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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

Mon, 16 Aug 2010 11:29:56 +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/16/t1281958172ubxtsfgt86mgmjr.htm/, Retrieved Thu, 16 May 2024 21:24:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78962, Retrieved Thu, 16 May 2024 21:24:04 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Magali de Reu

Estimated Impact

131

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

-       [Standard Deviation-Mean Plot] [tijdreeks 1 stap 26] [2010-08-16 11:29:56] [07915b1f88a41fb8d82e27c5eaa7bbed] [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=78962&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=78962&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78962&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	331.25	1.70782512765993	4
2	338.25	12.5266382827424	26
3	325	1.4142135623731	3
4	331	2.3094010767585	4
5	344.25	15.0194318578744	32
6	322	1.63299316185545	4
7	330	2.94392028877595	7
8	348.75	17.9698822107065	37
9	314.5	4.35889894354067	9
10	314.25	3.30403793359983	7
11	337.25	19.9728983041187	43
12	288.5	14.0593978059754	28
13	278	6.16441400296898	14
14	295	25.7293606605372	54
15	246.25	14.3614066163451	28
16	236.25	5.7373048260195	14
17	242	29.563490998189	63
18	206.75	12.8419884233972	29
19	201.5	8.10349718742881	19
20	219.75	20.9821352583573	45
21	188.75	17.0758113521242	35
22	174	7.87400787401181	18
23	171	23.7346441585572	51
24	143.25	12.1757956618859	27
25	130.25	7.76208734813001	18
26	131.5	25.2520626220249	53
27	99	9.62635271879577	22
28	80.5	13.9164171634321	31
29	84.75	22.4406624976477	49
30	63.5	5.06622805119022	11

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 331.25 & 1.70782512765993 & 4 \tabularnewline
2 & 338.25 & 12.5266382827424 & 26 \tabularnewline
3 & 325 & 1.4142135623731 & 3 \tabularnewline
4 & 331 & 2.3094010767585 & 4 \tabularnewline
5 & 344.25 & 15.0194318578744 & 32 \tabularnewline
6 & 322 & 1.63299316185545 & 4 \tabularnewline
7 & 330 & 2.94392028877595 & 7 \tabularnewline
8 & 348.75 & 17.9698822107065 & 37 \tabularnewline
9 & 314.5 & 4.35889894354067 & 9 \tabularnewline
10 & 314.25 & 3.30403793359983 & 7 \tabularnewline
11 & 337.25 & 19.9728983041187 & 43 \tabularnewline
12 & 288.5 & 14.0593978059754 & 28 \tabularnewline
13 & 278 & 6.16441400296898 & 14 \tabularnewline
14 & 295 & 25.7293606605372 & 54 \tabularnewline
15 & 246.25 & 14.3614066163451 & 28 \tabularnewline
16 & 236.25 & 5.7373048260195 & 14 \tabularnewline
17 & 242 & 29.563490998189 & 63 \tabularnewline
18 & 206.75 & 12.8419884233972 & 29 \tabularnewline
19 & 201.5 & 8.10349718742881 & 19 \tabularnewline
20 & 219.75 & 20.9821352583573 & 45 \tabularnewline
21 & 188.75 & 17.0758113521242 & 35 \tabularnewline
22 & 174 & 7.87400787401181 & 18 \tabularnewline
23 & 171 & 23.7346441585572 & 51 \tabularnewline
24 & 143.25 & 12.1757956618859 & 27 \tabularnewline
25 & 130.25 & 7.76208734813001 & 18 \tabularnewline
26 & 131.5 & 25.2520626220249 & 53 \tabularnewline
27 & 99 & 9.62635271879577 & 22 \tabularnewline
28 & 80.5 & 13.9164171634321 & 31 \tabularnewline
29 & 84.75 & 22.4406624976477 & 49 \tabularnewline
30 & 63.5 & 5.06622805119022 & 11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78962&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]331.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]338.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]325[/C][C]1.4142135623731[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]331[/C][C]2.3094010767585[/C][C]4[/C][/ROW]
[ROW][C]5[/C][C]344.25[/C][C]15.0194318578744[/C][C]32[/C][/ROW]
[ROW][C]6[/C][C]322[/C][C]1.63299316185545[/C][C]4[/C][/ROW]
[ROW][C]7[/C][C]330[/C][C]2.94392028877595[/C][C]7[/C][/ROW]
[ROW][C]8[/C][C]348.75[/C][C]17.9698822107065[/C][C]37[/C][/ROW]
[ROW][C]9[/C][C]314.5[/C][C]4.35889894354067[/C][C]9[/C][/ROW]
[ROW][C]10[/C][C]314.25[/C][C]3.30403793359983[/C][C]7[/C][/ROW]
[ROW][C]11[/C][C]337.25[/C][C]19.9728983041187[/C][C]43[/C][/ROW]
[ROW][C]12[/C][C]288.5[/C][C]14.0593978059754[/C][C]28[/C][/ROW]
[ROW][C]13[/C][C]278[/C][C]6.16441400296898[/C][C]14[/C][/ROW]
[ROW][C]14[/C][C]295[/C][C]25.7293606605372[/C][C]54[/C][/ROW]
[ROW][C]15[/C][C]246.25[/C][C]14.3614066163451[/C][C]28[/C][/ROW]
[ROW][C]16[/C][C]236.25[/C][C]5.7373048260195[/C][C]14[/C][/ROW]
[ROW][C]17[/C][C]242[/C][C]29.563490998189[/C][C]63[/C][/ROW]
[ROW][C]18[/C][C]206.75[/C][C]12.8419884233972[/C][C]29[/C][/ROW]
[ROW][C]19[/C][C]201.5[/C][C]8.10349718742881[/C][C]19[/C][/ROW]
[ROW][C]20[/C][C]219.75[/C][C]20.9821352583573[/C][C]45[/C][/ROW]
[ROW][C]21[/C][C]188.75[/C][C]17.0758113521242[/C][C]35[/C][/ROW]
[ROW][C]22[/C][C]174[/C][C]7.87400787401181[/C][C]18[/C][/ROW]
[ROW][C]23[/C][C]171[/C][C]23.7346441585572[/C][C]51[/C][/ROW]
[ROW][C]24[/C][C]143.25[/C][C]12.1757956618859[/C][C]27[/C][/ROW]
[ROW][C]25[/C][C]130.25[/C][C]7.76208734813001[/C][C]18[/C][/ROW]
[ROW][C]26[/C][C]131.5[/C][C]25.2520626220249[/C][C]53[/C][/ROW]
[ROW][C]27[/C][C]99[/C][C]9.62635271879577[/C][C]22[/C][/ROW]
[ROW][C]28[/C][C]80.5[/C][C]13.9164171634321[/C][C]31[/C][/ROW]
[ROW][C]29[/C][C]84.75[/C][C]22.4406624976477[/C][C]49[/C][/ROW]
[ROW][C]30[/C][C]63.5[/C][C]5.06622805119022[/C][C]11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78962&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78962&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	331.25	1.70782512765993	4
2	338.25	12.5266382827424	26
3	325	1.4142135623731	3
4	331	2.3094010767585	4
5	344.25	15.0194318578744	32
6	322	1.63299316185545	4
7	330	2.94392028877595	7
8	348.75	17.9698822107065	37
9	314.5	4.35889894354067	9
10	314.25	3.30403793359983	7
11	337.25	19.9728983041187	43
12	288.5	14.0593978059754	28
13	278	6.16441400296898	14
14	295	25.7293606605372	54
15	246.25	14.3614066163451	28
16	236.25	5.7373048260195	14
17	242	29.563490998189	63
18	206.75	12.8419884233972	29
19	201.5	8.10349718742881	19
20	219.75	20.9821352583573	45
21	188.75	17.0758113521242	35
22	174	7.87400787401181	18
23	171	23.7346441585572	51
24	143.25	12.1757956618859	27
25	130.25	7.76208734813001	18
26	131.5	25.2520626220249	53
27	99	9.62635271879577	22
28	80.5	13.9164171634321	31
29	84.75	22.4406624976477	49
30	63.5	5.06622805119022	11

