf8427e] [Current]
F RM        [Variance Reduction Matrix] [] [2008-12-07 14:22:02] [74be16979710d4c4e7c6647856088456] 
F RMP       [(Partial) Autocorrelation Function] [] [2008-12-07 14:24:22] [74be16979710d4c4e7c6647856088456] 
F RMP       [Spectral Analysis] [] [2008-12-07 14:31:10] [74be16979710d4c4e7c6647856088456] 
F RMP       [(Partial) Autocorrelation Function] [] [2008-12-07 15:05:18] [74be16979710d4c4e7c6647856088456] 
- RMP       [Spectral Analysis] [] [2008-12-07 15:08:41] [74be16979710d4c4e7c6647856088456] 

Feedback Forum

2008-12-13 13:48:00 [Ken Wright] [reply] 
Juist, maar besluit is niet volledig: de beta in de eerste tabel stelt een positieve of negatieve verband voor tussen de SD en het gemiddelde. Hier is dus duidelijk een positief verband. Ook  moet men zien of dat  beta wel significant verschillend is van 0, hier moeten we dan naar de p-waarde zien en deze is kleiner als 0.005 dus beta is significant van 0.  Het positief verband betekent wanneer het gemiddelde stijgt, dat de SD ook stijgt. Als men de grafiek bekijkt ziet men ook een positief verband , als men de outlier van linksboven niet zou meerekenen, dan zou er zelfs nog een groter positief verband zijn. Deze calculator heeft de volgende werking : Deze calculator gaat in dit geval de tijdreeks onderverdelen in de verschillende jaren. Hij berekent voor elk jaar het gemiddelde, de standaardafwijking en de range.
2008-12-14 18:43:40 [Vincent Vanden Poel] [reply] 
Jouw antwoord is juist maar onvolledig. Voor we naar de optimale lambda waarde kijken zien we eerst best naar het standard mean plot om eventueel storende outliers te ontdekken. Hier toont Standard Deviation-Mean plot toont ons een positief lineair verband. Wat wel onrustwekkend is, is de outlier die zich bovenaan bevindt. In dit geval stoort dit niet omdat deze niet volledig links of rechts ligt. Moest dit wel het geval zijn is het best om dit eerst te corrigeren omdat deze een grote storing kan veroorzaken op de helling van de curve.    
In de tabel zien we dat er minder dan 1% kans is dat we ons vergissen bij het verwerpen van de nul hypothese. Maar ook de helling is significant en dus niet aan het toeval te wijten. De optimale lambda voor de transformatie is 0,47. Een waarde van 0,5 zal gemakkelijker zijn voor de verdere uitwerking van de modelvergelijking en dus passen we deze optimale waarde lichtjes aan. Dit kan in dit geval omdat de SD 0,11 is en de lambada dus lichtjes kan schommelen rond de gegeven optimale waarde. 
 

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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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29999&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29999&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29999&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	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	227.733333333333	29.1940010442162	106
2	363.65	36.3267119348834	139.3
3	328.916666666667	93.5458451857438	273.6
4	205.45	30.3247123946491	89.5
5	188.333333333333	27.3773739803621	86
6	181.25	26.1571995999016	85.2
7	353.341666666667	36.2089506346236	110.8
8	285.308333333333	46.6051783766048	138.5
9	275.125	35.0509272345255	108.8
10	285.85	30.7409262296136	86.7
11	460.166666666667	56.0969831198748	147.3
12	373.95	53.1021228817215	150.3
13	385.1	35.1442999387072	115.5
14	471.358333333333	64.2130184808676	179.1
15	394.208333333333	40.6847628018454	138.7
16	407	46.6030432092544	147.6
17	378.575	49.9696839912143	132
18	336.633333333333	51.5290973993129	146.3
19	287.841666666667	33.2699826033054	112.7
20	297.566666666667	30.476438987082	117
21	281.666666666667	40.7140434412173	131.1
22	283.033333333333	28.4860837901065	109
23	408.85	48.934882520271	128.5
24	499.333333333333	37.5159925494408	109.6
25	484.008333333333	48.4390236808249	133.1
26	430.433333333333	37.4665022103584	108.4
27	507.583333333333	53.8722703730919	196.2
28	782.975	48.4555489832973	137.4
29	728.8	53.3077684940777	187
30	685.558333333333	72.5442618285032	222.9
31	604.716666666667	50.4040372360882	144

