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Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Tue, 16 Aug 2011 12:24:29 -0400

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/2011/Aug/16/t1313511989mgl1m6uwrr0o01c.htm/, Retrieved Tue, 14 May 2024 13:46:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123890, Retrieved Tue, 14 May 2024 13:46:14 +0000

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No (this computation is public)

User-defined keywords

mattias debbaut

Estimated Impact

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

-       [Standard Deviation-Mean Plot] [tijdreeks B - SD ...] [2011-08-16 16:24:29] [d41d8cd98f00b204e9800998ecf8427e] [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	'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123890&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123890&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123890&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	'AstonUniversity' @ aston.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	515	45.0924975282289	110
2	497.5	20.6155281280883	50
3	545	65.57438524302	150
4	472.5	78.049129826454	190
5	515	67.5771164423776	160
6	550	77.4596669241483	180
7	447.5	113.541475535007	250
8	500	96.6091783079296	220
9	540	83.6660026534076	190
10	435	119.023807142381	250
11	540	43.2049379893857	100
12	535	102.143689640297	240
13	437.5	132.759180473518	310
14	532.5	100.457287772798	240
15	495	136.747943311773	280
16	405	157.585955380971	360
17	530	136.626010212795	320
18	487.5	135	320
19	417.5	153.26991442115	340
20	570	143.990740443034	310
21	460	125.698050899765	290
22	405	158.640053790544	360
23	585	142.009389360939	310
24	482.5	161.941347407016	370
25	405	164.418166068514	360
26	550	125.698050899765	290
27	492.5	113.247516529061	260

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 515 & 45.0924975282289 & 110 \tabularnewline
2 & 497.5 & 20.6155281280883 & 50 \tabularnewline
3 & 545 & 65.57438524302 & 150 \tabularnewline
4 & 472.5 & 78.049129826454 & 190 \tabularnewline
5 & 515 & 67.5771164423776 & 160 \tabularnewline
6 & 550 & 77.4596669241483 & 180 \tabularnewline
7 & 447.5 & 113.541475535007 & 250 \tabularnewline
8 & 500 & 96.6091783079296 & 220 \tabularnewline
9 & 540 & 83.6660026534076 & 190 \tabularnewline
10 & 435 & 119.023807142381 & 250 \tabularnewline
11 & 540 & 43.2049379893857 & 100 \tabularnewline
12 & 535 & 102.143689640297 & 240 \tabularnewline
13 & 437.5 & 132.759180473518 & 310 \tabularnewline
14 & 532.5 & 100.457287772798 & 240 \tabularnewline
15 & 495 & 136.747943311773 & 280 \tabularnewline
16 & 405 & 157.585955380971 & 360 \tabularnewline
17 & 530 & 136.626010212795 & 320 \tabularnewline
18 & 487.5 & 135 & 320 \tabularnewline
19 & 417.5 & 153.26991442115 & 340 \tabularnewline
20 & 570 & 143.990740443034 & 310 \tabularnewline
21 & 460 & 125.698050899765 & 290 \tabularnewline
22 & 405 & 158.640053790544 & 360 \tabularnewline
23 & 585 & 142.009389360939 & 310 \tabularnewline
24 & 482.5 & 161.941347407016 & 370 \tabularnewline
25 & 405 & 164.418166068514 & 360 \tabularnewline
26 & 550 & 125.698050899765 & 290 \tabularnewline
27 & 492.5 & 113.247516529061 & 260 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123890&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]515[/C][C]45.0924975282289[/C][C]110[/C][/ROW]
[ROW][C]2[/C][C]497.5[/C][C]20.6155281280883[/C][C]50[/C][/ROW]
[ROW][C]3[/C][C]545[/C][C]65.57438524302[/C][C]150[/C][/ROW]
[ROW][C]4[/C][C]472.5[/C][C]78.049129826454[/C][C]190[/C][/ROW]
[ROW][C]5[/C][C]515[/C][C]67.5771164423776[/C][C]160[/C][/ROW]
[ROW][C]6[/C][C]550[/C][C]77.4596669241483[/C][C]180[/C][/ROW]
[ROW][C]7[/C][C]447.5[/C][C]113.541475535007[/C][C]250[/C][/ROW]
[ROW][C]8[/C][C]500[/C][C]96.6091783079296[/C][C]220[/C][/ROW]
[ROW][C]9[/C][C]540[/C][C]83.6660026534076[/C][C]190[/C][/ROW]
[ROW][C]10[/C][C]435[/C][C]119.023807142381[/C][C]250[/C][/ROW]
[ROW][C]11[/C][C]540[/C][C]43.2049379893857[/C][C]100[/C][/ROW]
[ROW][C]12[/C][C]535[/C][C]102.143689640297[/C][C]240[/C][/ROW]
[ROW][C]13[/C][C]437.5[/C][C]132.759180473518[/C][C]310[/C][/ROW]
[ROW][C]14[/C][C]532.5[/C][C]100.457287772798[/C][C]240[/C][/ROW]
[ROW][C]15[/C][C]495[/C][C]136.747943311773[/C][C]280[/C][/ROW]
[ROW][C]16[/C][C]405[/C][C]157.585955380971[/C][C]360[/C][/ROW]
[ROW][C]17[/C][C]530[/C][C]136.626010212795[/C][C]320[/C][/ROW]
[ROW][C]18[/C][C]487.5[/C][C]135[/C][C]320[/C][/ROW]
[ROW][C]19[/C][C]417.5[/C][C]153.26991442115[/C][C]340[/C][/ROW]
[ROW][C]20[/C][C]570[/C][C]143.990740443034[/C][C]310[/C][/ROW]
[ROW][C]21[/C][C]460[/C][C]125.698050899765[/C][C]290[/C][/ROW]
[ROW][C]22[/C][C]405[/C][C]158.640053790544[/C][C]360[/C][/ROW]
[ROW][C]23[/C][C]585[/C][C]142.009389360939[/C][C]310[/C][/ROW]
[ROW][C]24[/C][C]482.5[/C][C]161.941347407016[/C][C]370[/C][/ROW]
[ROW][C]25[/C][C]405[/C][C]164.418166068514[/C][C]360[/C][/ROW]
[ROW][C]26[/C][C]550[/C][C]125.698050899765[/C][C]290[/C][/ROW]
[ROW][C]27[/C][C]492.5[/C][C]113.247516529061[/C][C]260[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123890&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123890&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	515	45.0924975282289	110
2	497.5	20.6155281280883	50
3	545	65.57438524302	150
4	472.5	78.049129826454	190
5	515	67.5771164423776	160
6	550	77.4596669241483	180
7	447.5	113.541475535007	250
8	500	96.6091783079296	220
9	540	83.6660026534076	190
10	435	119.023807142381	250
11	540	43.2049379893857	100
12	535	102.143689640297	240
13	437.5	132.759180473518	310
14	532.5	100.457287772798	240
15	495	136.747943311773	280
16	405	157.585955380971	360
17	530	136.626010212795	320
18	487.5	135	320
19	417.5	153.26991442115	340
20	570	143.990740443034	310
21	460	125.698050899765	290
22	405	158.640053790544	360
23	585	142.009389360939	310
24	482.5	161.941347407016	370
25	405	164.418166068514	360
26	550	125.698050899765	290
27	492.5	113.247516529061	260

