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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, 18 Aug 2010 00:53:46 +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/18/t1282092810hrbtaowj6xnh6qm.htm/, Retrieved Thu, 16 May 2024 08:07:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79174, Retrieved Thu, 16 May 2024 08:07:41 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

168

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

-     [Standard Deviation Plot] [] [2010-08-18 00:34:42] [0054c34847e75ef4340aed26951eb951]
- RMP     [Standard Deviation-Mean Plot] [] [2010-08-18 00:53:46] [ea4db07d8da34007b79212461ea6aa7b] [Current]
- RMPD      [Standard Deviation Plot] [] [2010-08-18 00:59:42] [0054c34847e75ef4340aed26951eb951] 
-   PD      [Standard Deviation-Mean Plot] [] [2010-08-18 01:02:11] [0054c34847e75ef4340aed26951eb951] 

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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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79174&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79174&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79174&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	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	92.25	1.70782512765993	4
2	99.25	12.5266382827424	26
3	86	1.41421356237310	3
4	92	1.82574185835055	4
5	93.5	12.1243556529821	25
6	88	4.54606056566195	11
7	94	1.63299316185545	4
8	110	10.0995049383621	24
9	109	4.24264068711928	10
10	120.5	3.51188458428425	7
11	135	10.5514611942296	25
12	123.5	2.38047614284762	5
13	131.25	7.5	16
14	136	11.1952370824978	26
15	113.5	8.34665601703261	20
16	110.75	7.36545993132812	17
17	106.75	11.0867789130417	26
18	93.5	3.41565025531987	8
19	104.25	10.4363148029688	23
20	98.25	7.27438428093173	17
21	84.25	8.5	18
22	106.5	10.2794292967395	22
23	86.25	11.7011395456454	26
24	75.75	12.0381338531629	26
25	93.25	14.0564338768172	33
26	71.5	11.1205515450749	26
27	69.75	14.9303940559741	32
28	88.5	12.6095202129185	30
29	71.25	8.53912563829967	19
30	66.75	14.7507061977837	32

