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*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Mon, 18 Aug 2008 07:12:19 -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/2008/Aug/18/t12190652036xy90puyl5fvu36.htm/, Retrieved Tue, 14 May 2024 17:58:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=14639, Retrieved Tue, 14 May 2024 17:58:29 +0000

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No (this computation is public)

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Estimated Impact

258

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

-       [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-08-18 13:12:19] [b82ef19bb71ab1d2d730136b4505428a] [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	'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14639&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14639&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14639&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	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	95.1525	18.1650862462399	38.9
2	110.7625	24.1120058269734	52.23
3	100.7825	32.7940659012165	77.35
4	99.5325	8.28072209009174	19.6
5	94.2225	26.1476045747980	54.64
6	90.215	33.1873454798663	66.19
7	100.0225	3.52514184111789	7.19
8	108.625	13.982421106518	29.18
9	97.34	4.76220537146394	9.3
10	104.5675	17.7299565237294	41.19
11	129.305	49.0524144835569	94.45
12	97.655	10.1434790218478	23.21
13	130.25	50.2509780999335	108.48
14	129.3025	31.469521101112	66.16
15	119.2475	27.7434188892910	59.27
16	141.715	8.73770564850979	19.7100000000000
17	93.02	24.9402820085633	51.82
18	122.06	35.1872827405963	76.99
19	100.7075	16.0641866170269	34.78
20	100.1	35.9064014719753	84.41
21	108.695	24.8831515956748	56.16
22	137.57	48.7690127027398	101.55
23	141.97	33.2734057970225	74.88
24	117.1175	53.024811409377	117.65

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 95.1525 & 18.1650862462399 & 38.9 \tabularnewline
2 & 110.7625 & 24.1120058269734 & 52.23 \tabularnewline
3 & 100.7825 & 32.7940659012165 & 77.35 \tabularnewline
4 & 99.5325 & 8.28072209009174 & 19.6 \tabularnewline
5 & 94.2225 & 26.1476045747980 & 54.64 \tabularnewline
6 & 90.215 & 33.1873454798663 & 66.19 \tabularnewline
7 & 100.0225 & 3.52514184111789 & 7.19 \tabularnewline
8 & 108.625 & 13.982421106518 & 29.18 \tabularnewline
9 & 97.34 & 4.76220537146394 & 9.3 \tabularnewline
10 & 104.5675 & 17.7299565237294 & 41.19 \tabularnewline
11 & 129.305 & 49.0524144835569 & 94.45 \tabularnewline
12 & 97.655 & 10.1434790218478 & 23.21 \tabularnewline
13 & 130.25 & 50.2509780999335 & 108.48 \tabularnewline
14 & 129.3025 & 31.469521101112 & 66.16 \tabularnewline
15 & 119.2475 & 27.7434188892910 & 59.27 \tabularnewline
16 & 141.715 & 8.73770564850979 & 19.7100000000000 \tabularnewline
17 & 93.02 & 24.9402820085633 & 51.82 \tabularnewline
18 & 122.06 & 35.1872827405963 & 76.99 \tabularnewline
19 & 100.7075 & 16.0641866170269 & 34.78 \tabularnewline
20 & 100.1 & 35.9064014719753 & 84.41 \tabularnewline
21 & 108.695 & 24.8831515956748 & 56.16 \tabularnewline
22 & 137.57 & 48.7690127027398 & 101.55 \tabularnewline
23 & 141.97 & 33.2734057970225 & 74.88 \tabularnewline
24 & 117.1175 & 53.024811409377 & 117.65 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14639&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]95.1525[/C][C]18.1650862462399[/C][C]38.9[/C][/ROW]
[ROW][C]2[/C][C]110.7625[/C][C]24.1120058269734[/C][C]52.23[/C][/ROW]
[ROW][C]3[/C][C]100.7825[/C][C]32.7940659012165[/C][C]77.35[/C][/ROW]
[ROW][C]4[/C][C]99.5325[/C][C]8.28072209009174[/C][C]19.6[/C][/ROW]
[ROW][C]5[/C][C]94.2225[/C][C]26.1476045747980[/C][C]54.64[/C][/ROW]
[ROW][C]6[/C][C]90.215[/C][C]33.1873454798663[/C][C]66.19[/C][/ROW]
[ROW][C]7[/C][C]100.0225[/C][C]3.52514184111789[/C][C]7.19[/C][/ROW]
[ROW][C]8[/C][C]108.625[/C][C]13.982421106518[/C][C]29.18[/C][/ROW]
[ROW][C]9[/C][C]97.34[/C][C]4.76220537146394[/C][C]9.3[/C][/ROW]
[ROW][C]10[/C][C]104.5675[/C][C]17.7299565237294[/C][C]41.19[/C][/ROW]
[ROW][C]11[/C][C]129.305[/C][C]49.0524144835569[/C][C]94.45[/C][/ROW]
[ROW][C]12[/C][C]97.655[/C][C]10.1434790218478[/C][C]23.21[/C][/ROW]
[ROW][C]13[/C][C]130.25[/C][C]50.2509780999335[/C][C]108.48[/C][/ROW]
[ROW][C]14[/C][C]129.3025[/C][C]31.469521101112[/C][C]66.16[/C][/ROW]
[ROW][C]15[/C][C]119.2475[/C][C]27.7434188892910[/C][C]59.27[/C][/ROW]
[ROW][C]16[/C][C]141.715[/C][C]8.73770564850979[/C][C]19.7100000000000[/C][/ROW]
[ROW][C]17[/C][C]93.02[/C][C]24.9402820085633[/C][C]51.82[/C][/ROW]
[ROW][C]18[/C][C]122.06[/C][C]35.1872827405963[/C][C]76.99[/C][/ROW]
[ROW][C]19[/C][C]100.7075[/C][C]16.0641866170269[/C][C]34.78[/C][/ROW]
[ROW][C]20[/C][C]100.1[/C][C]35.9064014719753[/C][C]84.41[/C][/ROW]
[ROW][C]21[/C][C]108.695[/C][C]24.8831515956748[/C][C]56.16[/C][/ROW]
[ROW][C]22[/C][C]137.57[/C][C]48.7690127027398[/C][C]101.55[/C][/ROW]
[ROW][C]23[/C][C]141.97[/C][C]33.2734057970225[/C][C]74.88[/C][/ROW]
[ROW][C]24[/C][C]117.1175[/C][C]53.024811409377[/C][C]117.65[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14639&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14639&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	95.1525	18.1650862462399	38.9
2	110.7625	24.1120058269734	52.23
3	100.7825	32.7940659012165	77.35
4	99.5325	8.28072209009174	19.6
5	94.2225	26.1476045747980	54.64
6	90.215	33.1873454798663	66.19
7	100.0225	3.52514184111789	7.19
8	108.625	13.982421106518	29.18
9	97.34	4.76220537146394	9.3
10	104.5675	17.7299565237294	41.19
11	129.305	49.0524144835569	94.45
12	97.655	10.1434790218478	23.21
13	130.25	50.2509780999335	108.48
14	129.3025	31.469521101112	66.16
15	119.2475	27.7434188892910	59.27
16	141.715	8.73770564850979	19.7100000000000
17	93.02	24.9402820085633	51.82
18	122.06	35.1872827405963	76.99
19	100.7075	16.0641866170269	34.78
20	100.1	35.9064014719753	84.41
21	108.695	24.8831515956748	56.16
22	137.57	48.7690127027398	101.55
23	141.97	33.2734057970225	74.88
24	117.1175	53.024811409377	117.65

