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*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Sun, 07 Jun 2009 12:54:55 -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/Jun/07/t1244400930erwv57ihfce134f.htm/, Retrieved Sun, 12 May 2024 16:26:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42233, Retrieved Sun, 12 May 2024 16:26:47 +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] [Thomas Van den Bo...] [2009-06-07 18:54:55] [50e97696ebad247f45d73cd9926afb25] [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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42233&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42233&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42233&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' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	33.4825	3.53561286530827	8.07
2	26.44	1.40085688062700	3.4
3	33.65	1.50222057856583	3.4
4	33.85	0.910164820238619	2.02000000000000
5	28.2375	2.92690251517425	6.18
6	22.5475	2.93879085112681	6.38
7	19.6025	1.03300129073814	2.42
8	22.9275	0.495000000000001	1.05
9	25.9375	3.13260674199619	6.83
10	27	1.26066120217395	2.84
11	25.2425	1.27390148755702	2.9
12	22.435	1.32761691261699	2.59
13	21.8675	0.29848227194704	0.700
14	23.015	0.655718435509227	1.42000000000000
15	22.04	0.930089601418415	2.2
16	14.7325	4.55941059787337	10.65
17	10.9325	2.37272522640107	5.25
18	13.885	0.91726041376845	1.97
19	22.9575	0.735226722401556	1.65000000000000
20	22.435	0.427823951332009	1.04
21	17.495	3.82222884366352	8.02
22	10.1825	2.06029730864261	4.74
23	13.4925	1.00114517761745	1.97

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 33.4825 & 3.53561286530827 & 8.07 \tabularnewline
2 & 26.44 & 1.40085688062700 & 3.4 \tabularnewline
3 & 33.65 & 1.50222057856583 & 3.4 \tabularnewline
4 & 33.85 & 0.910164820238619 & 2.02000000000000 \tabularnewline
5 & 28.2375 & 2.92690251517425 & 6.18 \tabularnewline
6 & 22.5475 & 2.93879085112681 & 6.38 \tabularnewline
7 & 19.6025 & 1.03300129073814 & 2.42 \tabularnewline
8 & 22.9275 & 0.495000000000001 & 1.05 \tabularnewline
9 & 25.9375 & 3.13260674199619 & 6.83 \tabularnewline
10 & 27 & 1.26066120217395 & 2.84 \tabularnewline
11 & 25.2425 & 1.27390148755702 & 2.9 \tabularnewline
12 & 22.435 & 1.32761691261699 & 2.59 \tabularnewline
13 & 21.8675 & 0.29848227194704 & 0.700 \tabularnewline
14 & 23.015 & 0.655718435509227 & 1.42000000000000 \tabularnewline
15 & 22.04 & 0.930089601418415 & 2.2 \tabularnewline
16 & 14.7325 & 4.55941059787337 & 10.65 \tabularnewline
17 & 10.9325 & 2.37272522640107 & 5.25 \tabularnewline
18 & 13.885 & 0.91726041376845 & 1.97 \tabularnewline
19 & 22.9575 & 0.735226722401556 & 1.65000000000000 \tabularnewline
20 & 22.435 & 0.427823951332009 & 1.04 \tabularnewline
21 & 17.495 & 3.82222884366352 & 8.02 \tabularnewline
22 & 10.1825 & 2.06029730864261 & 4.74 \tabularnewline
23 & 13.4925 & 1.00114517761745 & 1.97 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42233&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]33.4825[/C][C]3.53561286530827[/C][C]8.07[/C][/ROW]
[ROW][C]2[/C][C]26.44[/C][C]1.40085688062700[/C][C]3.4[/C][/ROW]
[ROW][C]3[/C][C]33.65[/C][C]1.50222057856583[/C][C]3.4[/C][/ROW]
[ROW][C]4[/C][C]33.85[/C][C]0.910164820238619[/C][C]2.02000000000000[/C][/ROW]
[ROW][C]5[/C][C]28.2375[/C][C]2.92690251517425[/C][C]6.18[/C][/ROW]
[ROW][C]6[/C][C]22.5475[/C][C]2.93879085112681[/C][C]6.38[/C][/ROW]
[ROW][C]7[/C][C]19.6025[/C][C]1.03300129073814[/C][C]2.42[/C][/ROW]
[ROW][C]8[/C][C]22.9275[/C][C]0.495000000000001[/C][C]1.05[/C][/ROW]
[ROW][C]9[/C][C]25.9375[/C][C]3.13260674199619[/C][C]6.83[/C][/ROW]
[ROW][C]10[/C][C]27[/C][C]1.26066120217395[/C][C]2.84[/C][/ROW]
[ROW][C]11[/C][C]25.2425[/C][C]1.27390148755702[/C][C]2.9[/C][/ROW]
[ROW][C]12[/C][C]22.435[/C][C]1.32761691261699[/C][C]2.59[/C][/ROW]
[ROW][C]13[/C][C]21.8675[/C][C]0.29848227194704[/C][C]0.700[/C][/ROW]
[ROW][C]14[/C][C]23.015[/C][C]0.655718435509227[/C][C]1.42000000000000[/C][/ROW]
[ROW][C]15[/C][C]22.04[/C][C]0.930089601418415[/C][C]2.2[/C][/ROW]
[ROW][C]16[/C][C]14.7325[/C][C]4.55941059787337[/C][C]10.65[/C][/ROW]
[ROW][C]17[/C][C]10.9325[/C][C]2.37272522640107[/C][C]5.25[/C][/ROW]
[ROW][C]18[/C][C]13.885[/C][C]0.91726041376845[/C][C]1.97[/C][/ROW]
[ROW][C]19[/C][C]22.9575[/C][C]0.735226722401556[/C][C]1.65000000000000[/C][/ROW]
[ROW][C]20[/C][C]22.435[/C][C]0.427823951332009[/C][C]1.04[/C][/ROW]
[ROW][C]21[/C][C]17.495[/C][C]3.82222884366352[/C][C]8.02[/C][/ROW]
[ROW][C]22[/C][C]10.1825[/C][C]2.06029730864261[/C][C]4.74[/C][/ROW]
[ROW][C]23[/C][C]13.4925[/C][C]1.00114517761745[/C][C]1.97[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42233&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42233&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	33.4825	3.53561286530827	8.07
2	26.44	1.40085688062700	3.4
3	33.65	1.50222057856583	3.4
4	33.85	0.910164820238619	2.02000000000000
5	28.2375	2.92690251517425	6.18
6	22.5475	2.93879085112681	6.38
7	19.6025	1.03300129073814	2.42
8	22.9275	0.495000000000001	1.05
9	25.9375	3.13260674199619	6.83
10	27	1.26066120217395	2.84
11	25.2425	1.27390148755702	2.9
12	22.435	1.32761691261699	2.59
13	21.8675	0.29848227194704	0.700
14	23.015	0.655718435509227	1.42000000000000
15	22.04	0.930089601418415	2.2
16	14.7325	4.55941059787337	10.65
17	10.9325	2.37272522640107	5.25
18	13.885	0.91726041376845	1.97
19	22.9575	0.735226722401556	1.65000000000000
20	22.435	0.427823951332009	1.04
21	17.495	3.82222884366352	8.02
22	10.1825	2.06029730864261	4.74
23	13.4925	1.00114517761745	1.97

