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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, 04 Aug 2010 14:50:47 +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/04/t128093618292ppt7xjdxlszus.htm/, Retrieved Fri, 03 May 2024 13:40:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78344, Retrieved Fri, 03 May 2024 13:40:05 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Cols Julien

Estimated Impact

103

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

-       [Standard Deviation-Mean Plot] [Tijdreeks A-Stap 26] [2010-08-04 14:50:47] [de7054811a4039cd82332eb5d7e753fd] [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=78344&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=78344&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78344&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	354.25	1.70782512765993	4
2	361.25	12.5266382827424	26
3	348	1.41421356237310	3
4	350.75	2.06155281280883	5
5	356.5	16.9016764454496	35
6	331	2.58198889747161	6
7	339	4.69041575982343	9
8	351.5	18.1567251085284	39
9	315.75	3.30403793359983	8
10	316.75	4.78713553878169	11
11	321.75	20.3203510468364	44
12	287	3.65148371670111	8
13	288.25	5.7373048260195	13
14	288.25	22.8965062837106	48
15	249	4.54606056566195	11
16	251.25	5.1234753829798	12
17	261.75	20.3203510468364	49
18	223.5	6.35085296108588	11
19	232.5	3.41565025531987	8
20	229.75	27.2809457314075	62
21	181.75	9.74251849711699	22
22	184.5	5.97215762238964	14
23	198.75	21.2190951739229	51
24	165.25	10.8128010555391	26
25	163.25	8.9953691790091	17
26	167.75	25.0383039894212	59
27	126	13.7113092008021	30
28	126.5	7.72442015083764	16
29	140	27.1538824725551	64
30	95	15.8534959341255	31

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 354.25 & 1.70782512765993 & 4 \tabularnewline
2 & 361.25 & 12.5266382827424 & 26 \tabularnewline
3 & 348 & 1.41421356237310 & 3 \tabularnewline
4 & 350.75 & 2.06155281280883 & 5 \tabularnewline
5 & 356.5 & 16.9016764454496 & 35 \tabularnewline
6 & 331 & 2.58198889747161 & 6 \tabularnewline
7 & 339 & 4.69041575982343 & 9 \tabularnewline
8 & 351.5 & 18.1567251085284 & 39 \tabularnewline
9 & 315.75 & 3.30403793359983 & 8 \tabularnewline
10 & 316.75 & 4.78713553878169 & 11 \tabularnewline
11 & 321.75 & 20.3203510468364 & 44 \tabularnewline
12 & 287 & 3.65148371670111 & 8 \tabularnewline
13 & 288.25 & 5.7373048260195 & 13 \tabularnewline
14 & 288.25 & 22.8965062837106 & 48 \tabularnewline
15 & 249 & 4.54606056566195 & 11 \tabularnewline
16 & 251.25 & 5.1234753829798 & 12 \tabularnewline
17 & 261.75 & 20.3203510468364 & 49 \tabularnewline
18 & 223.5 & 6.35085296108588 & 11 \tabularnewline
19 & 232.5 & 3.41565025531987 & 8 \tabularnewline
20 & 229.75 & 27.2809457314075 & 62 \tabularnewline
21 & 181.75 & 9.74251849711699 & 22 \tabularnewline
22 & 184.5 & 5.97215762238964 & 14 \tabularnewline
23 & 198.75 & 21.2190951739229 & 51 \tabularnewline
24 & 165.25 & 10.8128010555391 & 26 \tabularnewline
25 & 163.25 & 8.9953691790091 & 17 \tabularnewline
26 & 167.75 & 25.0383039894212 & 59 \tabularnewline
27 & 126 & 13.7113092008021 & 30 \tabularnewline
28 & 126.5 & 7.72442015083764 & 16 \tabularnewline
29 & 140 & 27.1538824725551 & 64 \tabularnewline
30 & 95 & 15.8534959341255 & 31 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78344&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]354.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]361.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]348[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]350.75[/C][C]2.06155281280883[/C][C]5[/C][/ROW]
[ROW][C]5[/C][C]356.5[/C][C]16.9016764454496[/C][C]35[/C][/ROW]
[ROW][C]6[/C][C]331[/C][C]2.58198889747161[/C][C]6[/C][/ROW]
[ROW][C]7[/C][C]339[/C][C]4.69041575982343[/C][C]9[/C][/ROW]
[ROW][C]8[/C][C]351.5[/C][C]18.1567251085284[/C][C]39[/C][/ROW]
[ROW][C]9[/C][C]315.75[/C][C]3.30403793359983[/C][C]8[/C][/ROW]
[ROW][C]10[/C][C]316.75[/C][C]4.78713553878169[/C][C]11[/C][/ROW]
[ROW][C]11[/C][C]321.75[/C][C]20.3203510468364[/C][C]44[/C][/ROW]
[ROW][C]12[/C][C]287[/C][C]3.65148371670111[/C][C]8[/C][/ROW]
[ROW][C]13[/C][C]288.25[/C][C]5.7373048260195[/C][C]13[/C][/ROW]
[ROW][C]14[/C][C]288.25[/C][C]22.8965062837106[/C][C]48[/C][/ROW]
[ROW][C]15[/C][C]249[/C][C]4.54606056566195[/C][C]11[/C][/ROW]
[ROW][C]16[/C][C]251.25[/C][C]5.1234753829798[/C][C]12[/C][/ROW]
[ROW][C]17[/C][C]261.75[/C][C]20.3203510468364[/C][C]49[/C][/ROW]
[ROW][C]18[/C][C]223.5[/C][C]6.35085296108588[/C][C]11[/C][/ROW]
[ROW][C]19[/C][C]232.5[/C][C]3.41565025531987[/C][C]8[/C][/ROW]
[ROW][C]20[/C][C]229.75[/C][C]27.2809457314075[/C][C]62[/C][/ROW]
[ROW][C]21[/C][C]181.75[/C][C]9.74251849711699[/C][C]22[/C][/ROW]
[ROW][C]22[/C][C]184.5[/C][C]5.97215762238964[/C][C]14[/C][/ROW]
[ROW][C]23[/C][C]198.75[/C][C]21.2190951739229[/C][C]51[/C][/ROW]
[ROW][C]24[/C][C]165.25[/C][C]10.8128010555391[/C][C]26[/C][/ROW]
[ROW][C]25[/C][C]163.25[/C][C]8.9953691790091[/C][C]17[/C][/ROW]
[ROW][C]26[/C][C]167.75[/C][C]25.0383039894212[/C][C]59[/C][/ROW]
[ROW][C]27[/C][C]126[/C][C]13.7113092008021[/C][C]30[/C][/ROW]
[ROW][C]28[/C][C]126.5[/C][C]7.72442015083764[/C][C]16[/C][/ROW]
[ROW][C]29[/C][C]140[/C][C]27.1538824725551[/C][C]64[/C][/ROW]
[ROW][C]30[/C][C]95[/C][C]15.8534959341255[/C][C]31[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78344&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78344&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	354.25	1.70782512765993	4
2	361.25	12.5266382827424	26
3	348	1.41421356237310	3
4	350.75	2.06155281280883	5
5	356.5	16.9016764454496	35
6	331	2.58198889747161	6
7	339	4.69041575982343	9
8	351.5	18.1567251085284	39
9	315.75	3.30403793359983	8
10	316.75	4.78713553878169	11
11	321.75	20.3203510468364	44
12	287	3.65148371670111	8
13	288.25	5.7373048260195	13
14	288.25	22.8965062837106	48
15	249	4.54606056566195	11
16	251.25	5.1234753829798	12
17	261.75	20.3203510468364	49
18	223.5	6.35085296108588	11
19	232.5	3.41565025531987	8
20	229.75	27.2809457314075	62
21	181.75	9.74251849711699	22
22	184.5	5.97215762238964	14
23	198.75	21.2190951739229	51
24	165.25	10.8128010555391	26
25	163.25	8.9953691790091	17
26	167.75	25.0383039894212	59
27	126	13.7113092008021	30
28	126.5	7.72442015083764	16
29	140	27.1538824725551	64
30	95	15.8534959341255	31

