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*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Sun, 18 Dec 2011 11:40:42 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/18/t1324226476v4r0ewu59fdogxw.htm/, Retrieved Sun, 05 May 2024 16:58:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157067, Retrieved Sun, 05 May 2024 16:58:42 +0000

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

-       [Standard Deviation-Mean Plot] [] [2011-12-18 16:40:42] [c8f7c4812ba63eaa5bf379ee3b4bd6a3] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157067&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157067&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157067&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	'Gwilym Jenkins' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	186.463	5.30096360022488	13.398
2	197.554583333333	4.00804612245131	10.861
3	215.142416666667	6.97304561681927	18.102
4	227.63025	3.0441065602242	9.58799999999999
5	235.165583333333	2.69919747192091	7.85400000000001
6	241.790166666667	2.83185309818447	9.01700000000002
7	243.663	2.52078465417561	9.137
8	245.424083333333	1.21349693473287	4.19499999999999
9	247.580416666667	3.15059880191148	11.203
10	252.352833333333	2.94786304212925	9.89800000000002
11	257.373833333333	2.98291370165399	11.297
12	260.974333333333	1.96001541428695	7.57900000000001
13	265.824	2.7259829586608	8.01900000000001
14	268.858916666667	2.66300109098853	8.30400000000003
15	269.192416666667	2.76634719632336	8.66300000000001
16	272.554083333333	2.20848337340494	7.50299999999999
17	278.226	5.61605581427845	19.703
18	288.621666666667	2.73645840568802	11.216
19	318.95825	6.80888264929116	20.401
20	333.106833333333	7.8427201198811	25.196
21	346.353833333333	5.28287791460356	18.205

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 186.463 & 5.30096360022488 & 13.398 \tabularnewline
2 & 197.554583333333 & 4.00804612245131 & 10.861 \tabularnewline
3 & 215.142416666667 & 6.97304561681927 & 18.102 \tabularnewline
4 & 227.63025 & 3.0441065602242 & 9.58799999999999 \tabularnewline
5 & 235.165583333333 & 2.69919747192091 & 7.85400000000001 \tabularnewline
6 & 241.790166666667 & 2.83185309818447 & 9.01700000000002 \tabularnewline
7 & 243.663 & 2.52078465417561 & 9.137 \tabularnewline
8 & 245.424083333333 & 1.21349693473287 & 4.19499999999999 \tabularnewline
9 & 247.580416666667 & 3.15059880191148 & 11.203 \tabularnewline
10 & 252.352833333333 & 2.94786304212925 & 9.89800000000002 \tabularnewline
11 & 257.373833333333 & 2.98291370165399 & 11.297 \tabularnewline
12 & 260.974333333333 & 1.96001541428695 & 7.57900000000001 \tabularnewline
13 & 265.824 & 2.7259829586608 & 8.01900000000001 \tabularnewline
14 & 268.858916666667 & 2.66300109098853 & 8.30400000000003 \tabularnewline
15 & 269.192416666667 & 2.76634719632336 & 8.66300000000001 \tabularnewline
16 & 272.554083333333 & 2.20848337340494 & 7.50299999999999 \tabularnewline
17 & 278.226 & 5.61605581427845 & 19.703 \tabularnewline
18 & 288.621666666667 & 2.73645840568802 & 11.216 \tabularnewline
19 & 318.95825 & 6.80888264929116 & 20.401 \tabularnewline
20 & 333.106833333333 & 7.8427201198811 & 25.196 \tabularnewline
21 & 346.353833333333 & 5.28287791460356 & 18.205 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157067&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]186.463[/C][C]5.30096360022488[/C][C]13.398[/C][/ROW]
[ROW][C]2[/C][C]197.554583333333[/C][C]4.00804612245131[/C][C]10.861[/C][/ROW]
[ROW][C]3[/C][C]215.142416666667[/C][C]6.97304561681927[/C][C]18.102[/C][/ROW]
[ROW][C]4[/C][C]227.63025[/C][C]3.0441065602242[/C][C]9.58799999999999[/C][/ROW]
[ROW][C]5[/C][C]235.165583333333[/C][C]2.69919747192091[/C][C]7.85400000000001[/C][/ROW]
[ROW][C]6[/C][C]241.790166666667[/C][C]2.83185309818447[/C][C]9.01700000000002[/C][/ROW]
[ROW][C]7[/C][C]243.663[/C][C]2.52078465417561[/C][C]9.137[/C][/ROW]
[ROW][C]8[/C][C]245.424083333333[/C][C]1.21349693473287[/C][C]4.19499999999999[/C][/ROW]
[ROW][C]9[/C][C]247.580416666667[/C][C]3.15059880191148[/C][C]11.203[/C][/ROW]
[ROW][C]10[/C][C]252.352833333333[/C][C]2.94786304212925[/C][C]9.89800000000002[/C][/ROW]
[ROW][C]11[/C][C]257.373833333333[/C][C]2.98291370165399[/C][C]11.297[/C][/ROW]
[ROW][C]12[/C][C]260.974333333333[/C][C]1.96001541428695[/C][C]7.57900000000001[/C][/ROW]
[ROW][C]13[/C][C]265.824[/C][C]2.7259829586608[/C][C]8.01900000000001[/C][/ROW]
[ROW][C]14[/C][C]268.858916666667[/C][C]2.66300109098853[/C][C]8.30400000000003[/C][/ROW]
[ROW][C]15[/C][C]269.192416666667[/C][C]2.76634719632336[/C][C]8.66300000000001[/C][/ROW]
[ROW][C]16[/C][C]272.554083333333[/C][C]2.20848337340494[/C][C]7.50299999999999[/C][/ROW]
[ROW][C]17[/C][C]278.226[/C][C]5.61605581427845[/C][C]19.703[/C][/ROW]
[ROW][C]18[/C][C]288.621666666667[/C][C]2.73645840568802[/C][C]11.216[/C][/ROW]
[ROW][C]19[/C][C]318.95825[/C][C]6.80888264929116[/C][C]20.401[/C][/ROW]
[ROW][C]20[/C][C]333.106833333333[/C][C]7.8427201198811[/C][C]25.196[/C][/ROW]
[ROW][C]21[/C][C]346.353833333333[/C][C]5.28287791460356[/C][C]18.205[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157067&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157067&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	186.463	5.30096360022488	13.398
2	197.554583333333	4.00804612245131	10.861
3	215.142416666667	6.97304561681927	18.102
4	227.63025	3.0441065602242	9.58799999999999
5	235.165583333333	2.69919747192091	7.85400000000001
6	241.790166666667	2.83185309818447	9.01700000000002
7	243.663	2.52078465417561	9.137
8	245.424083333333	1.21349693473287	4.19499999999999
9	247.580416666667	3.15059880191148	11.203
10	252.352833333333	2.94786304212925	9.89800000000002
11	257.373833333333	2.98291370165399	11.297
12	260.974333333333	1.96001541428695	7.57900000000001
13	265.824	2.7259829586608	8.01900000000001
14	268.858916666667	2.66300109098853	8.30400000000003
15	269.192416666667	2.76634719632336	8.66300000000001
16	272.554083333333	2.20848337340494	7.50299999999999
17	278.226	5.61605581427845	19.703
18	288.621666666667	2.73645840568802	11.216
19	318.95825	6.80888264929116	20.401
20	333.106833333333	7.8427201198811	25.196
21	346.353833333333	5.28287791460356	18.205

