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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

Tue, 03 Aug 2010 14:12:39 +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/03/t1280844811ft6lwyxuzmkrfo9.htm/, Retrieved Fri, 03 May 2024 01:20:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78263, Retrieved Fri, 03 May 2024 01:20:01 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Lisa Bruggeman

Estimated Impact

149

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

-     [Quartiles] [Tijdreeks 1 - Stap 8] [2010-07-15 13:59:40] [e35b30db8ce3563ce7b9c1c6d8c0e4ae]
- RM D    [Standard Deviation-Mean Plot] [TIJDREEKS A - STA...] [2010-08-03 14:12:39] [0e6aef37627b8cf9d1bd74110cef2cca] [Current]

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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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78263&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78263&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78263&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	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	93.25	1.70782512765993	4
2	100.25	12.5266382827424	26
3	87	1.41421356237310	3
4	95	3.16227766016838	7
5	101	10.4880884817015	22
6	91	2.30940107675850	4
7	93	6.32455532033676	14
8	93.5	11.5614301306831	25
9	86.25	1.5	3
10	94	7.07106781186548	17
11	104.25	12.6852933220587	29
12	93.25	3.685557397916	9
13	100.75	7.41057802513857	15
14	109.75	12.5797456254091	30
15	99.25	7.08872343937891	15
16	95	10.8627804912002	23
17	104.25	9.63932916061417	22
18	108.5	9.8488578017961	18
19	116.25	12.0381338531629	26
20	138.25	7.63216876123687	18
21	161.75	6.34428877022476	15
22	178.75	15.3920975395385	31
23	194	8.86942313043338	20
24	221.5	8.38649708360608	20
25	242.5	14.4337567297406	31
26	265	11.4600756251141	27
27	286.75	7.8049129826454	17
28	310	16.8522995463527	36
29	330	11.6904519445001	28
30	346.5	10.4083299973307	23

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 93.25 & 1.70782512765993 & 4 \tabularnewline
2 & 100.25 & 12.5266382827424 & 26 \tabularnewline
3 & 87 & 1.41421356237310 & 3 \tabularnewline
4 & 95 & 3.16227766016838 & 7 \tabularnewline
5 & 101 & 10.4880884817015 & 22 \tabularnewline
6 & 91 & 2.30940107675850 & 4 \tabularnewline
7 & 93 & 6.32455532033676 & 14 \tabularnewline
8 & 93.5 & 11.5614301306831 & 25 \tabularnewline
9 & 86.25 & 1.5 & 3 \tabularnewline
10 & 94 & 7.07106781186548 & 17 \tabularnewline
11 & 104.25 & 12.6852933220587 & 29 \tabularnewline
12 & 93.25 & 3.685557397916 & 9 \tabularnewline
13 & 100.75 & 7.41057802513857 & 15 \tabularnewline
14 & 109.75 & 12.5797456254091 & 30 \tabularnewline
15 & 99.25 & 7.08872343937891 & 15 \tabularnewline
16 & 95 & 10.8627804912002 & 23 \tabularnewline
17 & 104.25 & 9.63932916061417 & 22 \tabularnewline
18 & 108.5 & 9.8488578017961 & 18 \tabularnewline
19 & 116.25 & 12.0381338531629 & 26 \tabularnewline
20 & 138.25 & 7.63216876123687 & 18 \tabularnewline
21 & 161.75 & 6.34428877022476 & 15 \tabularnewline
22 & 178.75 & 15.3920975395385 & 31 \tabularnewline
23 & 194 & 8.86942313043338 & 20 \tabularnewline
24 & 221.5 & 8.38649708360608 & 20 \tabularnewline
25 & 242.5 & 14.4337567297406 & 31 \tabularnewline
26 & 265 & 11.4600756251141 & 27 \tabularnewline
27 & 286.75 & 7.8049129826454 & 17 \tabularnewline
28 & 310 & 16.8522995463527 & 36 \tabularnewline
29 & 330 & 11.6904519445001 & 28 \tabularnewline
30 & 346.5 & 10.4083299973307 & 23 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78263&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]93.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]100.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]87[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]95[/C][C]3.16227766016838[/C][C]7[/C][/ROW]
[ROW][C]5[/C][C]101[/C][C]10.4880884817015[/C][C]22[/C][/ROW]
[ROW][C]6[/C][C]91[/C][C]2.30940107675850[/C][C]4[/C][/ROW]
[ROW][C]7[/C][C]93[/C][C]6.32455532033676[/C][C]14[/C][/ROW]
[ROW][C]8[/C][C]93.5[/C][C]11.5614301306831[/C][C]25[/C][/ROW]
[ROW][C]9[/C][C]86.25[/C][C]1.5[/C][C]3[/C][/ROW]
[ROW][C]10[/C][C]94[/C][C]7.07106781186548[/C][C]17[/C][/ROW]
[ROW][C]11[/C][C]104.25[/C][C]12.6852933220587[/C][C]29[/C][/ROW]
[ROW][C]12[/C][C]93.25[/C][C]3.685557397916[/C][C]9[/C][/ROW]
[ROW][C]13[/C][C]100.75[/C][C]7.41057802513857[/C][C]15[/C][/ROW]
[ROW][C]14[/C][C]109.75[/C][C]12.5797456254091[/C][C]30[/C][/ROW]
[ROW][C]15[/C][C]99.25[/C][C]7.08872343937891[/C][C]15[/C][/ROW]
[ROW][C]16[/C][C]95[/C][C]10.8627804912002[/C][C]23[/C][/ROW]
[ROW][C]17[/C][C]104.25[/C][C]9.63932916061417[/C][C]22[/C][/ROW]
[ROW][C]18[/C][C]108.5[/C][C]9.8488578017961[/C][C]18[/C][/ROW]
[ROW][C]19[/C][C]116.25[/C][C]12.0381338531629[/C][C]26[/C][/ROW]
[ROW][C]20[/C][C]138.25[/C][C]7.63216876123687[/C][C]18[/C][/ROW]
[ROW][C]21[/C][C]161.75[/C][C]6.34428877022476[/C][C]15[/C][/ROW]
[ROW][C]22[/C][C]178.75[/C][C]15.3920975395385[/C][C]31[/C][/ROW]
[ROW][C]23[/C][C]194[/C][C]8.86942313043338[/C][C]20[/C][/ROW]
[ROW][C]24[/C][C]221.5[/C][C]8.38649708360608[/C][C]20[/C][/ROW]
[ROW][C]25[/C][C]242.5[/C][C]14.4337567297406[/C][C]31[/C][/ROW]
[ROW][C]26[/C][C]265[/C][C]11.4600756251141[/C][C]27[/C][/ROW]
[ROW][C]27[/C][C]286.75[/C][C]7.8049129826454[/C][C]17[/C][/ROW]
[ROW][C]28[/C][C]310[/C][C]16.8522995463527[/C][C]36[/C][/ROW]
[ROW][C]29[/C][C]330[/C][C]11.6904519445001[/C][C]28[/C][/ROW]
[ROW][C]30[/C][C]346.5[/C][C]10.4083299973307[/C][C]23[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78263&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78263&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	93.25	1.70782512765993	4
2	100.25	12.5266382827424	26
3	87	1.41421356237310	3
4	95	3.16227766016838	7
5	101	10.4880884817015	22
6	91	2.30940107675850	4
7	93	6.32455532033676	14
8	93.5	11.5614301306831	25
9	86.25	1.5	3
10	94	7.07106781186548	17
11	104.25	12.6852933220587	29
12	93.25	3.685557397916	9
13	100.75	7.41057802513857	15
14	109.75	12.5797456254091	30
15	99.25	7.08872343937891	15
16	95	10.8627804912002	23
17	104.25	9.63932916061417	22
18	108.5	9.8488578017961	18
19	116.25	12.0381338531629	26
20	138.25	7.63216876123687	18
21	161.75	6.34428877022476	15
22	178.75	15.3920975395385	31
23	194	8.86942313043338	20
24	221.5	8.38649708360608	20
25	242.5	14.4337567297406	31
26	265	11.4600756251141	27
27	286.75	7.8049129826454	17
28	310	16.8522995463527	36
29	330	11.6904519445001	28
30	346.5	10.4083299973307	23