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	271.883566016065
beta	-0.325170201168863
S.D.	0.135305613290421
T-STAT	-2.40322772471321
p-value	0.0239947047550262

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 271.883566016065 \tabularnewline
beta & -0.325170201168863 \tabularnewline
S.D. & 0.135305613290421 \tabularnewline
T-STAT & -2.40322772471321 \tabularnewline
p-value & 0.0239947047550262 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123890&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]271.883566016065[/C][/ROW]
[ROW][C]beta[/C][C]-0.325170201168863[/C][/ROW]
[ROW][C]S.D.[/C][C]0.135305613290421[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.40322772471321[/C][/ROW]
[ROW][C]p-value[/C][C]0.0239947047550262[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123890&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123890&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	271.883566016065
beta	-0.325170201168863
S.D.	0.135305613290421
T-STAT	-2.40322772471321
p-value	0.0239947047550262

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	14.5395253643031
beta	-1.60049553974576
S.D.	0.82999895781561
T-STAT	-1.92831030048272
p-value	0.0652472496002418
Lambda	2.60049553974576

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 14.5395253643031 \tabularnewline
beta & -1.60049553974576 \tabularnewline
S.D. & 0.82999895781561 \tabularnewline
T-STAT & -1.92831030048272 \tabularnewline
p-value & 0.0652472496002418 \tabularnewline
Lambda & 2.60049553974576 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123890&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]14.5395253643031[/C][/ROW]
[ROW][C]beta[/C][C]-1.60049553974576[/C][/ROW]
[ROW][C]S.D.[/C][C]0.82999895781561[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.92831030048272[/C][/ROW]
[ROW][C]p-value[/C][C]0.0652472496002418[/C][/ROW]
[ROW][C]Lambda[/C][C]2.60049553974576[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123890&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123890&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	14.5395253643031
beta	-1.60049553974576
S.D.	0.82999895781561
T-STAT	-1.92831030048272
p-value	0.0652472496002418
Lambda	2.60049553974576

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code