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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 13:38:50 +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/t1281965911c2s7wymgck6lc42.htm/, Retrieved Thu, 16 May 2024 22:53:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78992, Retrieved Thu, 16 May 2024 22:53:38 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Jeroen_Kinne

Estimated Impact

109

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

-       [Standard Deviation-Mean Plot] [standard_Deviatio...] [2010-08-16 13:38:50] [6fe3b5976049c9b6736c06f51fce3033] [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	'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=78992&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=78992&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78992&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	34.25	1.70782512765993	4
2	41.25	12.5266382827424	26
3	28	1.41421356237310	3
4	27.5	1.73205080756888	4
5	45.5	10.6614570611463	23
6	38.25	1.89296944860009	4
7	36.5	3.3166247903554	7
8	71.25	14.5688022843335	30
9	72.5	3.3166247903554	8
10	70.25	7.88986691902975	18
11	109	8.52447456836295	19
12	111.75	5.90903263374528	14
13	110	5.09901951359278	12
14	156.25	11.6153633893506	26
15	166.75	6.39661368746516	14
16	167.25	3.30403793359983	8
17	203.25	19.9227675453654	44
18	203.75	11.5578256317239	25
19	218	5.09901951359278	12
20	258.5	22.3532249723986	50
21	246	9.83192080250175	22
22	253	2.44948974278318	5
23	280.5	28.1602556806574	66
24	267.25	11.3247516529061	24
25	271.25	5.31507290636732	12
26	309.25	26.2472220752343	58
27	298	11.6045967903528	26
28	304.75	13.8894444333338	31
29	359.5	29.1490422941589	63
30	350.5	8.7368949480541	19

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 34.25 & 1.70782512765993 & 4 \tabularnewline
2 & 41.25 & 12.5266382827424 & 26 \tabularnewline
3 & 28 & 1.41421356237310 & 3 \tabularnewline
4 & 27.5 & 1.73205080756888 & 4 \tabularnewline
5 & 45.5 & 10.6614570611463 & 23 \tabularnewline
6 & 38.25 & 1.89296944860009 & 4 \tabularnewline
7 & 36.5 & 3.3166247903554 & 7 \tabularnewline
8 & 71.25 & 14.5688022843335 & 30 \tabularnewline
9 & 72.5 & 3.3166247903554 & 8 \tabularnewline
10 & 70.25 & 7.88986691902975 & 18 \tabularnewline
11 & 109 & 8.52447456836295 & 19 \tabularnewline
12 & 111.75 & 5.90903263374528 & 14 \tabularnewline
13 & 110 & 5.09901951359278 & 12 \tabularnewline
14 & 156.25 & 11.6153633893506 & 26 \tabularnewline
15 & 166.75 & 6.39661368746516 & 14 \tabularnewline
16 & 167.25 & 3.30403793359983 & 8 \tabularnewline
17 & 203.25 & 19.9227675453654 & 44 \tabularnewline
18 & 203.75 & 11.5578256317239 & 25 \tabularnewline
19 & 218 & 5.09901951359278 & 12 \tabularnewline
20 & 258.5 & 22.3532249723986 & 50 \tabularnewline
21 & 246 & 9.83192080250175 & 22 \tabularnewline
22 & 253 & 2.44948974278318 & 5 \tabularnewline
23 & 280.5 & 28.1602556806574 & 66 \tabularnewline
24 & 267.25 & 11.3247516529061 & 24 \tabularnewline
25 & 271.25 & 5.31507290636732 & 12 \tabularnewline
26 & 309.25 & 26.2472220752343 & 58 \tabularnewline
27 & 298 & 11.6045967903528 & 26 \tabularnewline
28 & 304.75 & 13.8894444333338 & 31 \tabularnewline
29 & 359.5 & 29.1490422941589 & 63 \tabularnewline
30 & 350.5 & 8.7368949480541 & 19 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78992&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]34.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]41.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]28[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]27.5[/C][C]1.73205080756888[/C][C]4[/C][/ROW]
[ROW][C]5[/C][C]45.5[/C][C]10.6614570611463[/C][C]23[/C][/ROW]
[ROW][C]6[/C][C]38.25[/C][C]1.89296944860009[/C][C]4[/C][/ROW]
[ROW][C]7[/C][C]36.5[/C][C]3.3166247903554[/C][C]7[/C][/ROW]
[ROW][C]8[/C][C]71.25[/C][C]14.5688022843335[/C][C]30[/C][/ROW]
[ROW][C]9[/C][C]72.5[/C][C]3.3166247903554[/C][C]8[/C][/ROW]
[ROW][C]10[/C][C]70.25[/C][C]7.88986691902975[/C][C]18[/C][/ROW]
[ROW][C]11[/C][C]109[/C][C]8.52447456836295[/C][C]19[/C][/ROW]
[ROW][C]12[/C][C]111.75[/C][C]5.90903263374528[/C][C]14[/C][/ROW]
[ROW][C]13[/C][C]110[/C][C]5.09901951359278[/C][C]12[/C][/ROW]
[ROW][C]14[/C][C]156.25[/C][C]11.6153633893506[/C][C]26[/C][/ROW]
[ROW][C]15[/C][C]166.75[/C][C]6.39661368746516[/C][C]14[/C][/ROW]
[ROW][C]16[/C][C]167.25[/C][C]3.30403793359983[/C][C]8[/C][/ROW]
[ROW][C]17[/C][C]203.25[/C][C]19.9227675453654[/C][C]44[/C][/ROW]
[ROW][C]18[/C][C]203.75[/C][C]11.5578256317239[/C][C]25[/C][/ROW]
[ROW][C]19[/C][C]218[/C][C]5.09901951359278[/C][C]12[/C][/ROW]
[ROW][C]20[/C][C]258.5[/C][C]22.3532249723986[/C][C]50[/C][/ROW]
[ROW][C]21[/C][C]246[/C][C]9.83192080250175[/C][C]22[/C][/ROW]
[ROW][C]22[/C][C]253[/C][C]2.44948974278318[/C][C]5[/C][/ROW]
[ROW][C]23[/C][C]280.5[/C][C]28.1602556806574[/C][C]66[/C][/ROW]
[ROW][C]24[/C][C]267.25[/C][C]11.3247516529061[/C][C]24[/C][/ROW]
[ROW][C]25[/C][C]271.25[/C][C]5.31507290636732[/C][C]12[/C][/ROW]
[ROW][C]26[/C][C]309.25[/C][C]26.2472220752343[/C][C]58[/C][/ROW]
[ROW][C]27[/C][C]298[/C][C]11.6045967903528[/C][C]26[/C][/ROW]
[ROW][C]28[/C][C]304.75[/C][C]13.8894444333338[/C][C]31[/C][/ROW]
[ROW][C]29[/C][C]359.5[/C][C]29.1490422941589[/C][C]63[/C][/ROW]
[ROW][C]30[/C][C]350.5[/C][C]8.7368949480541[/C][C]19[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78992&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78992&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	34.25	1.70782512765993	4
2	41.25	12.5266382827424	26
3	28	1.41421356237310	3
4	27.5	1.73205080756888	4
5	45.5	10.6614570611463	23
6	38.25	1.89296944860009	4
7	36.5	3.3166247903554	7
8	71.25	14.5688022843335	30
9	72.5	3.3166247903554	8
10	70.25	7.88986691902975	18
11	109	8.52447456836295	19
12	111.75	5.90903263374528	14
13	110	5.09901951359278	12
14	156.25	11.6153633893506	26
15	166.75	6.39661368746516	14
16	167.25	3.30403793359983	8
17	203.25	19.9227675453654	44
18	203.75	11.5578256317239	25
19	218	5.09901951359278	12
20	258.5	22.3532249723986	50
21	246	9.83192080250175	22
22	253	2.44948974278318	5
23	280.5	28.1602556806574	66
24	267.25	11.3247516529061	24
25	271.25	5.31507290636732	12
26	309.25	26.2472220752343	58
27	298	11.6045967903528	26
28	304.75	13.8894444333338	31
29	359.5	29.1490422941589	63
30	350.5	8.7368949480541	19