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	5.23231782521091
beta	0.023391534836551
S.D.	0.00852047944486471
T-STAT	2.74533082180594
p-value	0.0104384565800472

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.23231782521091 \tabularnewline
beta & 0.023391534836551 \tabularnewline
S.D. & 0.00852047944486471 \tabularnewline
T-STAT & 2.74533082180594 \tabularnewline
p-value & 0.0104384565800472 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78263&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.23231782521091[/C][/ROW]
[ROW][C]beta[/C][C]0.023391534836551[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00852047944486471[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.74533082180594[/C][/ROW]
[ROW][C]p-value[/C][C]0.0104384565800472[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78263&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78263&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	5.23231782521091
beta	0.023391534836551
S.D.	0.00852047944486471
T-STAT	2.74533082180594
p-value	0.0104384565800472

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.52186922535830
beta	0.717554426997993
S.D.	0.246603154493645
T-STAT	2.90975364233017
p-value	0.00701376491692247
Lambda	0.282445573002007

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.52186922535830 \tabularnewline
beta & 0.717554426997993 \tabularnewline
S.D. & 0.246603154493645 \tabularnewline
T-STAT & 2.90975364233017 \tabularnewline
p-value & 0.00701376491692247 \tabularnewline
Lambda & 0.282445573002007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78263&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.52186922535830[/C][/ROW]
[ROW][C]beta[/C][C]0.717554426997993[/C][/ROW]
[ROW][C]S.D.[/C][C]0.246603154493645[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.90975364233017[/C][/ROW]
[ROW][C]p-value[/C][C]0.00701376491692247[/C][/ROW]
[ROW][C]Lambda[/C][C]0.282445573002007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78263&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78263&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	-1.52186922535830
beta	0.717554426997993
S.D.	0.246603154493645
T-STAT	2.90975364233017
p-value	0.00701376491692247
Lambda	0.282445573002007

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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