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Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Thu, 28 May 2009 08:44:49 -0600

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/2009/May/28/t1243522371xti39vdjtnzdbh7.htm/, Retrieved Mon, 06 May 2024 01:53:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40641, Retrieved Mon, 06 May 2024 01:53:40 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

167

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

-     [Univariate Data Series] [Datareeks-Werkloo...] [2009-02-15 13:51:16] [74be16979710d4c4e7c6647856088456]
- RMP   [Variability] [Robin Bosmans- Da...] [2009-05-28 09:34:32] [b9edf9f086957f8eb4568189a646cc4d]
- RMP       [Standard Deviation-Mean Plot] [Robin Bosmans-Dat...] [2009-05-28 14:44:49] [f565a348fef35d164bc634b6b1fffd89] [Current]

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Boxplots

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=40641&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=40641&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40641&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	454.5	10.9696551146029	24
2	465.25	38.2219395984383	79
3	489.5	21.7485631709315	42
4	470.5	6.85565460040104	15
5	488.25	37.9594081443147	70
6	515.75	6.39661368746516	14
7	513.75	4.99165971062398	10
8	539.25	41.0233673248146	79
9	561.25	13.3759734848222	31
10	555.5	8.2663978450915	18
11	571.25	36.8272996566406	74
12	603.25	10.1447851956888	19
13	584.25	8.05708797684788	18
14	596.5	33.0807093837683	62
15	608	15.3405779986718	33
16	584.25	8.80814017448254	19
17	598	28.9712501168544	53
18	582.75	28.0401497856199	63
19	542	15.9791530856092	35
20	532.5	32.3882694814033	66
21	523.25	14.4539498638492	32
22	502	12.7279220613579	27
23	502.25	33.4900482730816	65
24	510.5	7.72442015083764	16

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 454.5 & 10.9696551146029 & 24 \tabularnewline
2 & 465.25 & 38.2219395984383 & 79 \tabularnewline
3 & 489.5 & 21.7485631709315 & 42 \tabularnewline
4 & 470.5 & 6.85565460040104 & 15 \tabularnewline
5 & 488.25 & 37.9594081443147 & 70 \tabularnewline
6 & 515.75 & 6.39661368746516 & 14 \tabularnewline
7 & 513.75 & 4.99165971062398 & 10 \tabularnewline
8 & 539.25 & 41.0233673248146 & 79 \tabularnewline
9 & 561.25 & 13.3759734848222 & 31 \tabularnewline
10 & 555.5 & 8.2663978450915 & 18 \tabularnewline
11 & 571.25 & 36.8272996566406 & 74 \tabularnewline
12 & 603.25 & 10.1447851956888 & 19 \tabularnewline
13 & 584.25 & 8.05708797684788 & 18 \tabularnewline
14 & 596.5 & 33.0807093837683 & 62 \tabularnewline
15 & 608 & 15.3405779986718 & 33 \tabularnewline
16 & 584.25 & 8.80814017448254 & 19 \tabularnewline
17 & 598 & 28.9712501168544 & 53 \tabularnewline
18 & 582.75 & 28.0401497856199 & 63 \tabularnewline
19 & 542 & 15.9791530856092 & 35 \tabularnewline
20 & 532.5 & 32.3882694814033 & 66 \tabularnewline
21 & 523.25 & 14.4539498638492 & 32 \tabularnewline
22 & 502 & 12.7279220613579 & 27 \tabularnewline
23 & 502.25 & 33.4900482730816 & 65 \tabularnewline
24 & 510.5 & 7.72442015083764 & 16 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40641&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]454.5[/C][C]10.9696551146029[/C][C]24[/C][/ROW]
[ROW][C]2[/C][C]465.25[/C][C]38.2219395984383[/C][C]79[/C][/ROW]
[ROW][C]3[/C][C]489.5[/C][C]21.7485631709315[/C][C]42[/C][/ROW]
[ROW][C]4[/C][C]470.5[/C][C]6.85565460040104[/C][C]15[/C][/ROW]
[ROW][C]5[/C][C]488.25[/C][C]37.9594081443147[/C][C]70[/C][/ROW]
[ROW][C]6[/C][C]515.75[/C][C]6.39661368746516[/C][C]14[/C][/ROW]
[ROW][C]7[/C][C]513.75[/C][C]4.99165971062398[/C][C]10[/C][/ROW]
[ROW][C]8[/C][C]539.25[/C][C]41.0233673248146[/C][C]79[/C][/ROW]
[ROW][C]9[/C][C]561.25[/C][C]13.3759734848222[/C][C]31[/C][/ROW]
[ROW][C]10[/C][C]555.5[/C][C]8.2663978450915[/C][C]18[/C][/ROW]
[ROW][C]11[/C][C]571.25[/C][C]36.8272996566406[/C][C]74[/C][/ROW]
[ROW][C]12[/C][C]603.25[/C][C]10.1447851956888[/C][C]19[/C][/ROW]
[ROW][C]13[/C][C]584.25[/C][C]8.05708797684788[/C][C]18[/C][/ROW]
[ROW][C]14[/C][C]596.5[/C][C]33.0807093837683[/C][C]62[/C][/ROW]
[ROW][C]15[/C][C]608[/C][C]15.3405779986718[/C][C]33[/C][/ROW]
[ROW][C]16[/C][C]584.25[/C][C]8.80814017448254[/C][C]19[/C][/ROW]
[ROW][C]17[/C][C]598[/C][C]28.9712501168544[/C][C]53[/C][/ROW]
[ROW][C]18[/C][C]582.75[/C][C]28.0401497856199[/C][C]63[/C][/ROW]
[ROW][C]19[/C][C]542[/C][C]15.9791530856092[/C][C]35[/C][/ROW]
[ROW][C]20[/C][C]532.5[/C][C]32.3882694814033[/C][C]66[/C][/ROW]
[ROW][C]21[/C][C]523.25[/C][C]14.4539498638492[/C][C]32[/C][/ROW]
[ROW][C]22[/C][C]502[/C][C]12.7279220613579[/C][C]27[/C][/ROW]
[ROW][C]23[/C][C]502.25[/C][C]33.4900482730816[/C][C]65[/C][/ROW]
[ROW][C]24[/C][C]510.5[/C][C]7.72442015083764[/C][C]16[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40641&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40641&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	454.5	10.9696551146029	24
2	465.25	38.2219395984383	79
3	489.5	21.7485631709315	42
4	470.5	6.85565460040104	15
5	488.25	37.9594081443147	70
6	515.75	6.39661368746516	14
7	513.75	4.99165971062398	10
8	539.25	41.0233673248146	79
9	561.25	13.3759734848222	31
10	555.5	8.2663978450915	18
11	571.25	36.8272996566406	74
12	603.25	10.1447851956888	19
13	584.25	8.05708797684788	18
14	596.5	33.0807093837683	62
15	608	15.3405779986718	33
16	584.25	8.80814017448254	19
17	598	28.9712501168544	53
18	582.75	28.0401497856199	63
19	542	15.9791530856092	35
20	532.5	32.3882694814033	66
21	523.25	14.4539498638492	32
22	502	12.7279220613579	27
23	502.25	33.4900482730816	65
24	510.5	7.72442015083764	16

