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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

Thu, 19 Aug 2010 20:03:38 +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/Aug/19/t128224821509835iug8uojltx.htm/, Retrieved Fri, 03 May 2024 06:04:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79365, Retrieved Fri, 03 May 2024 06:04:44 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

ellen aerts

Estimated Impact

113

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

-       [Standard Deviation-Mean Plot] ["Tijdreeks A stap...] [2010-08-19 20:03:38] [6e43eada780a1520be8ab5bc59456d41] [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	2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79365&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79365&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79365&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	23.25	1.70782512765993	4
2	30.25	12.5266382827424	26
3	17	1.4142135623731	3
4	19.5	1.29099444873581	3
5	34.75	14.7280910734102	31
6	23.5	8.18535277187245	16
7	32.25	2.62995563967658	6
8	49	12.6491106406735	28
9	40.5	8.42614977317636	18
10	40.75	5.7373048260195	14
11	69.25	10.4682058316281	23
12	59.5	7.895146188218	16
13	63	10.6144555520604	23
14	87.75	5.43905629069357	12
15	91.5	12.5565388012249	25
16	91.5	4.65474668125631	11
17	112.5	5.5075705472861	12
18	122	18.4571575998762	37
19	127.75	7.5	16
20	150.5	8.81286937760152	20
21	158	20.5101600838869	43
22	162.25	7.5	16
23	189.25	10.6262254195301	23
24	191.5	19.8074060223274	44
25	188.25	5.90903263374528	13
26	208.25	8.13941029804985	19
27	226	19.2700112437262	41
28	222.25	9.9121138007995	24
29	245	6.97614984548545	17
30	266.25	18.1911150473704	40

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 23.25 & 1.70782512765993 & 4 \tabularnewline
2 & 30.25 & 12.5266382827424 & 26 \tabularnewline
3 & 17 & 1.4142135623731 & 3 \tabularnewline
4 & 19.5 & 1.29099444873581 & 3 \tabularnewline
5 & 34.75 & 14.7280910734102 & 31 \tabularnewline
6 & 23.5 & 8.18535277187245 & 16 \tabularnewline
7 & 32.25 & 2.62995563967658 & 6 \tabularnewline
8 & 49 & 12.6491106406735 & 28 \tabularnewline
9 & 40.5 & 8.42614977317636 & 18 \tabularnewline
10 & 40.75 & 5.7373048260195 & 14 \tabularnewline
11 & 69.25 & 10.4682058316281 & 23 \tabularnewline
12 & 59.5 & 7.895146188218 & 16 \tabularnewline
13 & 63 & 10.6144555520604 & 23 \tabularnewline
14 & 87.75 & 5.43905629069357 & 12 \tabularnewline
15 & 91.5 & 12.5565388012249 & 25 \tabularnewline
16 & 91.5 & 4.65474668125631 & 11 \tabularnewline
17 & 112.5 & 5.5075705472861 & 12 \tabularnewline
18 & 122 & 18.4571575998762 & 37 \tabularnewline
19 & 127.75 & 7.5 & 16 \tabularnewline
20 & 150.5 & 8.81286937760152 & 20 \tabularnewline
21 & 158 & 20.5101600838869 & 43 \tabularnewline
22 & 162.25 & 7.5 & 16 \tabularnewline
23 & 189.25 & 10.6262254195301 & 23 \tabularnewline
24 & 191.5 & 19.8074060223274 & 44 \tabularnewline
25 & 188.25 & 5.90903263374528 & 13 \tabularnewline
26 & 208.25 & 8.13941029804985 & 19 \tabularnewline
27 & 226 & 19.2700112437262 & 41 \tabularnewline
28 & 222.25 & 9.9121138007995 & 24 \tabularnewline
29 & 245 & 6.97614984548545 & 17 \tabularnewline
30 & 266.25 & 18.1911150473704 & 40 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79365&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]23.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]30.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]17[/C][C]1.4142135623731[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]19.5[/C][C]1.29099444873581[/C][C]3[/C][/ROW]
[ROW][C]5[/C][C]34.75[/C][C]14.7280910734102[/C][C]31[/C][/ROW]
[ROW][C]6[/C][C]23.5[/C][C]8.18535277187245[/C][C]16[/C][/ROW]
[ROW][C]7[/C][C]32.25[/C][C]2.62995563967658[/C][C]6[/C][/ROW]
[ROW][C]8[/C][C]49[/C][C]12.6491106406735[/C][C]28[/C][/ROW]
[ROW][C]9[/C][C]40.5[/C][C]8.42614977317636[/C][C]18[/C][/ROW]
[ROW][C]10[/C][C]40.75[/C][C]5.7373048260195[/C][C]14[/C][/ROW]
[ROW][C]11[/C][C]69.25[/C][C]10.4682058316281[/C][C]23[/C][/ROW]
[ROW][C]12[/C][C]59.5[/C][C]7.895146188218[/C][C]16[/C][/ROW]
[ROW][C]13[/C][C]63[/C][C]10.6144555520604[/C][C]23[/C][/ROW]
[ROW][C]14[/C][C]87.75[/C][C]5.43905629069357[/C][C]12[/C][/ROW]
[ROW][C]15[/C][C]91.5[/C][C]12.5565388012249[/C][C]25[/C][/ROW]
[ROW][C]16[/C][C]91.5[/C][C]4.65474668125631[/C][C]11[/C][/ROW]
[ROW][C]17[/C][C]112.5[/C][C]5.5075705472861[/C][C]12[/C][/ROW]
[ROW][C]18[/C][C]122[/C][C]18.4571575998762[/C][C]37[/C][/ROW]
[ROW][C]19[/C][C]127.75[/C][C]7.5[/C][C]16[/C][/ROW]
[ROW][C]20[/C][C]150.5[/C][C]8.81286937760152[/C][C]20[/C][/ROW]
[ROW][C]21[/C][C]158[/C][C]20.5101600838869[/C][C]43[/C][/ROW]
[ROW][C]22[/C][C]162.25[/C][C]7.5[/C][C]16[/C][/ROW]
[ROW][C]23[/C][C]189.25[/C][C]10.6262254195301[/C][C]23[/C][/ROW]
[ROW][C]24[/C][C]191.5[/C][C]19.8074060223274[/C][C]44[/C][/ROW]
[ROW][C]25[/C][C]188.25[/C][C]5.90903263374528[/C][C]13[/C][/ROW]
[ROW][C]26[/C][C]208.25[/C][C]8.13941029804985[/C][C]19[/C][/ROW]
[ROW][C]27[/C][C]226[/C][C]19.2700112437262[/C][C]41[/C][/ROW]
[ROW][C]28[/C][C]222.25[/C][C]9.9121138007995[/C][C]24[/C][/ROW]
[ROW][C]29[/C][C]245[/C][C]6.97614984548545[/C][C]17[/C][/ROW]
[ROW][C]30[/C][C]266.25[/C][C]18.1911150473704[/C][C]40[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79365&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79365&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	23.25	1.70782512765993	4
2	30.25	12.5266382827424	26
3	17	1.4142135623731	3
4	19.5	1.29099444873581	3
5	34.75	14.7280910734102	31
6	23.5	8.18535277187245	16
7	32.25	2.62995563967658	6
8	49	12.6491106406735	28
9	40.5	8.42614977317636	18
10	40.75	5.7373048260195	14
11	69.25	10.4682058316281	23
12	59.5	7.895146188218	16
13	63	10.6144555520604	23
14	87.75	5.43905629069357	12
15	91.5	12.5565388012249	25
16	91.5	4.65474668125631	11
17	112.5	5.5075705472861	12
18	122	18.4571575998762	37
19	127.75	7.5	16
20	150.5	8.81286937760152	20
21	158	20.5101600838869	43
22	162.25	7.5	16
23	189.25	10.6262254195301	23
24	191.5	19.8074060223274	44
25	188.25	5.90903263374528	13
26	208.25	8.13941029804985	19
27	226	19.2700112437262	41
28	222.25	9.9121138007995	24
29	245	6.97614984548545	17
30	266.25	18.1911150473704	40

