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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

Sun, 03 Jan 2010 13:02:26 -0700

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/Jan/03/t1262549187asuzg1ne96zyae6.htm/, Retrieved Fri, 03 May 2024 07:41:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71560, Retrieved Fri, 03 May 2024 07:41:43 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

164

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

-     [] [] [1970-01-01 00:00:00] [8c7c3dc396eba234a49aa27457495c03]
- RMPD  [(Partial) Autocorrelation Function] [] [2010-01-03 19:03:42] [8c7c3dc396eba234a49aa27457495c03]
- RMP       [Standard Deviation-Mean Plot] [] [2010-01-03 20:02:26] [4ed6a647410123598b51b3bdc215cd7e] [Current]

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Dataseries X:

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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	'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=71560&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=71560&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71560&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	8.755	0.117046999107196	0.24
2	8.4575	0.055602757725374	0.119999999999999
3	7.72	0.255473416751463	0.55
4	7.3675	0.040311288741493	0.0900000000000007
5	7.3325	0.0492442890089806	0.110000000000000
6	7.3225	0.00957427107756356	0.0200000000000005
7	7.4425	0.193627649540727	0.430000000000001
8	7.805	0.0288675134594814	0.0700000000000003
9	7.8025	0.0170782512765993	0.04
10	7.555	0.211423745118660	0.45
11	7.3325	0.0394757309410899	0.0899999999999999
12	7.245	0.0369684550213648	0.08
13	7.2025	0.00957427107756318	0.0199999999999996
14	7.1225	0.0449999999999998	0.109999999999999
15	7.065	0.0129099444873582	0.0300000000000002
16	7.08	0.00816496580927709	0.0199999999999996
17	7.0075	0.0349999999999997	0.0699999999999994
18	6.95	0.0294392028877596	0.0700000000000003
19	6.895	0.0191485421551268	0.04
20	6.885	0.0264575131106462	0.0600000000000005
21	6.8275	0.0250000000000002	0.0600000000000005
22	7.02	0.182391520270726	0.37
23	7.335	0.100166528008778	0.230000000000000
24	7.4375	0.0386221007541882	0.0899999999999999
25	7.33	0.202155056000751	0.470000000000001
26	7.6825	0.0170782512765994	0.04
27	7.705	0.0173205080756888	0.04
28	7.78	0.0816496580927728	0.180000000000001
29	7.9625	0.00957427107756318	0.0199999999999996
30	7.95	0.0316227766016840	0.0700000000000003
31	7.9975	0.0309569593683441	0.0699999999999994
32	8.255	0.0591607978309962	0.130000000000001
33	8.2975	0.0262995563967663	0.0500000000000007

