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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

Sun, 16 Aug 2009 10:22:21 -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/Aug/16/t1250439756851wtljg7nk7071.htm/, Retrieved Sun, 05 May 2024 12:50:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42659, Retrieved Sun, 05 May 2024 12:50:08 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

160

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

-     [Central Tendency] [Maarten Verhaegen...] [2008-08-17 13:34:14] [b57209f6d0b19d479b8c06a8ae81c48a]
- RMPD    [Standard Deviation-Mean Plot] [] [2009-08-16 16:22:21] [e921d89db97faa9283224ee60d8fb091] [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	'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42659&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42659&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42659&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	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	73.48	0.526877594892776	1.11999999999999
2	138.8275	60.3006674230615	139.76
3	101.38	10.9914906480726	26.56
4	136.18	3.17037326929601	7.03
5	144.645	30.5531804127383	73.64
6	86.0575	4.89980526823941	10.43
7	80.955	1.50187660389705	3.22
8	141.76	46.790130725756	106.62
9	105.865	10.3885594124819	22.19
10	96.975	0.628304597044035	1.42000000000000
11	191.4475	65.1821204395807	142.08
12	138.995	6.44851145614241	14.26
13	132.0425	1.52209011997757	3.65000000000001
14	172.6175	34.7983489790344	76.18
15	125.525	7.59928286090208	16.9500000000000
16	118.69	1.21312269233852	2.78
17	194.75	49.7292368732922	106.89
18	180.88	5.89129866837526	13.0100000000000
19	172.995	2.14523502985881	4.81
20	221.6925	33.1667799411801	74.98
21	154.4525	15.3722116712810	34.84
22	142.535	0.494806359430972	1.16000000000000
23	176.455	22.2065343236325	49.48
24	177.8425	2.07477508821237	4.59999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 73.48 & 0.526877594892776 & 1.11999999999999 \tabularnewline
2 & 138.8275 & 60.3006674230615 & 139.76 \tabularnewline
3 & 101.38 & 10.9914906480726 & 26.56 \tabularnewline
4 & 136.18 & 3.17037326929601 & 7.03 \tabularnewline
5 & 144.645 & 30.5531804127383 & 73.64 \tabularnewline
6 & 86.0575 & 4.89980526823941 & 10.43 \tabularnewline
7 & 80.955 & 1.50187660389705 & 3.22 \tabularnewline
8 & 141.76 & 46.790130725756 & 106.62 \tabularnewline
9 & 105.865 & 10.3885594124819 & 22.19 \tabularnewline
10 & 96.975 & 0.628304597044035 & 1.42000000000000 \tabularnewline
11 & 191.4475 & 65.1821204395807 & 142.08 \tabularnewline
12 & 138.995 & 6.44851145614241 & 14.26 \tabularnewline
13 & 132.0425 & 1.52209011997757 & 3.65000000000001 \tabularnewline
14 & 172.6175 & 34.7983489790344 & 76.18 \tabularnewline
15 & 125.525 & 7.59928286090208 & 16.9500000000000 \tabularnewline
16 & 118.69 & 1.21312269233852 & 2.78 \tabularnewline
17 & 194.75 & 49.7292368732922 & 106.89 \tabularnewline
18 & 180.88 & 5.89129866837526 & 13.0100000000000 \tabularnewline
19 & 172.995 & 2.14523502985881 & 4.81 \tabularnewline
20 & 221.6925 & 33.1667799411801 & 74.98 \tabularnewline
21 & 154.4525 & 15.3722116712810 & 34.84 \tabularnewline
22 & 142.535 & 0.494806359430972 & 1.16000000000000 \tabularnewline
23 & 176.455 & 22.2065343236325 & 49.48 \tabularnewline
24 & 177.8425 & 2.07477508821237 & 4.59999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42659&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]73.48[/C][C]0.526877594892776[/C][C]1.11999999999999[/C][/ROW]
[ROW][C]2[/C][C]138.8275[/C][C]60.3006674230615[/C][C]139.76[/C][/ROW]
[ROW][C]3[/C][C]101.38[/C][C]10.9914906480726[/C][C]26.56[/C][/ROW]
[ROW][C]4[/C][C]136.18[/C][C]3.17037326929601[/C][C]7.03[/C][/ROW]
[ROW][C]5[/C][C]144.645[/C][C]30.5531804127383[/C][C]73.64[/C][/ROW]
[ROW][C]6[/C][C]86.0575[/C][C]4.89980526823941[/C][C]10.43[/C][/ROW]
[ROW][C]7[/C][C]80.955[/C][C]1.50187660389705[/C][C]3.22[/C][/ROW]
[ROW][C]8[/C][C]141.76[/C][C]46.790130725756[/C][C]106.62[/C][/ROW]
[ROW][C]9[/C][C]105.865[/C][C]10.3885594124819[/C][C]22.19[/C][/ROW]
[ROW][C]10[/C][C]96.975[/C][C]0.628304597044035[/C][C]1.42000000000000[/C][/ROW]
[ROW][C]11[/C][C]191.4475[/C][C]65.1821204395807[/C][C]142.08[/C][/ROW]
[ROW][C]12[/C][C]138.995[/C][C]6.44851145614241[/C][C]14.26[/C][/ROW]
[ROW][C]13[/C][C]132.0425[/C][C]1.52209011997757[/C][C]3.65000000000001[/C][/ROW]
[ROW][C]14[/C][C]172.6175[/C][C]34.7983489790344[/C][C]76.18[/C][/ROW]
[ROW][C]15[/C][C]125.525[/C][C]7.59928286090208[/C][C]16.9500000000000[/C][/ROW]
[ROW][C]16[/C][C]118.69[/C][C]1.21312269233852[/C][C]2.78[/C][/ROW]
[ROW][C]17[/C][C]194.75[/C][C]49.7292368732922[/C][C]106.89[/C][/ROW]
[ROW][C]18[/C][C]180.88[/C][C]5.89129866837526[/C][C]13.0100000000000[/C][/ROW]
[ROW][C]19[/C][C]172.995[/C][C]2.14523502985881[/C][C]4.81[/C][/ROW]
[ROW][C]20[/C][C]221.6925[/C][C]33.1667799411801[/C][C]74.98[/C][/ROW]
[ROW][C]21[/C][C]154.4525[/C][C]15.3722116712810[/C][C]34.84[/C][/ROW]
[ROW][C]22[/C][C]142.535[/C][C]0.494806359430972[/C][C]1.16000000000000[/C][/ROW]
[ROW][C]23[/C][C]176.455[/C][C]22.2065343236325[/C][C]49.48[/C][/ROW]
[ROW][C]24[/C][C]177.8425[/C][C]2.07477508821237[/C][C]4.59999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42659&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42659&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	73.48	0.526877594892776	1.11999999999999
2	138.8275	60.3006674230615	139.76
3	101.38	10.9914906480726	26.56
4	136.18	3.17037326929601	7.03
5	144.645	30.5531804127383	73.64
6	86.0575	4.89980526823941	10.43
7	80.955	1.50187660389705	3.22
8	141.76	46.790130725756	106.62
9	105.865	10.3885594124819	22.19
10	96.975	0.628304597044035	1.42000000000000
11	191.4475	65.1821204395807	142.08
12	138.995	6.44851145614241	14.26
13	132.0425	1.52209011997757	3.65000000000001
14	172.6175	34.7983489790344	76.18
15	125.525	7.59928286090208	16.9500000000000
16	118.69	1.21312269233852	2.78
17	194.75	49.7292368732922	106.89
18	180.88	5.89129866837526	13.0100000000000
19	172.995	2.14523502985881	4.81
20	221.6925	33.1667799411801	74.98
21	154.4525	15.3722116712810	34.84
22	142.535	0.494806359430972	1.16000000000000
23	176.455	22.2065343236325	49.48
24	177.8425	2.07477508821237	4.59999999999999

