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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

Thu, 28 Jul 2011 06:27:55 -0400

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/Jul/28/t1311848915dgs5gsot2qjthuu.htm/, Retrieved Thu, 16 May 2024 22:20:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123194, Retrieved Thu, 16 May 2024 22:20:35 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

vicky koopmans

Estimated Impact

204

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

-       [Standard Deviation-Mean Plot] [tijdreeks1-stap26] [2011-07-28 10:27:55] [30681199eb2b91d06bf445c1ee7d20a2] [Current]

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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' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123194&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' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123194&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123194&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' @ wold.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	5097	17.5689119374726	41
2	5169.25	129.211390106807	268
3	5032.25	14.6144905259586	31
4	4973	56.7274184147313	134
5	4949.75	180.562777633339	383
6	4678.25	38.964727639238	93
7	4650	51.9230199429887	124
8	4572.5	178.442334289447	362
9	4216.25	43.9194338154156	93
10	4159.25	76.7913840653147	176
11	4040.25	235.972279445418	506
12	3559.75	45.8139352890217	103
13	3603.75	75.8084208163359	166
14	3668.25	174.199837351627	372
15	3231.75	85.5155931200075	206
16	3265.25	90.1863810856902	175
17	3304.25	179.395977286746	382
18	2779.75	95.0942514911741	217
19	2823.75	147.255729939449	320
20	2844	250.062658814413	537
21	2257.75	102.115539137456	227
22	2247.5	137.493030126379	299
23	2296.5	225.395208467261	475
24	1767.25	102.193851739394	196
25	1810.75	135.885674986978	290
26	1718	320.229084667003	682
27	971.25	115.147369343232	258
28	992	165.680415257809	393
29	1113.5	233.280232052925	506
30	480.5	104.235310715707	238

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5097 & 17.5689119374726 & 41 \tabularnewline
2 & 5169.25 & 129.211390106807 & 268 \tabularnewline
3 & 5032.25 & 14.6144905259586 & 31 \tabularnewline
4 & 4973 & 56.7274184147313 & 134 \tabularnewline
5 & 4949.75 & 180.562777633339 & 383 \tabularnewline
6 & 4678.25 & 38.964727639238 & 93 \tabularnewline
7 & 4650 & 51.9230199429887 & 124 \tabularnewline
8 & 4572.5 & 178.442334289447 & 362 \tabularnewline
9 & 4216.25 & 43.9194338154156 & 93 \tabularnewline
10 & 4159.25 & 76.7913840653147 & 176 \tabularnewline
11 & 4040.25 & 235.972279445418 & 506 \tabularnewline
12 & 3559.75 & 45.8139352890217 & 103 \tabularnewline
13 & 3603.75 & 75.8084208163359 & 166 \tabularnewline
14 & 3668.25 & 174.199837351627 & 372 \tabularnewline
15 & 3231.75 & 85.5155931200075 & 206 \tabularnewline
16 & 3265.25 & 90.1863810856902 & 175 \tabularnewline
17 & 3304.25 & 179.395977286746 & 382 \tabularnewline
18 & 2779.75 & 95.0942514911741 & 217 \tabularnewline
19 & 2823.75 & 147.255729939449 & 320 \tabularnewline
20 & 2844 & 250.062658814413 & 537 \tabularnewline
21 & 2257.75 & 102.115539137456 & 227 \tabularnewline
22 & 2247.5 & 137.493030126379 & 299 \tabularnewline
23 & 2296.5 & 225.395208467261 & 475 \tabularnewline
24 & 1767.25 & 102.193851739394 & 196 \tabularnewline
25 & 1810.75 & 135.885674986978 & 290 \tabularnewline
26 & 1718 & 320.229084667003 & 682 \tabularnewline
27 & 971.25 & 115.147369343232 & 258 \tabularnewline
28 & 992 & 165.680415257809 & 393 \tabularnewline
29 & 1113.5 & 233.280232052925 & 506 \tabularnewline
30 & 480.5 & 104.235310715707 & 238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123194&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]5097[/C][C]17.5689119374726[/C][C]41[/C][/ROW]
[ROW][C]2[/C][C]5169.25[/C][C]129.211390106807[/C][C]268[/C][/ROW]
[ROW][C]3[/C][C]5032.25[/C][C]14.6144905259586[/C][C]31[/C][/ROW]
[ROW][C]4[/C][C]4973[/C][C]56.7274184147313[/C][C]134[/C][/ROW]
[ROW][C]5[/C][C]4949.75[/C][C]180.562777633339[/C][C]383[/C][/ROW]
[ROW][C]6[/C][C]4678.25[/C][C]38.964727639238[/C][C]93[/C][/ROW]
[ROW][C]7[/C][C]4650[/C][C]51.9230199429887[/C][C]124[/C][/ROW]
[ROW][C]8[/C][C]4572.5[/C][C]178.442334289447[/C][C]362[/C][/ROW]
[ROW][C]9[/C][C]4216.25[/C][C]43.9194338154156[/C][C]93[/C][/ROW]
[ROW][C]10[/C][C]4159.25[/C][C]76.7913840653147[/C][C]176[/C][/ROW]
[ROW][C]11[/C][C]4040.25[/C][C]235.972279445418[/C][C]506[/C][/ROW]
[ROW][C]12[/C][C]3559.75[/C][C]45.8139352890217[/C][C]103[/C][/ROW]
[ROW][C]13[/C][C]3603.75[/C][C]75.8084208163359[/C][C]166[/C][/ROW]
[ROW][C]14[/C][C]3668.25[/C][C]174.199837351627[/C][C]372[/C][/ROW]
[ROW][C]15[/C][C]3231.75[/C][C]85.5155931200075[/C][C]206[/C][/ROW]
[ROW][C]16[/C][C]3265.25[/C][C]90.1863810856902[/C][C]175[/C][/ROW]
[ROW][C]17[/C][C]3304.25[/C][C]179.395977286746[/C][C]382[/C][/ROW]
[ROW][C]18[/C][C]2779.75[/C][C]95.0942514911741[/C][C]217[/C][/ROW]
[ROW][C]19[/C][C]2823.75[/C][C]147.255729939449[/C][C]320[/C][/ROW]
[ROW][C]20[/C][C]2844[/C][C]250.062658814413[/C][C]537[/C][/ROW]
[ROW][C]21[/C][C]2257.75[/C][C]102.115539137456[/C][C]227[/C][/ROW]
[ROW][C]22[/C][C]2247.5[/C][C]137.493030126379[/C][C]299[/C][/ROW]
[ROW][C]23[/C][C]2296.5[/C][C]225.395208467261[/C][C]475[/C][/ROW]
[ROW][C]24[/C][C]1767.25[/C][C]102.193851739394[/C][C]196[/C][/ROW]
[ROW][C]25[/C][C]1810.75[/C][C]135.885674986978[/C][C]290[/C][/ROW]
[ROW][C]26[/C][C]1718[/C][C]320.229084667003[/C][C]682[/C][/ROW]
[ROW][C]27[/C][C]971.25[/C][C]115.147369343232[/C][C]258[/C][/ROW]
[ROW][C]28[/C][C]992[/C][C]165.680415257809[/C][C]393[/C][/ROW]
[ROW][C]29[/C][C]1113.5[/C][C]233.280232052925[/C][C]506[/C][/ROW]
[ROW][C]30[/C][C]480.5[/C][C]104.235310715707[/C][C]238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123194&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123194&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	5097	17.5689119374726	41
2	5169.25	129.211390106807	268
3	5032.25	14.6144905259586	31
4	4973	56.7274184147313	134
5	4949.75	180.562777633339	383
6	4678.25	38.964727639238	93
7	4650	51.9230199429887	124
8	4572.5	178.442334289447	362
9	4216.25	43.9194338154156	93
10	4159.25	76.7913840653147	176
11	4040.25	235.972279445418	506
12	3559.75	45.8139352890217	103
13	3603.75	75.8084208163359	166
14	3668.25	174.199837351627	372
15	3231.75	85.5155931200075	206
16	3265.25	90.1863810856902	175
17	3304.25	179.395977286746	382
18	2779.75	95.0942514911741	217
19	2823.75	147.255729939449	320
20	2844	250.062658814413	537
21	2257.75	102.115539137456	227
22	2247.5	137.493030126379	299
23	2296.5	225.395208467261	475
24	1767.25	102.193851739394	196
25	1810.75	135.885674986978	290
26	1718	320.229084667003	682
27	971.25	115.147369343232	258
28	992	165.680415257809	393
29	1113.5	233.280232052925	506
30	480.5	104.235310715707	238