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.178763898169491
beta	0.0136681171444113
S.D.	0.0100183573139044
T-STAT	1.36430721286427
p-value	0.188414131138202

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.178763898169491 \tabularnewline
beta & 0.0136681171444113 \tabularnewline
S.D. & 0.0100183573139044 \tabularnewline
T-STAT & 1.36430721286427 \tabularnewline
p-value & 0.188414131138202 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157067&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.178763898169491[/C][/ROW]
[ROW][C]beta[/C][C]0.0136681171444113[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0100183573139044[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.36430721286427[/C][/ROW]
[ROW][C]p-value[/C][C]0.188414131138202[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157067&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157067&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	0.178763898169491
beta	0.0136681171444113
S.D.	0.0100183573139044
T-STAT	1.36430721286427
p-value	0.188414131138202

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.76331833811804
beta	0.536029975141226
S.D.	0.687712895264515
T-STAT	0.779438598334053
p-value	0.445322241883591
Lambda	0.463970024858774

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.76331833811804 \tabularnewline
beta & 0.536029975141226 \tabularnewline
S.D. & 0.687712895264515 \tabularnewline
T-STAT & 0.779438598334053 \tabularnewline
p-value & 0.445322241883591 \tabularnewline
Lambda & 0.463970024858774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157067&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.76331833811804[/C][/ROW]
[ROW][C]beta[/C][C]0.536029975141226[/C][/ROW]
[ROW][C]S.D.[/C][C]0.687712895264515[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.779438598334053[/C][/ROW]
[ROW][C]p-value[/C][C]0.445322241883591[/C][/ROW]
[ROW][C]Lambda[/C][C]0.463970024858774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157067&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157067&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	-1.76331833811804
beta	0.536029975141226
S.D.	0.687712895264515
T-STAT	0.779438598334053
p-value	0.445322241883591
Lambda	0.463970024858774

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