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	2.02052018073938
beta	-0.0135194176769613
S.D.	0.0390854153609575
T-STAT	-0.345894179506811
p-value	0.732863469932662

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.02052018073938 \tabularnewline
beta & -0.0135194176769613 \tabularnewline
S.D. & 0.0390854153609575 \tabularnewline
T-STAT & -0.345894179506811 \tabularnewline
p-value & 0.732863469932662 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42233&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.02052018073938[/C][/ROW]
[ROW][C]beta[/C][C]-0.0135194176769613[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0390854153609575[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.345894179506811[/C][/ROW]
[ROW][C]p-value[/C][C]0.732863469932662[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42233&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42233&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	2.02052018073938
beta	-0.0135194176769613
S.D.	0.0390854153609575
T-STAT	-0.345894179506811
p-value	0.732863469932662

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	1.03113935881853
beta	-0.240617679273467
S.D.	0.478683348018038
T-STAT	-0.502665656262603
p-value	0.620430165194945
Lambda	1.24061767927347

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.03113935881853 \tabularnewline
beta & -0.240617679273467 \tabularnewline
S.D. & 0.478683348018038 \tabularnewline
T-STAT & -0.502665656262603 \tabularnewline
p-value & 0.620430165194945 \tabularnewline
Lambda & 1.24061767927347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42233&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.03113935881853[/C][/ROW]
[ROW][C]beta[/C][C]-0.240617679273467[/C][/ROW]
[ROW][C]S.D.[/C][C]0.478683348018038[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.502665656262603[/C][/ROW]
[ROW][C]p-value[/C][C]0.620430165194945[/C][/ROW]
[ROW][C]Lambda[/C][C]1.24061767927347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42233&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42233&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	1.03113935881853
beta	-0.240617679273467
S.D.	0.478683348018038
T-STAT	-0.502665656262603
p-value	0.620430165194945
Lambda	1.24061767927347

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code