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	198.267049179984
beta	-0.0222109963660185
S.D.	0.00925532112547739
T-STAT	-2.39980829026857
p-value	0.0232994460349838

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 198.267049179984 \tabularnewline
beta & -0.0222109963660185 \tabularnewline
S.D. & 0.00925532112547739 \tabularnewline
T-STAT & -2.39980829026857 \tabularnewline
p-value & 0.0232994460349838 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123194&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]198.267049179984[/C][/ROW]
[ROW][C]beta[/C][C]-0.0222109963660185[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00925532112547739[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.39980829026857[/C][/ROW]
[ROW][C]p-value[/C][C]0.0232994460349838[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123194&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123194&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	198.267049179984
beta	-0.0222109963660185
S.D.	0.00925532112547739
T-STAT	-2.39980829026857
p-value	0.0232994460349838

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	8.66892480913111
beta	-0.509206265097767
S.D.	0.218136435139374
T-STAT	-2.33434760576527
p-value	0.026977529104012
Lambda	1.50920626509777

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 8.66892480913111 \tabularnewline
beta & -0.509206265097767 \tabularnewline
S.D. & 0.218136435139374 \tabularnewline
T-STAT & -2.33434760576527 \tabularnewline
p-value & 0.026977529104012 \tabularnewline
Lambda & 1.50920626509777 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123194&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.66892480913111[/C][/ROW]
[ROW][C]beta[/C][C]-0.509206265097767[/C][/ROW]
[ROW][C]S.D.[/C][C]0.218136435139374[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.33434760576527[/C][/ROW]
[ROW][C]p-value[/C][C]0.026977529104012[/C][/ROW]
[ROW][C]Lambda[/C][C]1.50920626509777[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123194&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123194&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	8.66892480913111
beta	-0.509206265097767
S.D.	0.218136435139374
T-STAT	-2.33434760576527
p-value	0.026977529104012
Lambda	1.50920626509777

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