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*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Mon, 28 Apr 2014 11:32:58 -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/2014/Apr/28/t1398699199h7a6l43onnblnc1.htm/, Retrieved Fri, 17 May 2024 04:05:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234693, Retrieved Fri, 17 May 2024 04:05:05 +0000

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Estimated Impact

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

-       [Standard Deviation-Mean Plot] [] [2014-04-28 15:32:58] [7924821bfd3c647737470140bc76edc8] [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	'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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234693&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234693&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234693&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	75.4708333333333	3.31115595946171	10.38
2	79.5275	2.57709887981886	9.33
3	81.7775	3.54307038136032	10.99
4	82.7483333333333	3.1889862548047	10.02
5	83.6633333333333	3.04934965744064	10.58
6	94.1841666666667	6.47130373029245	23.03
7	100.59	5.58585225856766	18.27
8	101.935833333333	6.63111324581234	17.88
9	97.9233333333333	5.51838305259353	16.41
10	95.7666666666667	3.7902442553418	13.42
11	99.9991666666667	4.29010374600838	14.18
12	100.1625	1.88325214359725	5.47
13	108.5425	4.02873570287707	11.17
14	105.648333333333	3.44275743959385	9.47
15	107.0675	2.73415808879908	9.13
16	111.0675	2.98836569807889	9.25
17	113.318333333333	3.56995246551836	12.73
18	121.684166666667	4.76750260205551	15.08

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 75.4708333333333 & 3.31115595946171 & 10.38 \tabularnewline
2 & 79.5275 & 2.57709887981886 & 9.33 \tabularnewline
3 & 81.7775 & 3.54307038136032 & 10.99 \tabularnewline
4 & 82.7483333333333 & 3.1889862548047 & 10.02 \tabularnewline
5 & 83.6633333333333 & 3.04934965744064 & 10.58 \tabularnewline
6 & 94.1841666666667 & 6.47130373029245 & 23.03 \tabularnewline
7 & 100.59 & 5.58585225856766 & 18.27 \tabularnewline
8 & 101.935833333333 & 6.63111324581234 & 17.88 \tabularnewline
9 & 97.9233333333333 & 5.51838305259353 & 16.41 \tabularnewline
10 & 95.7666666666667 & 3.7902442553418 & 13.42 \tabularnewline
11 & 99.9991666666667 & 4.29010374600838 & 14.18 \tabularnewline
12 & 100.1625 & 1.88325214359725 & 5.47 \tabularnewline
13 & 108.5425 & 4.02873570287707 & 11.17 \tabularnewline
14 & 105.648333333333 & 3.44275743959385 & 9.47 \tabularnewline
15 & 107.0675 & 2.73415808879908 & 9.13 \tabularnewline
16 & 111.0675 & 2.98836569807889 & 9.25 \tabularnewline
17 & 113.318333333333 & 3.56995246551836 & 12.73 \tabularnewline
18 & 121.684166666667 & 4.76750260205551 & 15.08 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234693&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]75.4708333333333[/C][C]3.31115595946171[/C][C]10.38[/C][/ROW]
[ROW][C]2[/C][C]79.5275[/C][C]2.57709887981886[/C][C]9.33[/C][/ROW]
[ROW][C]3[/C][C]81.7775[/C][C]3.54307038136032[/C][C]10.99[/C][/ROW]
[ROW][C]4[/C][C]82.7483333333333[/C][C]3.1889862548047[/C][C]10.02[/C][/ROW]
[ROW][C]5[/C][C]83.6633333333333[/C][C]3.04934965744064[/C][C]10.58[/C][/ROW]
[ROW][C]6[/C][C]94.1841666666667[/C][C]6.47130373029245[/C][C]23.03[/C][/ROW]
[ROW][C]7[/C][C]100.59[/C][C]5.58585225856766[/C][C]18.27[/C][/ROW]
[ROW][C]8[/C][C]101.935833333333[/C][C]6.63111324581234[/C][C]17.88[/C][/ROW]
[ROW][C]9[/C][C]97.9233333333333[/C][C]5.51838305259353[/C][C]16.41[/C][/ROW]
[ROW][C]10[/C][C]95.7666666666667[/C][C]3.7902442553418[/C][C]13.42[/C][/ROW]
[ROW][C]11[/C][C]99.9991666666667[/C][C]4.29010374600838[/C][C]14.18[/C][/ROW]
[ROW][C]12[/C][C]100.1625[/C][C]1.88325214359725[/C][C]5.47[/C][/ROW]
[ROW][C]13[/C][C]108.5425[/C][C]4.02873570287707[/C][C]11.17[/C][/ROW]
[ROW][C]14[/C][C]105.648333333333[/C][C]3.44275743959385[/C][C]9.47[/C][/ROW]
[ROW][C]15[/C][C]107.0675[/C][C]2.73415808879908[/C][C]9.13[/C][/ROW]
[ROW][C]16[/C][C]111.0675[/C][C]2.98836569807889[/C][C]9.25[/C][/ROW]
[ROW][C]17[/C][C]113.318333333333[/C][C]3.56995246551836[/C][C]12.73[/C][/ROW]
[ROW][C]18[/C][C]121.684166666667[/C][C]4.76750260205551[/C][C]15.08[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234693&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234693&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	75.4708333333333	3.31115595946171	10.38
2	79.5275	2.57709887981886	9.33
3	81.7775	3.54307038136032	10.99
4	82.7483333333333	3.1889862548047	10.02
5	83.6633333333333	3.04934965744064	10.58
6	94.1841666666667	6.47130373029245	23.03
7	100.59	5.58585225856766	18.27
8	101.935833333333	6.63111324581234	17.88
9	97.9233333333333	5.51838305259353	16.41
10	95.7666666666667	3.7902442553418	13.42
11	99.9991666666667	4.29010374600838	14.18
12	100.1625	1.88325214359725	5.47
13	108.5425	4.02873570287707	11.17
14	105.648333333333	3.44275743959385	9.47
15	107.0675	2.73415808879908	9.13
16	111.0675	2.98836569807889	9.25
17	113.318333333333	3.56995246551836	12.73
18	121.684166666667	4.76750260205551	15.08

