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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, 17 May 2010 14:46:44 +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/May/17/t1274107658ywkmtqj05l5w5m9.htm/, Retrieved Sun, 05 May 2024 14:36:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76077, Retrieved Sun, 05 May 2024 14:36:27 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

188

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

-       [Standard Deviation-Mean Plot] [Spreidings- en ge...] [2010-05-17 14:46:44] [d4eb12efc488666eba544481d350541e] [Current]
- RMPD    [Classical Decomposition] [decompositie wiss...] [2010-05-20 11:57:43] [05bbf10299dcd1da03eee55b39d86f8c] 
-   PD      [Classical Decomposition] [Decompositie wiss...] [2010-05-27 15:51:13] [05bbf10299dcd1da03eee55b39d86f8c] 
-   P     [Standard Deviation-Mean Plot] [Spreidings- en ge...] [2010-05-27 14:28:21] [05bbf10299dcd1da03eee55b39d86f8c] 

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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=76077&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=76077&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76077&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	1.109525	0.0390126795627610	0.089
2	1.04955	0.0141271606017156	0.026
3	1.041025	0.0252922089453123	0.0596000000000001
4	0.976425	0.0290662891795060	0.0681999999999999
5	0.924875	0.0232393882593038	0.046
6	0.868875	0.0209870396514928	0.0458000000000000
7	0.914725	0.0190774517865114	0.0451
8	0.8728	0.0211655380276524	0.0484
9	0.898975	0.0110315834463296	0.0231
10	0.879125	0.0068611830855424	0.0153000000000000
11	0.961175	0.0332091729295788	0.0765
12	0.995625	0.0185408333146059	0.0388000000000001
13	1.07665	0.0102099624550404	0.024
14	1.14375	0.0227330156380538	0.0519000000000001
15	1.174725	0.0422870646100357	0.1031
16	1.2382	0.0316854330358079	0.0650999999999999
17	1.215075	0.0112027898311090	0.0266000000000000
18	1.27835	0.05236350510295	0.1182
19	1.3066	0.0108547992458022	0.0242
20	1.2297	0.0286184089937462	0.0656000000000001
21	1.19765	0.0197376965896902	0.0445
22	1.209175	0.0142731391081290	0.0333000000000001
23	1.272975	0.00705472654797236	0.0148999999999999
24	1.2858	0.0256830683525158	0.0588
25	1.3208	0.0228821619025243	0.052
26	1.357275	0.0132094347595447	0.0305
27	1.434625	0.0347276426880182	0.0773
28	1.519025	0.0524785908728502	0.102600000000000
29	1.54575	0.0348157531394434	0.0804
30	1.346575	0.0666004191678501	0.1598
31	1.30725	0.0201511786255792	0.0447
32	1.40045	0.0261183843298164	0.062
33	1.472075	0.0169753497754832	0.0332999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.109525 & 0.0390126795627610 & 0.089 \tabularnewline
2 & 1.04955 & 0.0141271606017156 & 0.026 \tabularnewline
3 & 1.041025 & 0.0252922089453123 & 0.0596000000000001 \tabularnewline
4 & 0.976425 & 0.0290662891795060 & 0.0681999999999999 \tabularnewline
5 & 0.924875 & 0.0232393882593038 & 0.046 \tabularnewline
6 & 0.868875 & 0.0209870396514928 & 0.0458000000000000 \tabularnewline
7 & 0.914725 & 0.0190774517865114 & 0.0451 \tabularnewline
8 & 0.8728 & 0.0211655380276524 & 0.0484 \tabularnewline
9 & 0.898975 & 0.0110315834463296 & 0.0231 \tabularnewline
10 & 0.879125 & 0.0068611830855424 & 0.0153000000000000 \tabularnewline
11 & 0.961175 & 0.0332091729295788 & 0.0765 \tabularnewline
12 & 0.995625 & 0.0185408333146059 & 0.0388000000000001 \tabularnewline
13 & 1.07665 & 0.0102099624550404 & 0.024 \tabularnewline
14 & 1.14375 & 0.0227330156380538 & 0.0519000000000001 \tabularnewline
15 & 1.174725 & 0.0422870646100357 & 0.1031 \tabularnewline
16 & 1.2382 & 0.0316854330358079 & 0.0650999999999999 \tabularnewline
17 & 1.215075 & 0.0112027898311090 & 0.0266000000000000 \tabularnewline
18 & 1.27835 & 0.05236350510295 & 0.1182 \tabularnewline
19 & 1.3066 & 0.0108547992458022 & 0.0242 \tabularnewline
20 & 1.2297 & 0.0286184089937462 & 0.0656000000000001 \tabularnewline
21 & 1.19765 & 0.0197376965896902 & 0.0445 \tabularnewline
22 & 1.209175 & 0.0142731391081290 & 0.0333000000000001 \tabularnewline
23 & 1.272975 & 0.00705472654797236 & 0.0148999999999999 \tabularnewline
24 & 1.2858 & 0.0256830683525158 & 0.0588 \tabularnewline
25 & 1.3208 & 0.0228821619025243 & 0.052 \tabularnewline
26 & 1.357275 & 0.0132094347595447 & 0.0305 \tabularnewline
27 & 1.434625 & 0.0347276426880182 & 0.0773 \tabularnewline
28 & 1.519025 & 0.0524785908728502 & 0.102600000000000 \tabularnewline