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.755 & 0.117046999107196 & 0.24 \tabularnewline
2 & 8.4575 & 0.055602757725374 & 0.119999999999999 \tabularnewline
3 & 7.72 & 0.255473416751463 & 0.55 \tabularnewline
4 & 7.3675 & 0.040311288741493 & 0.0900000000000007 \tabularnewline
5 & 7.3325 & 0.0492442890089806 & 0.110000000000000 \tabularnewline
6 & 7.3225 & 0.00957427107756356 & 0.0200000000000005 \tabularnewline
7 & 7.4425 & 0.193627649540727 & 0.430000000000001 \tabularnewline
8 & 7.805 & 0.0288675134594814 & 0.0700000000000003 \tabularnewline
9 & 7.8025 & 0.0170782512765993 & 0.04 \tabularnewline
10 & 7.555 & 0.211423745118660 & 0.45 \tabularnewline
11 & 7.3325 & 0.0394757309410899 & 0.0899999999999999 \tabularnewline
12 & 7.245 & 0.0369684550213648 & 0.08 \tabularnewline
13 & 7.2025 & 0.00957427107756318 & 0.0199999999999996 \tabularnewline
14 & 7.1225 & 0.0449999999999998 & 0.109999999999999 \tabularnewline
15 & 7.065 & 0.0129099444873582 & 0.0300000000000002 \tabularnewline
16 & 7.08 & 0.00816496580927709 & 0.0199999999999996 \tabularnewline
17 & 7.0075 & 0.0349999999999997 & 0.0699999999999994 \tabularnewline
18 & 6.95 & 0.0294392028877596 & 0.0700000000000003 \tabularnewline
19 & 6.895 & 0.0191485421551268 & 0.04 \tabularnewline
20 & 6.885 & 0.0264575131106462 & 0.0600000000000005 \tabularnewline
21 & 6.8275 & 0.0250000000000002 & 0.0600000000000005 \tabularnewline
22 & 7.02 & 0.182391520270726 & 0.37 \tabularnewline
23 & 7.335 & 0.100166528008778 & 0.230000000000000 \tabularnewline
24 & 7.4375 & 0.0386221007541882 & 0.0899999999999999 \tabularnewline
25 & 7.33 & 0.202155056000751 & 0.470000000000001 \tabularnewline
26 & 7.6825 & 0.0170782512765994 & 0.04 \tabularnewline
27 & 7.705 & 0.0173205080756888 & 0.04 \tabularnewline
28 & 7.78 & 0.0816496580927728 & 0.180000000000001 \tabularnewline
29 & 7.9625 & 0.00957427107756318 & 0.0199999999999996 \tabularnewline
30 & 7.95 & 0.0316227766016840 & 0.0700000000000003 \tabularnewline
31 & 7.9975 & 0.0309569593683441 & 0.0699999999999994 \tabularnewline
32 & 8.255 & 0.0591607978309962 & 0.130000000000001 \tabularnewline
33 & 8.2975 & 0.0262995563967663 & 0.0500000000000007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71560&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]8.755[/C][C]0.117046999107196[/C][C]0.24[/C][/ROW]
[ROW][C]2[/C][C]8.4575[/C][C]0.055602757725374[/C][C]0.119999999999999[/C][/ROW]
[ROW][C]3[/C][C]7.72[/C][C]0.255473416751463[/C][C]0.55[/C][/ROW]
[ROW][C]4[/C][C]7.3675[/C][C]0.040311288741493[/C][C]0.0900000000000007[/C][/ROW]
[ROW][C]5[/C][C]7.3325[/C][C]0.0492442890089806[/C][C]0.110000000000000[/C][/ROW]
[ROW][C]6[/C][C]7.3225[/C][C]0.00957427107756356[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]7[/C][C]7.4425[/C][C]0.193627649540727[/C][C]0.430000000000001[/C][/ROW]
[ROW][C]8[/C][C]7.805[/C][C]0.0288675134594814[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]9[/C][C]7.8025[/C][C]0.0170782512765993[/C][C]0.04[/C][/ROW]
[ROW][C]10[/C][C]7.555[/C][C]0.211423745118660[/C][C]0.45[/C][/ROW]
[ROW][C]11[/C][C]7.3325[/C][C]0.0394757309410899[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]12[/C][C]7.245[/C][C]0.0369684550213648[/C][C]0.08[/C][/ROW]
[ROW][C]13[/C][C]7.2025[/C][C]0.00957427107756318[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]14[/C][C]7.1225[/C][C]0.0449999999999998[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]15[/C][C]7.065[/C][C]0.0129099444873582[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]16[/C][C]7.08[/C][C]0.00816496580927709[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]17[/C][C]7.0075[/C][C]0.0349999999999997[/C][C]0.0699999999999994[/C][/ROW]
[ROW][C]18[/C][C]6.95[/C][C]0.0294392028877596[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]19[/C][C]6.895[/C][C]0.0191485421551268[/C][C]0.04[/C][/ROW]
[ROW][C]20[/C][C]6.885[/C][C]0.0264575131106462[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]21[/C][C]6.8275[/C][C]0.0250000000000002[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]22[/C][C]7.02[/C][C]0.182391520270726[/C][C]0.37[/C][/ROW]
[ROW][C]23[/C][C]7.335[/C][C]0.100166528008778[/C][C]0.230000000000000[/C][/ROW]
[ROW][C]24[/C][C]7.4375[/C][C]0.0386221007541882[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]25[/C][C]7.33[/C][C]0.202155056000751[/C][C]0.470000000000001[/C][/ROW]
[ROW][C]26[/C][C]7.6825[/C][C]0.0170782512765994[/C][C]0.04[/C][/ROW]
[ROW][C]27[/C][C]7.705[/C][C]0.0173205080756888[/C][C]0.04[/C][/ROW]
[ROW][C]28[/C][C]7.78[/C][C]0.0816496580927728[/C][C]0.180000000000001[/C][/ROW]
[ROW][C]29[/C][C]7.9625[/C][C]0.00957427107756318[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]30[/C][C]7.95[/C][C]0.0316227766016840[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]31[/C][C]7.9975[/C][C]0.0309569593683441[/C][C]0.0699999999999994[/C][/ROW]
[ROW][C]32[/C][C]8.255[/C][C]0.0591607978309962[/C][C]0.130000000000001[/C][/ROW]
[ROW][C]33[/C][C]8.2975[/C][C]0.0262995563967663[/C][C]0.0500000000000007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71560&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71560&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	8.755	0.117046999107196	0.24
2	8.4575	0.055602757725374	0.119999999999999
3	7.72	0.255473416751463	0.55
4	7.3675	0.040311288741493	0.0900000000000007
5	7.3325	0.0492442890089806	0.110000000000000
6	7.3225	0.00957427107756356	0.0200000000000005
7	7.4425	0.193627649540727	0.430000000000001
8	7.805	0.0288675134594814	0.0700000000000003
9	7.8025	0.0170782512765993	0.04
10	7.555	0.211423745118660	0.45
11	7.3325	0.0394757309410899	0.0899999999999999
12	7.245	0.0369684550213648	0.08
13	7.2025	0.00957427107756318	0.0199999999999996
14	7.1225	0.0449999999999998	0.109999999999999
15	7.065	0.0129099444873582	0.0300000000000002
16	7.08	0.00816496580927709	0.0199999999999996
17	7.0075	0.0349999999999997	0.0699999999999994
18	6.95	0.0294392028877596	0.0700000000000003
19	6.895	0.0191485421551268	0.04
20	6.885	0.0264575131106462	0.0600000000000005
21	6.8275	0.0250000000000002	0.0600000000000005
22	7.02	0.182391520270726	0.37
23	7.335	0.100166528008778	0.230000000000000
24	7.4375	0.0386221007541882	0.0899999999999999
25	7.33	0.202155056000751	0.470000000000001
26	7.6825	0.0170782512765994	0.04
27	7.705	0.0173205080756888	0.04
28	7.78	0.0816496580927728	0.180000000000001
29	7.9625	0.00957427107756318	0.0199999999999996
30	7.95	0.0316227766016840	0.0700000000000003
31	7.9975	0.0309569593683441	0.0699999999999994
32	8.255	0.0591607978309962	0.130000000000001
33	8.2975	0.0262995563967663	0.0500000000000007