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 227.733333333333 & 29.1940010442162 & 106 \tabularnewline
2 & 363.65 & 36.3267119348834 & 139.3 \tabularnewline
3 & 328.916666666667 & 93.5458451857438 & 273.6 \tabularnewline
4 & 205.45 & 30.3247123946491 & 89.5 \tabularnewline
5 & 188.333333333333 & 27.3773739803621 & 86 \tabularnewline
6 & 181.25 & 26.1571995999016 & 85.2 \tabularnewline
7 & 353.341666666667 & 36.2089506346236 & 110.8 \tabularnewline
8 & 285.308333333333 & 46.6051783766048 & 138.5 \tabularnewline
9 & 275.125 & 35.0509272345255 & 108.8 \tabularnewline
10 & 285.85 & 30.7409262296136 & 86.7 \tabularnewline
11 & 460.166666666667 & 56.0969831198748 & 147.3 \tabularnewline
12 & 373.95 & 53.1021228817215 & 150.3 \tabularnewline
13 & 385.1 & 35.1442999387072 & 115.5 \tabularnewline
14 & 471.358333333333 & 64.2130184808676 & 179.1 \tabularnewline
15 & 394.208333333333 & 40.6847628018454 & 138.7 \tabularnewline
16 & 407 & 46.6030432092544 & 147.6 \tabularnewline
17 & 378.575 & 49.9696839912143 & 132 \tabularnewline
18 & 336.633333333333 & 51.5290973993129 & 146.3 \tabularnewline
19 & 287.841666666667 & 33.2699826033054 & 112.7 \tabularnewline
20 & 297.566666666667 & 30.476438987082 & 117 \tabularnewline
21 & 281.666666666667 & 40.7140434412173 & 131.1 \tabularnewline
22 & 283.033333333333 & 28.4860837901065 & 109 \tabularnewline
23 & 408.85 & 48.934882520271 & 128.5 \tabularnewline
24 & 499.333333333333 & 37.5159925494408 & 109.6 \tabularnewline
25 & 484.008333333333 & 48.4390236808249 & 133.1 \tabularnewline
26 & 430.433333333333 & 37.4665022103584 & 108.4 \tabularnewline
27 & 507.583333333333 & 53.8722703730919 & 196.2 \tabularnewline
28 & 782.975 & 48.4555489832973 & 137.4 \tabularnewline
29 & 728.8 & 53.3077684940777 & 187 \tabularnewline
30 & 685.558333333333 & 72.5442618285032 & 222.9 \tabularnewline
31 & 604.716666666667 & 50.4040372360882 & 144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29999&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]227.733333333333[/C][C]29.1940010442162[/C][C]106[/C][/ROW]
[ROW][C]2[/C][C]363.65[/C][C]36.3267119348834[/C][C]139.3[/C][/ROW]
[ROW][C]3[/C][C]328.916666666667[/C][C]93.5458451857438[/C][C]273.6[/C][/ROW]
[ROW][C]4[/C][C]205.45[/C][C]30.3247123946491[/C][C]89.5[/C][/ROW]
[ROW][C]5[/C][C]188.333333333333[/C][C]27.3773739803621[/C][C]86[/C][/ROW]
[ROW][C]6[/C][C]181.25[/C][C]26.1571995999016[/C][C]85.2[/C][/ROW]
[ROW][C]7[/C][C]353.341666666667[/C][C]36.2089506346236[/C][C]110.8[/C][/ROW]
[ROW][C]8[/C][C]285.308333333333[/C][C]46.6051783766048[/C][C]138.5[/C][/ROW]
[ROW][C]9[/C][C]275.125[/C][C]35.0509272345255[/C][C]108.8[/C][/ROW]
[ROW][C]10[/C][C]285.85[/C][C]30.7409262296136[/C][C]86.7[/C][/ROW]
[ROW][C]11[/C][C]460.166666666667[/C][C]56.0969831198748[/C][C]147.3[/C][/ROW]
[ROW][C]12[/C][C]373.95[/C][C]53.1021228817215[/C][C]150.3[/C][/ROW]
[ROW][C]13[/C][C]385.1[/C][C]35.1442999387072[/C][C]115.5[/C][/ROW]
[ROW][C]14[/C][C]471.358333333333[/C][C]64.2130184808676[/C][C]179.1[/C][/ROW]
[ROW][C]15[/C][C]394.208333333333[/C][C]40.6847628018454[/C][C]138.7[/C][/ROW]
[ROW][C]16[/C][C]407[/C][C]46.6030432092544[/C][C]147.6[/C][/ROW]
[ROW][C]17[/C][C]378.575[/C][C]49.9696839912143[/C][C]132[/C][/ROW]
[ROW][C]18[/C][C]336.633333333333[/C][C]51.5290973993129[/C][C]146.3[/C][/ROW]
[ROW][C]19[/C][C]287.841666666667[/C][C]33.2699826033054[/C][C]112.7[/C][/ROW]
[ROW][C]20[/C][C]297.566666666667[/C][C]30.476438987082[/C][C]117[/C][/ROW]
[ROW][C]21[/C][C]281.666666666667[/C][C]40.7140434412173[/C][C]131.1[/C][/ROW]
[ROW][C]22[/C][C]283.033333333333[/C][C]28.4860837901065[/C][C]109[/C][/ROW]
[ROW][C]23[/C][C]408.85[/C][C]48.934882520271[/C][C]128.5[/C][/ROW]
[ROW][C]24[/C][C]499.333333333333[/C][C]37.5159925494408[/C][C]109.6[/C][/ROW]
[ROW][C]25[/C][C]484.008333333333[/C][C]48.4390236808249[/C][C]133.1[/C][/ROW]
[ROW][C]26[/C][C]430.433333333333[/C][C]37.4665022103584[/C][C]108.4[/C][/ROW]
[ROW][C]27[/C][C]507.583333333333[/C][C]53.8722703730919[/C][C]196.2[/C][/ROW]
[ROW][C]28[/C][C]782.975[/C][C]48.4555489832973[/C][C]137.4[/C][/ROW]
[ROW][C]29[/C][C]728.8[/C][C]53.3077684940777[/C][C]187[/C][/ROW]
[ROW][C]30[/C][C]685.558333333333[/C][C]72.5442618285032[/C][C]222.9[/C][/ROW]
[ROW][C]31[/C][C]604.716666666667[/C][C]50.4040372360882[/C][C]144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29999&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29999&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	227.733333333333	29.1940010442162	106
2	363.65	36.3267119348834	139.3
3	328.916666666667	93.5458451857438	273.6
4	205.45	30.3247123946491	89.5
5	188.333333333333	27.3773739803621	86
6	181.25	26.1571995999016	85.2
7	353.341666666667	36.2089506346236	110.8
8	285.308333333333	46.6051783766048	138.5
9	275.125	35.0509272345255	108.8
10	285.85	30.7409262296136	86.7
11	460.166666666667	56.0969831198748	147.3
12	373.95	53.1021228817215	150.3
13	385.1	35.1442999387072	115.5
14	471.358333333333	64.2130184808676	179.1
15	394.208333333333	40.6847628018454	138.7
16	407	46.6030432092544	147.6
17	378.575	49.9696839912143	132
18	336.633333333333	51.5290973993129	146.3
19	287.841666666667	33.2699826033054	112.7
20	297.566666666667	30.476438987082	117
21	281.666666666667	40.7140434412173	131.1
22	283.033333333333	28.4860837901065	109
23	408.85	48.934882520271	128.5
24	499.333333333333	37.5159925494408	109.6
25	484.008333333333	48.4390236808249	133.1
26	430.433333333333	37.4665022103584	108.4
27	507.583333333333	53.8722703730919	196.2
28	782.975	48.4555489832973	137.4
29	728.8	53.3077684940777	187
30	685.558333333333	72.5442618285032	222.9
31	604.716666666667	50.4040372360882	144