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-19.1749194490449
beta	0.409122188562961
S.D.	0.169594202464220
T-STAT	2.41235951829943
p-value	0.024631994639896

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -19.1749194490449 \tabularnewline
beta & 0.409122188562961 \tabularnewline
S.D. & 0.169594202464220 \tabularnewline
T-STAT & 2.41235951829943 \tabularnewline
p-value & 0.024631994639896 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14639&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-19.1749194490449[/C][/ROW]
[ROW][C]beta[/C][C]0.409122188562961[/C][/ROW]
[ROW][C]S.D.[/C][C]0.169594202464220[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.41235951829943[/C][/ROW]
[ROW][C]p-value[/C][C]0.024631994639896[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14639&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14639&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	-19.1749194490449
beta	0.409122188562961
S.D.	0.169594202464220
T-STAT	2.41235951829943
p-value	0.024631994639896

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-6.07688301140078
beta	1.94437579938096
S.D.	1.01542759328881
T-STAT	1.91483451132488
p-value	0.068606061651676
Lambda	-0.944375799380963

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.07688301140078 \tabularnewline
beta & 1.94437579938096 \tabularnewline
S.D. & 1.01542759328881 \tabularnewline
T-STAT & 1.91483451132488 \tabularnewline
p-value & 0.068606061651676 \tabularnewline
Lambda & -0.944375799380963 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=14639&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.07688301140078[/C][/ROW]
[ROW][C]beta[/C][C]1.94437579938096[/C][/ROW]
[ROW][C]S.D.[/C][C]1.01542759328881[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.91483451132488[/C][/ROW]
[ROW][C]p-value[/C][C]0.068606061651676[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.944375799380963[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=14639&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=14639&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	-6.07688301140078
beta	1.94437579938096
S.D.	1.01542759328881
T-STAT	1.91483451132488
p-value	0.068606061651676
Lambda	-0.944375799380963

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