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 92.25 & 1.70782512765993 & 4 \tabularnewline
2 & 99.25 & 12.5266382827424 & 26 \tabularnewline
3 & 86 & 1.41421356237310 & 3 \tabularnewline
4 & 92 & 1.82574185835055 & 4 \tabularnewline
5 & 93.5 & 12.1243556529821 & 25 \tabularnewline
6 & 88 & 4.54606056566195 & 11 \tabularnewline
7 & 94 & 1.63299316185545 & 4 \tabularnewline
8 & 110 & 10.0995049383621 & 24 \tabularnewline
9 & 109 & 4.24264068711928 & 10 \tabularnewline
10 & 120.5 & 3.51188458428425 & 7 \tabularnewline
11 & 135 & 10.5514611942296 & 25 \tabularnewline
12 & 123.5 & 2.38047614284762 & 5 \tabularnewline
13 & 131.25 & 7.5 & 16 \tabularnewline
14 & 136 & 11.1952370824978 & 26 \tabularnewline
15 & 113.5 & 8.34665601703261 & 20 \tabularnewline
16 & 110.75 & 7.36545993132812 & 17 \tabularnewline
17 & 106.75 & 11.0867789130417 & 26 \tabularnewline
18 & 93.5 & 3.41565025531987 & 8 \tabularnewline
19 & 104.25 & 10.4363148029688 & 23 \tabularnewline
20 & 98.25 & 7.27438428093173 & 17 \tabularnewline
21 & 84.25 & 8.5 & 18 \tabularnewline
22 & 106.5 & 10.2794292967395 & 22 \tabularnewline
23 & 86.25 & 11.7011395456454 & 26 \tabularnewline
24 & 75.75 & 12.0381338531629 & 26 \tabularnewline
25 & 93.25 & 14.0564338768172 & 33 \tabularnewline
26 & 71.5 & 11.1205515450749 & 26 \tabularnewline
27 & 69.75 & 14.9303940559741 & 32 \tabularnewline
28 & 88.5 & 12.6095202129185 & 30 \tabularnewline
29 & 71.25 & 8.53912563829967 & 19 \tabularnewline
30 & 66.75 & 14.7507061977837 & 32 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79174&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]92.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]99.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]86[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]92[/C][C]1.82574185835055[/C][C]4[/C][/ROW]
[ROW][C]5[/C][C]93.5[/C][C]12.1243556529821[/C][C]25[/C][/ROW]
[ROW][C]6[/C][C]88[/C][C]4.54606056566195[/C][C]11[/C][/ROW]
[ROW][C]7[/C][C]94[/C][C]1.63299316185545[/C][C]4[/C][/ROW]
[ROW][C]8[/C][C]110[/C][C]10.0995049383621[/C][C]24[/C][/ROW]
[ROW][C]9[/C][C]109[/C][C]4.24264068711928[/C][C]10[/C][/ROW]
[ROW][C]10[/C][C]120.5[/C][C]3.51188458428425[/C][C]7[/C][/ROW]
[ROW][C]11[/C][C]135[/C][C]10.5514611942296[/C][C]25[/C][/ROW]
[ROW][C]12[/C][C]123.5[/C][C]2.38047614284762[/C][C]5[/C][/ROW]
[ROW][C]13[/C][C]131.25[/C][C]7.5[/C][C]16[/C][/ROW]
[ROW][C]14[/C][C]136[/C][C]11.1952370824978[/C][C]26[/C][/ROW]
[ROW][C]15[/C][C]113.5[/C][C]8.34665601703261[/C][C]20[/C][/ROW]
[ROW][C]16[/C][C]110.75[/C][C]7.36545993132812[/C][C]17[/C][/ROW]
[ROW][C]17[/C][C]106.75[/C][C]11.0867789130417[/C][C]26[/C][/ROW]
[ROW][C]18[/C][C]93.5[/C][C]3.41565025531987[/C][C]8[/C][/ROW]
[ROW][C]19[/C][C]104.25[/C][C]10.4363148029688[/C][C]23[/C][/ROW]
[ROW][C]20[/C][C]98.25[/C][C]7.27438428093173[/C][C]17[/C][/ROW]
[ROW][C]21[/C][C]84.25[/C][C]8.5[/C][C]18[/C][/ROW]
[ROW][C]22[/C][C]106.5[/C][C]10.2794292967395[/C][C]22[/C][/ROW]
[ROW][C]23[/C][C]86.25[/C][C]11.7011395456454[/C][C]26[/C][/ROW]
[ROW][C]24[/C][C]75.75[/C][C]12.0381338531629[/C][C]26[/C][/ROW]
[ROW][C]25[/C][C]93.25[/C][C]14.0564338768172[/C][C]33[/C][/ROW]
[ROW][C]26[/C][C]71.5[/C][C]11.1205515450749[/C][C]26[/C][/ROW]
[ROW][C]27[/C][C]69.75[/C][C]14.9303940559741[/C][C]32[/C][/ROW]
[ROW][C]28[/C][C]88.5[/C][C]12.6095202129185[/C][C]30[/C][/ROW]
[ROW][C]29[/C][C]71.25[/C][C]8.53912563829967[/C][C]19[/C][/ROW]
[ROW][C]30[/C][C]66.75[/C][C]14.7507061977837[/C][C]32[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79174&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79174&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	92.25	1.70782512765993	4
2	99.25	12.5266382827424	26
3	86	1.41421356237310	3
4	92	1.82574185835055	4
5	93.5	12.1243556529821	25
6	88	4.54606056566195	11
7	94	1.63299316185545	4
8	110	10.0995049383621	24
9	109	4.24264068711928	10
10	120.5	3.51188458428425	7
11	135	10.5514611942296	25
12	123.5	2.38047614284762	5
13	131.25	7.5	16
14	136	11.1952370824978	26
15	113.5	8.34665601703261	20
16	110.75	7.36545993132812	17
17	106.75	11.0867789130417	26
18	93.5	3.41565025531987	8
19	104.25	10.4363148029688	23
20	98.25	7.27438428093173	17
21	84.25	8.5	18
22	106.5	10.2794292967395	22
23	86.25	11.7011395456454	26
24	75.75	12.0381338531629	26
25	93.25	14.0564338768172	33
26	71.5	11.1205515450749	26
27	69.75	14.9303940559741	32
28	88.5	12.6095202129185	30
29	71.25	8.53912563829967	19
30	66.75	14.7507061977837	32

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	13.1404442873218
beta	-0.0482899414963233
S.D.	0.0415490211757219
T-STAT	-1.16224017148544
p-value	0.254949001968249

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 13.1404442873218 \tabularnewline
beta & -0.0482899414963233 \tabularnewline
S.D. & 0.0415490211757219 \tabularnewline
T-STAT & -1.16224017148544 \tabularnewline
p-value & 0.254949001968249 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79174&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]13.1404442873218[/C][/ROW]
[ROW][C]beta[/C][C]-0.0482899414963233[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0415490211757219[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.16224017148544[/C][/ROW]
[ROW][C]p-value[/C][C]0.254949001968249[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79174&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79174&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	13.1404442873218
beta	-0.0482899414963233
S.D.	0.0415490211757219
T-STAT	-1.16224017148544
p-value	0.254949001968249

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.26879912544983
beta	-0.512387006672243
S.D.	0.708123831830356
T-STAT	-0.72358390388843
p-value	0.475323357359544
Lambda	1.51238700667224

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.26879912544983 \tabularnewline
beta & -0.512387006672243 \tabularnewline
S.D. & 0.708123831830356 \tabularnewline
T-STAT & -0.72358390388843 \tabularnewline
p-value & 0.475323357359544 \tabularnewline
Lambda & 1.51238700667224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79174&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.26879912544983[/C][/ROW]
[ROW][C]beta[/C][C]-0.512387006672243[/C][/ROW]
[ROW][C]S.D.[/C][C]0.708123831830356[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.72358390388843[/C][/ROW]
[ROW][C]p-value[/C][C]0.475323357359544[/C][/ROW]
[ROW][C]Lambda[/C][C]1.51238700667224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79174&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79174&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	4.26879912544983
beta	-0.512387006672243
S.D.	0.708123831830356
T-STAT	-0.72358390388843
p-value	0.475323357359544
Lambda	1.51238700667224

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