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.90182371489844
beta	0.0210885430617622
S.D.	0.0254316761589156
T-STAT	0.829223482163963
p-value	0.419177645520711

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.90182371489844 \tabularnewline
beta & 0.0210885430617622 \tabularnewline
S.D. & 0.0254316761589156 \tabularnewline
T-STAT & 0.829223482163963 \tabularnewline
p-value & 0.419177645520711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234693&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.90182371489844[/C][/ROW]
[ROW][C]beta[/C][C]0.0210885430617622[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0254316761589156[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.829223482163963[/C][/ROW]
[ROW][C]p-value[/C][C]0.419177645520711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234693&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234693&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	1.90182371489844
beta	0.0210885430617622
S.D.	0.0254316761589156
T-STAT	0.829223482163963
p-value	0.419177645520711

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.18379475621089
beta	0.548476602914166
S.D.	0.600257192925118
T-STAT	0.913735994135081
p-value	0.374419991499867
Lambda	0.451523397085834

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.18379475621089 \tabularnewline
beta & 0.548476602914166 \tabularnewline
S.D. & 0.600257192925118 \tabularnewline
T-STAT & 0.913735994135081 \tabularnewline
p-value & 0.374419991499867 \tabularnewline
Lambda & 0.451523397085834 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234693&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.18379475621089[/C][/ROW]
[ROW][C]beta[/C][C]0.548476602914166[/C][/ROW]
[ROW][C]S.D.[/C][C]0.600257192925118[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.913735994135081[/C][/ROW]
[ROW][C]p-value[/C][C]0.374419991499867[/C][/ROW]
[ROW][C]Lambda[/C][C]0.451523397085834[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234693&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234693&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	-1.18379475621089
beta	0.548476602914166
S.D.	0.600257192925118
T-STAT	0.913735994135081
p-value	0.374419991499867
Lambda	0.451523397085834

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code