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	19.2015839322187
beta	-0.0318213335180496
S.D.	0.0180337573820749
T-STAT	-1.76454262103356
p-value	0.0885484960332208

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 19.2015839322187 \tabularnewline
beta & -0.0318213335180496 \tabularnewline
S.D. & 0.0180337573820749 \tabularnewline
T-STAT & -1.76454262103356 \tabularnewline
p-value & 0.0885484960332208 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78344&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]19.2015839322187[/C][/ROW]
[ROW][C]beta[/C][C]-0.0318213335180496[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0180337573820749[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.76454262103356[/C][/ROW]
[ROW][C]p-value[/C][C]0.0885484960332208[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78344&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78344&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	19.2015839322187
beta	-0.0318213335180496
S.D.	0.0180337573820749
T-STAT	-1.76454262103356
p-value	0.0885484960332208

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	7.41887035212966
beta	-0.974738003063468
S.D.	0.403964773424291
T-STAT	-2.41292822342132
p-value	0.0226198423338434
Lambda	1.97473800306347

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.41887035212966 \tabularnewline
beta & -0.974738003063468 \tabularnewline
S.D. & 0.403964773424291 \tabularnewline
T-STAT & -2.41292822342132 \tabularnewline
p-value & 0.0226198423338434 \tabularnewline
Lambda & 1.97473800306347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78344&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.41887035212966[/C][/ROW]
[ROW][C]beta[/C][C]-0.974738003063468[/C][/ROW]
[ROW][C]S.D.[/C][C]0.403964773424291[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.41292822342132[/C][/ROW]
[ROW][C]p-value[/C][C]0.0226198423338434[/C][/ROW]
[ROW][C]Lambda[/C][C]1.97473800306347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78344&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78344&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	7.41887035212966
beta	-0.974738003063468
S.D.	0.403964773424291
T-STAT	-2.41292822342132
p-value	0.0226198423338434
Lambda	1.97473800306347

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