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-0.0313717288736456
beta	0.0124943182167304
S.D.	0.0251209049852402
T-STAT	0.497367360931919
p-value	0.622439568101046

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0313717288736456 \tabularnewline
beta & 0.0124943182167304 \tabularnewline
S.D. & 0.0251209049852402 \tabularnewline
T-STAT & 0.497367360931919 \tabularnewline
p-value & 0.622439568101046 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71560&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0313717288736456[/C][/ROW]
[ROW][C]beta[/C][C]0.0124943182167304[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0251209049852402[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.497367360931919[/C][/ROW]
[ROW][C]p-value[/C][C]0.622439568101046[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71560&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71560&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	-0.0313717288736456
beta	0.0124943182167304
S.D.	0.0251209049852402
T-STAT	0.497367360931919
p-value	0.622439568101046

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-8.4731068761664
beta	2.59329427594423
S.D.	2.69688842846645
T-STAT	0.961587527526627
p-value	0.343697827739917
Lambda	-1.59329427594423

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -8.4731068761664 \tabularnewline
beta & 2.59329427594423 \tabularnewline
S.D. & 2.69688842846645 \tabularnewline
T-STAT & 0.961587527526627 \tabularnewline
p-value & 0.343697827739917 \tabularnewline
Lambda & -1.59329427594423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71560&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8.4731068761664[/C][/ROW]
[ROW][C]beta[/C][C]2.59329427594423[/C][/ROW]
[ROW][C]S.D.[/C][C]2.69688842846645[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.961587527526627[/C][/ROW]
[ROW][C]p-value[/C][C]0.343697827739917[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.59329427594423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71560&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71560&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	-8.4731068761664
beta	2.59329427594423
S.D.	2.69688842846645
T-STAT	0.961587527526627
p-value	0.343697827739917
Lambda	-1.59329427594423

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