29 & 1.54575 & 0.0348157531394434 & 0.0804 \tabularnewline
30 & 1.346575 & 0.0666004191678501 & 0.1598 \tabularnewline
31 & 1.30725 & 0.0201511786255792 & 0.0447 \tabularnewline
32 & 1.40045 & 0.0261183843298164 & 0.062 \tabularnewline
33 & 1.472075 & 0.0169753497754832 & 0.0332999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76077&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]1.109525[/C][C]0.0390126795627610[/C][C]0.089[/C][/ROW]
[ROW][C]2[/C][C]1.04955[/C][C]0.0141271606017156[/C][C]0.026[/C][/ROW]
[ROW][C]3[/C][C]1.041025[/C][C]0.0252922089453123[/C][C]0.0596000000000001[/C][/ROW]
[ROW][C]4[/C][C]0.976425[/C][C]0.0290662891795060[/C][C]0.0681999999999999[/C][/ROW]
[ROW][C]5[/C][C]0.924875[/C][C]0.0232393882593038[/C][C]0.046[/C][/ROW]
[ROW][C]6[/C][C]0.868875[/C][C]0.0209870396514928[/C][C]0.0458000000000000[/C][/ROW]
[ROW][C]7[/C][C]0.914725[/C][C]0.0190774517865114[/C][C]0.0451[/C][/ROW]
[ROW][C]8[/C][C]0.8728[/C][C]0.0211655380276524[/C][C]0.0484[/C][/ROW]
[ROW][C]9[/C][C]0.898975[/C][C]0.0110315834463296[/C][C]0.0231[/C][/ROW]
[ROW][C]10[/C][C]0.879125[/C][C]0.0068611830855424[/C][C]0.0153000000000000[/C][/ROW]
[ROW][C]11[/C][C]0.961175[/C][C]0.0332091729295788[/C][C]0.0765[/C][/ROW]
[ROW][C]12[/C][C]0.995625[/C][C]0.0185408333146059[/C][C]0.0388000000000001[/C][/ROW]
[ROW][C]13[/C][C]1.07665[/C][C]0.0102099624550404[/C][C]0.024[/C][/ROW]
[ROW][C]14[/C][C]1.14375[/C][C]0.0227330156380538[/C][C]0.0519000000000001[/C][/ROW]
[ROW][C]15[/C][C]1.174725[/C][C]0.0422870646100357[/C][C]0.1031[/C][/ROW]
[ROW][C]16[/C][C]1.2382[/C][C]0.0316854330358079[/C][C]0.0650999999999999[/C][/ROW]
[ROW][C]17[/C][C]1.215075[/C][C]0.0112027898311090[/C][C]0.0266000000000000[/C][/ROW]
[ROW][C]18[/C][C]1.27835[/C][C]0.05236350510295[/C][C]0.1182[/C][/ROW]
[ROW][C]19[/C][C]1.3066[/C][C]0.0108547992458022[/C][C]0.0242[/C][/ROW]
[ROW][C]20[/C][C]1.2297[/C][C]0.0286184089937462[/C][C]0.0656000000000001[/C][/ROW]
[ROW][C]21[/C][C]1.19765[/C][C]0.0197376965896902[/C][C]0.0445[/C][/ROW]
[ROW][C]22[/C][C]1.209175[/C][C]0.0142731391081290[/C][C]0.0333000000000001[/C][/ROW]
[ROW][C]23[/C][C]1.272975[/C][C]0.00705472654797236[/C][C]0.0148999999999999[/C][/ROW]
[ROW][C]24[/C][C]1.2858[/C][C]0.0256830683525158[/C][C]0.0588[/C][/ROW]
[ROW][C]25[/C][C]1.3208[/C][C]0.0228821619025243[/C][C]0.052[/C][/ROW]
[ROW][C]26[/C][C]1.357275[/C][C]0.0132094347595447[/C][C]0.0305[/C][/ROW]
[ROW][C]27[/C][C]1.434625[/C][C]0.0347276426880182[/C][C]0.0773[/C][/ROW]
[ROW][C]28[/C][C]1.519025[/C][C]0.0524785908728502[/C][C]0.102600000000000[/C][/ROW]
[ROW][C]29[/C][C]1.54575[/C][C]0.0348157531394434[/C][C]0.0804[/C][/ROW]
[ROW][C]30[/C][C]1.346575[/C][C]0.0666004191678501[/C][C]0.1598[/C][/ROW]
[ROW][C]31[/C][C]1.30725[/C][C]0.0201511786255792[/C][C]0.0447[/C][/ROW]
[ROW][C]32[/C][C]1.40045[/C][C]0.0261183843298164[/C][C]0.062[/C][/ROW]
[ROW][C]33[/C][C]1.472075[/C][C]0.0169753497754832[/C][C]0.0332999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76077&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76077&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	1.109525	0.0390126795627610	0.089
2	1.04955	0.0141271606017156	0.026
3	1.041025	0.0252922089453123	0.0596000000000001
4	0.976425	0.0290662891795060	0.0681999999999999
5	0.924875	0.0232393882593038	0.046
6	0.868875	0.0209870396514928	0.0458000000000000
7	0.914725	0.0190774517865114	0.0451
8	0.8728	0.0211655380276524	0.0484
9	0.898975	0.0110315834463296	0.0231
10	0.879125	0.0068611830855424	0.0153000000000000
11	0.961175	0.0332091729295788	0.0765
12	0.995625	0.0185408333146059	0.0388000000000001
13	1.07665	0.0102099624550404	0.024
14	1.14375	0.0227330156380538	0.0519000000000001
15	1.174725	0.0422870646100357	0.1031
16	1.2382	0.0316854330358079	0.0650999999999999
17	1.215075	0.0112027898311090	0.0266000000000000
18	1.27835	0.05236350510295	0.1182
19	1.3066	0.0108547992458022	0.0242
20	1.2297	0.0286184089937462	0.0656000000000001
21	1.19765	0.0197376965896902	0.0445
22	1.209175	0.0142731391081290	0.0333000000000001
23	1.272975	0.00705472654797236	0.0148999999999999
24	1.2858	0.0256830683525158	0.0588
25	1.3208	0.0228821619025243	0.052
26	1.357275	0.0132094347595447	0.0305
27	1.434625	0.0347276426880182	0.0773
28	1.519025	0.0524785908728502	0.102600000000000
29	1.54575	0.0348157531394434	0.0804
30	1.346575	0.0666004191678501	0.1598
31	1.30725	0.0201511786255792	0.0447
32	1.40045	0.0261183843298164	0.062
33	1.472075	0.0169753497754832	0.0332999999999999