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-20.2612786891337
beta	0.265293328675708
S.D.	0.0964998671882017
T-STAT	2.74915744866583
p-value	0.0117087227791648

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -20.2612786891337 \tabularnewline
beta & 0.265293328675708 \tabularnewline
S.D. & 0.0964998671882017 \tabularnewline
T-STAT & 2.74915744866583 \tabularnewline
p-value & 0.0117087227791648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42659&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-20.2612786891337[/C][/ROW]
[ROW][C]beta[/C][C]0.265293328675708[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0964998671882017[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.74915744866583[/C][/ROW]
[ROW][C]p-value[/C][C]0.0117087227791648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42659&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42659&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	-20.2612786891337
beta	0.265293328675708
S.D.	0.0964998671882017
T-STAT	2.74915744866583
p-value	0.0117087227791648

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-12.5243197076913
beta	2.93902427765588
S.D.	0.958925356060677
T-STAT	3.0649145515659
p-value	0.00567106532999836
Lambda	-1.93902427765588

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -12.5243197076913 \tabularnewline
beta & 2.93902427765588 \tabularnewline
S.D. & 0.958925356060677 \tabularnewline
T-STAT & 3.0649145515659 \tabularnewline
p-value & 0.00567106532999836 \tabularnewline
Lambda & -1.93902427765588 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42659&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-12.5243197076913[/C][/ROW]
[ROW][C]beta[/C][C]2.93902427765588[/C][/ROW]
[ROW][C]S.D.[/C][C]0.958925356060677[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.0649145515659[/C][/ROW]
[ROW][C]p-value[/C][C]0.00567106532999836[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.93902427765588[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42659&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42659&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	-12.5243197076913
beta	2.93902427765588
S.D.	0.958925356060677
T-STAT	3.0649145515659
p-value	0.00567106532999836
Lambda	-1.93902427765588

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code