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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

Fri, 14 May 2010 16:41:16 +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/2010/May/14/t127385537716k2k7bslfrxon8.htm/, Retrieved Thu, 02 May 2024 17:12:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76000, Retrieved Thu, 02 May 2024 17:12:41 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

166

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

-       [Standard Deviation-Mean Plot] [Standard deviatio...] [2010-05-14 16:41:16] [e8bb75392cb2cf20c26f170b87ccd1b7] [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	5 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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76000&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]5 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=76000&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76000&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	5 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	77.8333333333333	42.6399656034883	118
2	215.833333333333	75.2261036254482	203
3	109.333333333333	46.7061737532274	122
4	258.333333333333	91.430119034521	208
5	115.5	54.0435009968821	148
6	325.833333333333	137.103488893123	353
7	210.833333333333	82.6060933991353	205
8	429.833333333333	154.551501664224	389
9	302.333333333333	134.32746058296	332
10	509.166666666667	188.928999009328	464
11	341	149.485785277397	424
12	637	232.375558095080	571

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 77.8333333333333 & 42.6399656034883 & 118 \tabularnewline
2 & 215.833333333333 & 75.2261036254482 & 203 \tabularnewline
3 & 109.333333333333 & 46.7061737532274 & 122 \tabularnewline
4 & 258.333333333333 & 91.430119034521 & 208 \tabularnewline
5 & 115.5 & 54.0435009968821 & 148 \tabularnewline
6 & 325.833333333333 & 137.103488893123 & 353 \tabularnewline
7 & 210.833333333333 & 82.6060933991353 & 205 \tabularnewline
8 & 429.833333333333 & 154.551501664224 & 389 \tabularnewline
9 & 302.333333333333 & 134.32746058296 & 332 \tabularnewline
10 & 509.166666666667 & 188.928999009328 & 464 \tabularnewline
11 & 341 & 149.485785277397 & 424 \tabularnewline
12 & 637 & 232.375558095080 & 571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76000&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]77.8333333333333[/C][C]42.6399656034883[/C][C]118[/C][/ROW]
[ROW][C]2[/C][C]215.833333333333[/C][C]75.2261036254482[/C][C]203[/C][/ROW]
[ROW][C]3[/C][C]109.333333333333[/C][C]46.7061737532274[/C][C]122[/C][/ROW]
[ROW][C]4[/C][C]258.333333333333[/C][C]91.430119034521[/C][C]208[/C][/ROW]
[ROW][C]5[/C][C]115.5[/C][C]54.0435009968821[/C][C]148[/C][/ROW]
[ROW][C]6[/C][C]325.833333333333[/C][C]137.103488893123[/C][C]353[/C][/ROW]
[ROW][C]7[/C][C]210.833333333333[/C][C]82.6060933991353[/C][C]205[/C][/ROW]
[ROW][C]8[/C][C]429.833333333333[/C][C]154.551501664224[/C][C]389[/C][/ROW]
[ROW][C]9[/C][C]302.333333333333[/C][C]134.32746058296[/C][C]332[/C][/ROW]
[ROW][C]10[/C][C]509.166666666667[/C][C]188.928999009328[/C][C]464[/C][/ROW]
[ROW][C]11[/C][C]341[/C][C]149.485785277397[/C][C]424[/C][/ROW]
[ROW][C]12[/C][C]637[/C][C]232.375558095080[/C][C]571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76000&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76000&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	77.8333333333333	42.6399656034883	118
2	215.833333333333	75.2261036254482	203
3	109.333333333333	46.7061737532274	122
4	258.333333333333	91.430119034521	208
5	115.5	54.0435009968821	148
6	325.833333333333	137.103488893123	353
7	210.833333333333	82.6060933991353	205
8	429.833333333333	154.551501664224	389
9	302.333333333333	134.32746058296	332
10	509.166666666667	188.928999009328	464
11	341	149.485785277397	424
12	637	232.375558095080	571

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	12.4036616739632
beta	0.351157468466459
S.D.	0.0187281706683778
T-STAT	18.7502279151793
p-value	4.02900884933773e-09

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 12.4036616739632 \tabularnewline
beta & 0.351157468466459 \tabularnewline
S.D. & 0.0187281706683778 \tabularnewline
T-STAT & 18.7502279151793 \tabularnewline
p-value & 4.02900884933773e-09 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76000&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]12.4036616739632[/C][/ROW]
[ROW][C]beta[/C][C]0.351157468466459[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0187281706683778[/C][/ROW]
[ROW][C]T-STAT[/C][C]18.7502279151793[/C][/ROW]
[ROW][C]p-value[/C][C]4.02900884933773e-09[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76000&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76000&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	12.4036616739632
beta	0.351157468466459
S.D.	0.0187281706683778
T-STAT	18.7502279151793
p-value	4.02900884933773e-09

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.105226492021323
beta	0.856365049021251
S.D.	0.0492837950018413
T-STAT	17.3761993975760
p-value	8.44660777004667e-09
Lambda	0.143634950978749

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.105226492021323 \tabularnewline
beta & 0.856365049021251 \tabularnewline
S.D. & 0.0492837950018413 \tabularnewline
T-STAT & 17.3761993975760 \tabularnewline
p-value & 8.44660777004667e-09 \tabularnewline
Lambda & 0.143634950978749 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76000&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.105226492021323[/C][/ROW]
[ROW][C]beta[/C][C]0.856365049021251[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0492837950018413[/C][/ROW]
[ROW][C]T-STAT[/C][C]17.3761993975760[/C][/ROW]
[ROW][C]p-value[/C][C]8.44660777004667e-09[/C][/ROW]
[ROW][C]Lambda[/C][C]0.143634950978749[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76000&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76000&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	-0.105226492021323
beta	0.856365049021251
S.D.	0.0492837950018413
T-STAT	17.3761993975760
p-value	8.44660777004667e-09
Lambda	0.143634950978749

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 6 ;

Parameters (R input):

par1 = 6 ;

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