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	25.0818554501784
beta	0.0488516650103526
S.D.	0.0155384837695400
T-STAT	3.14391453728042
p-value	0.00382792717820021

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 25.0818554501784 \tabularnewline
beta & 0.0488516650103526 \tabularnewline
S.D. & 0.0155384837695400 \tabularnewline
T-STAT & 3.14391453728042 \tabularnewline
p-value & 0.00382792717820021 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29999&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]25.0818554501784[/C][/ROW]
[ROW][C]beta[/C][C]0.0488516650103526[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0155384837695400[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.14391453728042[/C][/ROW]
[ROW][C]p-value[/C][C]0.00382792717820021[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29999&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29999&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	25.0818554501784
beta	0.0488516650103526
S.D.	0.0155384837695400
T-STAT	3.14391453728042
p-value	0.00382792717820021

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.596066412617842
beta	0.532942026074986
S.D.	0.115396834084912
T-STAT	4.61834183148243
p-value	7.31833172336408e-05
Lambda	0.467057973925014

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.596066412617842 \tabularnewline
beta & 0.532942026074986 \tabularnewline
S.D. & 0.115396834084912 \tabularnewline
T-STAT & 4.61834183148243 \tabularnewline
p-value & 7.31833172336408e-05 \tabularnewline
Lambda & 0.467057973925014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29999&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.596066412617842[/C][/ROW]
[ROW][C]beta[/C][C]0.532942026074986[/C][/ROW]
[ROW][C]S.D.[/C][C]0.115396834084912[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.61834183148243[/C][/ROW]
[ROW][C]p-value[/C][C]7.31833172336408e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]0.467057973925014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29999&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29999&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	0.596066412617842
beta	0.532942026074986
S.D.	0.115396834084912
T-STAT	4.61834183148243
p-value	7.31833172336408e-05
Lambda	0.467057973925014

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