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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, 10 May 2011 14:06:22 +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/May/10/t1305036255rs7chir29n2p7gl.htm/, Retrieved Mon, 13 May 2024 13:18:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121402, Retrieved Mon, 13 May 2024 13:18:12 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

117

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

-       [Standard Deviation-Mean Plot] [Standaarddeviatie...] [2011-05-10 14:06:22] [aa971e749556000e4c6ae2b60b566045] [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	2 seconds
R Server	'Gwilym Jenkins' @ www.wessa.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121402&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121402&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121402&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	2 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	470.5	6.85565460040104	15
2	488.25	37.9594081443147	70
3	515.75	6.39661368746516	14
4	513.75	4.99165971062398	10
5	539.25	41.0233673248146	79
6	561.25	13.3759734848222	31
7	555.5	8.2663978450915	18
8	571.25	36.8272996566406	74
9	603.25	10.1447851956888	19
10	584.25	8.05708797684788	18
11	596.5	33.0807093837683	62
12	608	15.3405779986718	33
13	584.25	8.80814017448254	19
14	598	28.9712501168544	53
15	587.75	23.3005722390388	54
16	542	15.9791530856092	35
17	532.5	32.3882694814033	66
18	523.25	14.4539498638492	32
19	502	12.7279220613579	27
20	502.25	33.4900482730816	65
21	510.5	7.72442015083764	16
22	533.5	4.04145188432738	9
23	561	36.3593179253957	73
24	569.5	10.4083299973307	23
25	567.5	12.5565388012249	28
26	571.75	35.6779577143461	67
27	562.5	17.019596548293	37

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 470.5 & 6.85565460040104 & 15 \tabularnewline
2 & 488.25 & 37.9594081443147 & 70 \tabularnewline
3 & 515.75 & 6.39661368746516 & 14 \tabularnewline
4 & 513.75 & 4.99165971062398 & 10 \tabularnewline
5 & 539.25 & 41.0233673248146 & 79 \tabularnewline
6 & 561.25 & 13.3759734848222 & 31 \tabularnewline
7 & 555.5 & 8.2663978450915 & 18 \tabularnewline
8 & 571.25 & 36.8272996566406 & 74 \tabularnewline
9 & 603.25 & 10.1447851956888 & 19 \tabularnewline
10 & 584.25 & 8.05708797684788 & 18 \tabularnewline
11 & 596.5 & 33.0807093837683 & 62 \tabularnewline
12 & 608 & 15.3405779986718 & 33 \tabularnewline
13 & 584.25 & 8.80814017448254 & 19 \tabularnewline
14 & 598 & 28.9712501168544 & 53 \tabularnewline
15 & 587.75 & 23.3005722390388 & 54 \tabularnewline
16 & 542 & 15.9791530856092 & 35 \tabularnewline
17 & 532.5 & 32.3882694814033 & 66 \tabularnewline
18 & 523.25 & 14.4539498638492 & 32 \tabularnewline
19 & 502 & 12.7279220613579 & 27 \tabularnewline
20 & 502.25 & 33.4900482730816 & 65 \tabularnewline
21 & 510.5 & 7.72442015083764 & 16 \tabularnewline
22 & 533.5 & 4.04145188432738 & 9 \tabularnewline
23 & 561 & 36.3593179253957 & 73 \tabularnewline
24 & 569.5 & 10.4083299973307 & 23 \tabularnewline
25 & 567.5 & 12.5565388012249 & 28 \tabularnewline
26 & 571.75 & 35.6779577143461 & 67 \tabularnewline
27 & 562.5 & 17.019596548293 & 37 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121402&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]470.5[/C][C]6.85565460040104[/C][C]15[/C][/ROW]
[ROW][C]2[/C][C]488.25[/C][C]37.9594081443147[/C][C]70[/C][/ROW]
[ROW][C]3[/C][C]515.75[/C][C]6.39661368746516[/C][C]14[/C][/ROW]
[ROW][C]4[/C][C]513.75[/C][C]4.99165971062398[/C][C]10[/C][/ROW]
[ROW][C]5[/C][C]539.25[/C][C]41.0233673248146[/C][C]79[/C][/ROW]
[ROW][C]6[/C][C]561.25[/C][C]13.3759734848222[/C][C]31[/C][/ROW]
[ROW][C]7[/C][C]555.5[/C][C]8.2663978450915[/C][C]18[/C][/ROW]
[ROW][C]8[/C][C]571.25[/C][C]36.8272996566406[/C][C]74[/C][/ROW]
[ROW][C]9[/C][C]603.25[/C][C]10.1447851956888[/C][C]19[/C][/ROW]
[ROW][C]10[/C][C]584.25[/C][C]8.05708797684788[/C][C]18[/C][/ROW]
[ROW][C]11[/C][C]596.5[/C][C]33.0807093837683[/C][C]62[/C][/ROW]
[ROW][C]12[/C][C]608[/C][C]15.3405779986718[/C][C]33[/C][/ROW]
[ROW][C]13[/C][C]584.25[/C][C]8.80814017448254[/C][C]19[/C][/ROW]
[ROW][C]14[/C][C]598[/C][C]28.9712501168544[/C][C]53[/C][/ROW]
[ROW][C]15[/C][C]587.75[/C][C]23.3005722390388[/C][C]54[/C][/ROW]
[ROW][C]16[/C][C]542[/C][C]15.9791530856092[/C][C]35[/C][/ROW]
[ROW][C]17[/C][C]532.5[/C][C]32.3882694814033[/C][C]66[/C][/ROW]
[ROW][C]18[/C][C]523.25[/C][C]14.4539498638492[/C][C]32[/C][/ROW]
[ROW][C]19[/C][C]502[/C][C]12.7279220613579[/C][C]27[/C][/ROW]
[ROW][C]20[/C][C]502.25[/C][C]33.4900482730816[/C][C]65[/C][/ROW]
[ROW][C]21[/C][C]510.5[/C][C]7.72442015083764[/C][C]16[/C][/ROW]
[ROW][C]22[/C][C]533.5[/C][C]4.04145188432738[/C][C]9[/C][/ROW]
[ROW][C]23[/C][C]561[/C][C]36.3593179253957[/C][C]73[/C][/ROW]
[ROW][C]24[/C][C]569.5[/C][C]10.4083299973307[/C][C]23[/C][/ROW]
[ROW][C]25[/C][C]567.5[/C][C]12.5565388012249[/C][C]28[/C][/ROW]
[ROW][C]26[/C][C]571.75[/C][C]35.6779577143461[/C][C]67[/C][/ROW]
[ROW][C]27[/C][C]562.5[/C][C]17.019596548293[/C][C]37[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121402&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121402&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	470.5	6.85565460040104	15
2	488.25	37.9594081443147	70
3	515.75	6.39661368746516	14
4	513.75	4.99165971062398	10
5	539.25	41.0233673248146	79
6	561.25	13.3759734848222	31
7	555.5	8.2663978450915	18
8	571.25	36.8272996566406	74
9	603.25	10.1447851956888	19
10	584.25	8.05708797684788	18
11	596.5	33.0807093837683	62
12	608	15.3405779986718	33
13	584.25	8.80814017448254	19
14	598	28.9712501168544	53
15	587.75	23.3005722390388	54
16	542	15.9791530856092	35
17	532.5	32.3882694814033	66
18	523.25	14.4539498638492	32
19	502	12.7279220613579	27
20	502.25	33.4900482730816	65
21	510.5	7.72442015083764	16
22	533.5	4.04145188432738	9
23	561	36.3593179253957	73
24	569.5	10.4083299973307	23
25	567.5	12.5565388012249	28
26	571.75	35.6779577143461	67
27	562.5	17.019596548293	37