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-0.00324673511815485
beta	0.0240414965923884
S.D.	0.011710874657833
T-STAT	2.05292066517917
p-value	0.0486021634004753

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.00324673511815485 \tabularnewline
beta & 0.0240414965923884 \tabularnewline
S.D. & 0.011710874657833 \tabularnewline
T-STAT & 2.05292066517917 \tabularnewline
p-value & 0.0486021634004753 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76077&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.00324673511815485[/C][/ROW]
[ROW][C]beta[/C][C]0.0240414965923884[/C][/ROW]
[ROW][C]S.D.[/C][C]0.011710874657833[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.05292066517917[/C][/ROW]
[ROW][C]p-value[/C][C]0.0486021634004753[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76077&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76077&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	-0.00324673511815485
beta	0.0240414965923884
S.D.	0.011710874657833
T-STAT	2.05292066517917
p-value	0.0486021634004753

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.97456301302267
beta	0.965326519283815
S.D.	0.550260323577679
T-STAT	1.75430878426317
p-value	0.089259440986057
Lambda	0.0346734807161853

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.97456301302267 \tabularnewline
beta & 0.965326519283815 \tabularnewline
S.D. & 0.550260323577679 \tabularnewline
T-STAT & 1.75430878426317 \tabularnewline
p-value & 0.089259440986057 \tabularnewline
Lambda & 0.0346734807161853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76077&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.97456301302267[/C][/ROW]
[ROW][C]beta[/C][C]0.965326519283815[/C][/ROW]
[ROW][C]S.D.[/C][C]0.550260323577679[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.75430878426317[/C][/ROW]
[ROW][C]p-value[/C][C]0.089259440986057[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0346734807161853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76077&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76077&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	-3.97456301302267
beta	0.965326519283815
S.D.	0.550260323577679
T-STAT	1.75430878426317
p-value	0.089259440986057
Lambda	0.0346734807161853

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