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	20.1855623489394
beta	-0.00066777831113293
S.D.	0.0561387830997442
T-STAT	-0.0118951333509752
p-value	0.990616492614581

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 20.1855623489394 \tabularnewline
beta & -0.00066777831113293 \tabularnewline
S.D. & 0.0561387830997442 \tabularnewline
T-STAT & -0.0118951333509752 \tabularnewline
p-value & 0.990616492614581 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40641&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]20.1855623489394[/C][/ROW]
[ROW][C]beta[/C][C]-0.00066777831113293[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0561387830997442[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0118951333509752[/C][/ROW]
[ROW][C]p-value[/C][C]0.990616492614581[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40641&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40641&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	20.1855623489394
beta	-0.00066777831113293
S.D.	0.0561387830997442
T-STAT	-0.0118951333509752
p-value	0.990616492614581

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.214509123891609
beta	0.408186362421121
S.D.	1.63773237931207
T-STAT	0.249238744728598
p-value	0.805488352685408
Lambda	0.59181363757888

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.214509123891609 \tabularnewline
beta & 0.408186362421121 \tabularnewline
S.D. & 1.63773237931207 \tabularnewline
T-STAT & 0.249238744728598 \tabularnewline
p-value & 0.805488352685408 \tabularnewline
Lambda & 0.59181363757888 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40641&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.214509123891609[/C][/ROW]
[ROW][C]beta[/C][C]0.408186362421121[/C][/ROW]
[ROW][C]S.D.[/C][C]1.63773237931207[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.249238744728598[/C][/ROW]
[ROW][C]p-value[/C][C]0.805488352685408[/C][/ROW]
[ROW][C]Lambda[/C][C]0.59181363757888[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40641&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40641&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	0.214509123891609
beta	0.408186362421121
S.D.	1.63773237931207
T-STAT	0.249238744728598
p-value	0.805488352685408
Lambda	0.59181363757888

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code