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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

Wed, 21 Jul 2010 11:12:51 +0000

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/2010/Jul/21/t127971078458lti6kqmq6kvqi.htm/, Retrieved Mon, 29 Apr 2024 03:38:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78048, Retrieved Mon, 29 Apr 2024 03:38:35 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Van de Walle Mathias

Estimated Impact

215

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

-       [Standard Deviation-Mean Plot] [tijdreeks 1 - sta...] [2010-07-21 11:12:51] [589929edeb20bd59f78e9be1ffd92c80] [Current]

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Boxplots

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78048&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78048&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78048&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	266.25	1.70782512765993	4
2	273.25	12.5266382827424	26
3	260	1.4142135623731	3
4	257.5	1.73205080756888	4
5	279	11.0453610171873	21
6	280.25	4.78713553878169	10
7	275	3.91578004149024	9
8	285.75	13.9612559129423	28
9	287.5	5.44671154612273	13
10	277.75	7.8049129826454	17
11	276	20.1163283594862	43
12	276	5.41602560309064	12
13	262	2.58198889747161	6
14	266.25	28.8140590684478	63
15	257.25	8.05708797684788	19
16	237.75	3.40342964277702	8
17	234.5	32.1506868770586	71
18	221.75	8.5	20
19	203	5.47722557505166	12
20	202	30.5177543953243	68
21	200.5	12.7671453348037	29
22	182.75	6.7515430335097	15
23	182.75	32.1908372056397	73
24	187.5	15.1547572288924	32
25	170.5	6.95221787153807	13
26	172.5	37.8109331631298	85
27	166.5	13.228756555323	29
28	146.25	9.06917857360853	22
29	148	30.0776772152815	66
30	145.25	10.8742815854658	23

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 266.25 & 1.70782512765993 & 4 \tabularnewline
2 & 273.25 & 12.5266382827424 & 26 \tabularnewline
3 & 260 & 1.4142135623731 & 3 \tabularnewline
4 & 257.5 & 1.73205080756888 & 4 \tabularnewline
5 & 279 & 11.0453610171873 & 21 \tabularnewline
6 & 280.25 & 4.78713553878169 & 10 \tabularnewline
7 & 275 & 3.91578004149024 & 9 \tabularnewline
8 & 285.75 & 13.9612559129423 & 28 \tabularnewline
9 & 287.5 & 5.44671154612273 & 13 \tabularnewline
10 & 277.75 & 7.8049129826454 & 17 \tabularnewline
11 & 276 & 20.1163283594862 & 43 \tabularnewline
12 & 276 & 5.41602560309064 & 12 \tabularnewline
13 & 262 & 2.58198889747161 & 6 \tabularnewline
14 & 266.25 & 28.8140590684478 & 63 \tabularnewline
15 & 257.25 & 8.05708797684788 & 19 \tabularnewline
16 & 237.75 & 3.40342964277702 & 8 \tabularnewline
17 & 234.5 & 32.1506868770586 & 71 \tabularnewline
18 & 221.75 & 8.5 & 20 \tabularnewline
19 & 203 & 5.47722557505166 & 12 \tabularnewline
20 & 202 & 30.5177543953243 & 68 \tabularnewline
21 & 200.5 & 12.7671453348037 & 29 \tabularnewline
22 & 182.75 & 6.7515430335097 & 15 \tabularnewline
23 & 182.75 & 32.1908372056397 & 73 \tabularnewline
24 & 187.5 & 15.1547572288924 & 32 \tabularnewline
25 & 170.5 & 6.95221787153807 & 13 \tabularnewline
26 & 172.5 & 37.8109331631298 & 85 \tabularnewline
27 & 166.5 & 13.228756555323 & 29 \tabularnewline
28 & 146.25 & 9.06917857360853 & 22 \tabularnewline
29 & 148 & 30.0776772152815 & 66 \tabularnewline
30 & 145.25 & 10.8742815854658 & 23 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78048&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]266.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]273.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]260[/C][C]1.4142135623731[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]257.5[/C][C]1.73205080756888[/C][C]4[/C][/ROW]
[ROW][C]5[/C][C]279[/C][C]11.0453610171873[/C][C]21[/C][/ROW]
[ROW][C]6[/C][C]280.25[/C][C]4.78713553878169[/C][C]10[/C][/ROW]
[ROW][C]7[/C][C]275[/C][C]3.91578004149024[/C][C]9[/C][/ROW]
[ROW][C]8[/C][C]285.75[/C][C]13.9612559129423[/C][C]28[/C][/ROW]
[ROW][C]9[/C][C]287.5[/C][C]5.44671154612273[/C][C]13[/C][/ROW]
[ROW][C]10[/C][C]277.75[/C][C]7.8049129826454[/C][C]17[/C][/ROW]
[ROW][C]11[/C][C]276[/C][C]20.1163283594862[/C][C]43[/C][/ROW]
[ROW][C]12[/C][C]276[/C][C]5.41602560309064[/C][C]12[/C][/ROW]
[ROW][C]13[/C][C]262[/C][C]2.58198889747161[/C][C]6[/C][/ROW]
[ROW][C]14[/C][C]266.25[/C][C]28.8140590684478[/C][C]63[/C][/ROW]
[ROW][C]15[/C][C]257.25[/C][C]8.05708797684788[/C][C]19[/C][/ROW]
[ROW][C]16[/C][C]237.75[/C][C]3.40342964277702[/C][C]8[/C][/ROW]
[ROW][C]17[/C][C]234.5[/C][C]32.1506868770586[/C][C]71[/C][/ROW]
[ROW][C]18[/C][C]221.75[/C][C]8.5[/C][C]20[/C][/ROW]
[ROW][C]19[/C][C]203[/C][C]5.47722557505166[/C][C]12[/C][/ROW]
[ROW][C]20[/C][C]202[/C][C]30.5177543953243[/C][C]68[/C][/ROW]
[ROW][C]21[/C][C]200.5[/C][C]12.7671453348037[/C][C]29[/C][/ROW]
[ROW][C]22[/C][C]182.75[/C][C]6.7515430335097[/C][C]15[/C][/ROW]
[ROW][C]23[/C][C]182.75[/C][C]32.1908372056397[/C][C]73[/C][/ROW]
[ROW][C]24[/C][C]187.5[/C][C]15.1547572288924[/C][C]32[/C][/ROW]
[ROW][C]25[/C][C]170.5[/C][C]6.95221787153807[/C][C]13[/C][/ROW]
[ROW][C]26[/C][C]172.5[/C][C]37.8109331631298[/C][C]85[/C][/ROW]
[ROW][C]27[/C][C]166.5[/C][C]13.228756555323[/C][C]29[/C][/ROW]
[ROW][C]28[/C][C]146.25[/C][C]9.06917857360853[/C][C]22[/C][/ROW]
[ROW][C]29[/C][C]148[/C][C]30.0776772152815[/C][C]66[/C][/ROW]
[ROW][C]30[/C][C]145.25[/C][C]10.8742815854658[/C][C]23[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78048&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78048&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	266.25	1.70782512765993	4
2	273.25	12.5266382827424	26
3	260	1.4142135623731	3
4	257.5	1.73205080756888	4
5	279	11.0453610171873	21
6	280.25	4.78713553878169	10
7	275	3.91578004149024	9
8	285.75	13.9612559129423	28
9	287.5	5.44671154612273	13
10	277.75	7.8049129826454	17
11	276	20.1163283594862	43
12	276	5.41602560309064	12
13	262	2.58198889747161	6
14	266.25	28.8140590684478	63
15	257.25	8.05708797684788	19
16	237.75	3.40342964277702	8
17	234.5	32.1506868770586	71
18	221.75	8.5	20
19	203	5.47722557505166	12
20	202	30.5177543953243	68
21	200.5	12.7671453348037	29
22	182.75	6.7515430335097	15
23	182.75	32.1908372056397	73
24	187.5	15.1547572288924	32
25	170.5	6.95221787153807	13
26	172.5	37.8109331631298	85
27	166.5	13.228756555323	29
28	146.25	9.06917857360853	22
29	148	30.0776772152815	66
30	145.25	10.8742815854658	23