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	6.03916973717239
beta	0.0319676683505637
S.D.	0.0119780818303328
T-STAT	2.66884704941738
p-value	0.0125186826221147

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6.03916973717239 \tabularnewline
beta & 0.0319676683505637 \tabularnewline
S.D. & 0.0119780818303328 \tabularnewline
T-STAT & 2.66884704941738 \tabularnewline
p-value & 0.0125186826221147 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79365&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.03916973717239[/C][/ROW]
[ROW][C]beta[/C][C]0.0319676683505637[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0119780818303328[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.66884704941738[/C][/ROW]
[ROW][C]p-value[/C][C]0.0125186826221147[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79365&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79365&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	6.03916973717239
beta	0.0319676683505637
S.D.	0.0119780818303328
T-STAT	2.66884704941738
p-value	0.0125186826221147

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.178414117002972
beta	0.505500031981645
S.D.	0.133307475420074
T-STAT	3.79198563612978
p-value	0.000731894777659911
Lambda	0.494499968018355

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.178414117002972 \tabularnewline
beta & 0.505500031981645 \tabularnewline
S.D. & 0.133307475420074 \tabularnewline
T-STAT & 3.79198563612978 \tabularnewline
p-value & 0.000731894777659911 \tabularnewline
Lambda & 0.494499968018355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79365&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.178414117002972[/C][/ROW]
[ROW][C]beta[/C][C]0.505500031981645[/C][/ROW]
[ROW][C]S.D.[/C][C]0.133307475420074[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.79198563612978[/C][/ROW]
[ROW][C]p-value[/C][C]0.000731894777659911[/C][/ROW]
[ROW][C]Lambda[/C][C]0.494499968018355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79365&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79365&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	-0.178414117002972
beta	0.505500031981645
S.D.	0.133307475420074
T-STAT	3.79198563612978
p-value	0.000731894777659911
Lambda	0.494499968018355

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