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	2.59424335376658
beta	0.0300342885936344
S.D.	0.065328677394248
T-STAT	0.459741262055289
p-value	0.64967513230144

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.59424335376658 \tabularnewline
beta & 0.0300342885936344 \tabularnewline
S.D. & 0.065328677394248 \tabularnewline
T-STAT & 0.459741262055289 \tabularnewline
p-value & 0.64967513230144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121402&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.59424335376658[/C][/ROW]
[ROW][C]beta[/C][C]0.0300342885936344[/C][/ROW]
[ROW][C]S.D.[/C][C]0.065328677394248[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.459741262055289[/C][/ROW]
[ROW][C]p-value[/C][C]0.64967513230144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121402&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121402&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	2.59424335376658
beta	0.0300342885936344
S.D.	0.065328677394248
T-STAT	0.459741262055289
p-value	0.64967513230144

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-9.22062150223519
beta	1.89425444969994
S.D.	1.98993625125974
T-STAT	0.951917152371474
p-value	0.35025236145121
Lambda	-0.894254449699935

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -9.22062150223519 \tabularnewline
beta & 1.89425444969994 \tabularnewline
S.D. & 1.98993625125974 \tabularnewline
T-STAT & 0.951917152371474 \tabularnewline
p-value & 0.35025236145121 \tabularnewline
Lambda & -0.894254449699935 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121402&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-9.22062150223519[/C][/ROW]
[ROW][C]beta[/C][C]1.89425444969994[/C][/ROW]
[ROW][C]S.D.[/C][C]1.98993625125974[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.951917152371474[/C][/ROW]
[ROW][C]p-value[/C][C]0.35025236145121[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.894254449699935[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121402&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121402&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	-9.22062150223519
beta	1.89425444969994
S.D.	1.98993625125974
T-STAT	0.951917152371474
p-value	0.35025236145121
Lambda	-0.894254449699935

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