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	31.1217827317606
beta	-0.0798400992509438
S.D.	0.0389175348184229
T-STAT	-2.05151995426876
p-value	0.0496759303685089

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 31.1217827317606 \tabularnewline
beta & -0.0798400992509438 \tabularnewline
S.D. & 0.0389175348184229 \tabularnewline
T-STAT & -2.05151995426876 \tabularnewline
p-value & 0.0496759303685089 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78048&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]31.1217827317606[/C][/ROW]
[ROW][C]beta[/C][C]-0.0798400992509438[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0389175348184229[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.05151995426876[/C][/ROW]
[ROW][C]p-value[/C][C]0.0496759303685089[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78048&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78048&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	31.1217827317606
beta	-0.0798400992509438
S.D.	0.0389175348184229
T-STAT	-2.05151995426876
p-value	0.0496759303685089

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	10.8291231333678
beta	-1.59758331950446
S.D.	0.702098848537444
T-STAT	-2.27543931005217
p-value	0.0307310213465471
Lambda	2.59758331950446

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 10.8291231333678 \tabularnewline
beta & -1.59758331950446 \tabularnewline
S.D. & 0.702098848537444 \tabularnewline
T-STAT & -2.27543931005217 \tabularnewline
p-value & 0.0307310213465471 \tabularnewline
Lambda & 2.59758331950446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78048&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]10.8291231333678[/C][/ROW]
[ROW][C]beta[/C][C]-1.59758331950446[/C][/ROW]
[ROW][C]S.D.[/C][C]0.702098848537444[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.27543931005217[/C][/ROW]
[ROW][C]p-value[/C][C]0.0307310213465471[/C][/ROW]
[ROW][C]Lambda[/C][C]2.59758331950446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78048&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78048&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	10.8291231333678
beta	-1.59758331950446
S.D.	0.702098848537444
T-STAT	-2.27543931005217
p-value	0.0307310213465471
Lambda	2.59758331950446

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code