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	17.2875222484245
beta	-0.0214976059401029
S.D.	0.0163488224932178
T-STAT	-1.31493298364582
p-value	0.199200658932226

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 17.2875222484245 \tabularnewline
beta & -0.0214976059401029 \tabularnewline
S.D. & 0.0163488224932178 \tabularnewline
T-STAT & -1.31493298364582 \tabularnewline
p-value & 0.199200658932226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78962&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]17.2875222484245[/C][/ROW]
[ROW][C]beta[/C][C]-0.0214976059401029[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0163488224932178[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.31493298364582[/C][/ROW]
[ROW][C]p-value[/C][C]0.199200658932226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78962&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78962&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	17.2875222484245
beta	-0.0214976059401029
S.D.	0.0163488224932178
T-STAT	-1.31493298364582
p-value	0.199200658932226

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	5.04169444590167
beta	-0.530727102366918
S.D.	0.328613750387784
T-STAT	-1.61504837134973
p-value	0.117514222729145
Lambda	1.53072710236692

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.04169444590167 \tabularnewline
beta & -0.530727102366918 \tabularnewline
S.D. & 0.328613750387784 \tabularnewline
T-STAT & -1.61504837134973 \tabularnewline
p-value & 0.117514222729145 \tabularnewline
Lambda & 1.53072710236692 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78962&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.04169444590167[/C][/ROW]
[ROW][C]beta[/C][C]-0.530727102366918[/C][/ROW]
[ROW][C]S.D.[/C][C]0.328613750387784[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.61504837134973[/C][/ROW]
[ROW][C]p-value[/C][C]0.117514222729145[/C][/ROW]
[ROW][C]Lambda[/C][C]1.53072710236692[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78962&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78962&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	5.04169444590167
beta	-0.530727102366918
S.D.	0.328613750387784
T-STAT	-1.61504837134973
p-value	0.117514222729145
Lambda	1.53072710236692

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