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	2.90611321242171
beta	0.0427288511995813
S.D.	0.0111685176842500
T-STAT	3.82583010633882
p-value	0.000668989676680618

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.90611321242171 \tabularnewline
beta & 0.0427288511995813 \tabularnewline
S.D. & 0.0111685176842500 \tabularnewline
T-STAT & 3.82583010633882 \tabularnewline
p-value & 0.000668989676680618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78992&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.90611321242171[/C][/ROW]
[ROW][C]beta[/C][C]0.0427288511995813[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0111685176842500[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.82583010633882[/C][/ROW]
[ROW][C]p-value[/C][C]0.000668989676680618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78992&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78992&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	2.90611321242171
beta	0.0427288511995813
S.D.	0.0111685176842500
T-STAT	3.82583010633882
p-value	0.000668989676680618

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.13593946279489
beta	0.645538194601525
S.D.	0.149546636616888
T-STAT	4.31663465795811
p-value	0.00017885129120927
Lambda	0.354461805398475

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.13593946279489 \tabularnewline
beta & 0.645538194601525 \tabularnewline
S.D. & 0.149546636616888 \tabularnewline
T-STAT & 4.31663465795811 \tabularnewline
p-value & 0.00017885129120927 \tabularnewline
Lambda & 0.354461805398475 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78992&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.13593946279489[/C][/ROW]
[ROW][C]beta[/C][C]0.645538194601525[/C][/ROW]
[ROW][C]S.D.[/C][C]0.149546636616888[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.31663465795811[/C][/ROW]
[ROW][C]p-value[/C][C]0.00017885129120927[/C][/ROW]
[ROW][C]Lambda[/C][C]0.354461805398475[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78992&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78992&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	-1.13593946279489
beta	0.645538194601525
S.D.	0.149546636616888
T-STAT	4.31663465795811
p-value	0.00017885129120927
Lambda	0.354461805398475

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