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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Sat, 18 Dec 2010 12:19:36 +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/Dec/18/t1292674789q022xg0aj5pbqd5.htm/, Retrieved Tue, 30 Apr 2024 01:19:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111881, Retrieved Tue, 30 Apr 2024 01:19:41 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

166

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

-     [Standard Deviation-Mean Plot] [Standard deviatio...] [2008-12-11 16:40:34] [12d343c4448a5f9e527bb31caeac580b]
-  M D  [Standard Deviation-Mean Plot] [Paper SMP] [2009-12-20 19:13:30] [83058a88a37d754675a5cd22dab372fc]
-   PD      [Standard Deviation-Mean Plot] [paper] [2010-12-18 12:19:36] [912a7c71b856221ca57f8714938acfc7] [Current]

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Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111881&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]3 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=111881&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111881&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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	100.515	0.470850294679742	1.14
2	102.84	0.842021377400832	1.81999999999999
3	105.335	1.42832069228167	3.28
4	108.9925	1.16939799327118	2.5
5	111.7775	1.31124304891707	2.79000000000001
6	115.3825	1.22099344797587	2.60000000000001
7	118.875	1.55663097746383	3.5
8	124.5725	2.37227563041622	5.44
9	132.0025	2.68579442003045	6.10000000000002
10	140.785	3.15479000885954	7.22999999999999
11	150.49	3.26709861089826	7.43
12	161.0525	4.15979466640683	9.53
13	173.165	4.4142987363038	10.13
14	188.2175	5.71859758448986	13.1400000000000
15	205.9325	6.29781642052757	14.4200000000000
16	218.34	2.34882949572761	4.98000000000002
17	221.1125	2.86401088219534	6.75
18	208.25	6.31835949172462	13.7700000000000
19	198.455	1.98061438279473	4.34

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100.515 & 0.470850294679742 & 1.14 \tabularnewline
2 & 102.84 & 0.842021377400832 & 1.81999999999999 \tabularnewline
3 & 105.335 & 1.42832069228167 & 3.28 \tabularnewline
4 & 108.9925 & 1.16939799327118 & 2.5 \tabularnewline
5 & 111.7775 & 1.31124304891707 & 2.79000000000001 \tabularnewline
6 & 115.3825 & 1.22099344797587 & 2.60000000000001 \tabularnewline
7 & 118.875 & 1.55663097746383 & 3.5 \tabularnewline
8 & 124.5725 & 2.37227563041622 & 5.44 \tabularnewline
9 & 132.0025 & 2.68579442003045 & 6.10000000000002 \tabularnewline
10 & 140.785 & 3.15479000885954 & 7.22999999999999 \tabularnewline
11 & 150.49 & 3.26709861089826 & 7.43 \tabularnewline
12 & 161.0525 & 4.15979466640683 & 9.53 \tabularnewline
13 & 173.165 & 4.4142987363038 & 10.13 \tabularnewline
14 & 188.2175 & 5.71859758448986 & 13.1400000000000 \tabularnewline
15 & 205.9325 & 6.29781642052757 & 14.4200000000000 \tabularnewline
16 & 218.34 & 2.34882949572761 & 4.98000000000002 \tabularnewline
17 & 221.1125 & 2.86401088219534 & 6.75 \tabularnewline
18 & 208.25 & 6.31835949172462 & 13.7700000000000 \tabularnewline
19 & 198.455 & 1.98061438279473 & 4.34 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111881&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]100.515[/C][C]0.470850294679742[/C][C]1.14[/C][/ROW]
[ROW][C]2[/C][C]102.84[/C][C]0.842021377400832[/C][C]1.81999999999999[/C][/ROW]
[ROW][C]3[/C][C]105.335[/C][C]1.42832069228167[/C][C]3.28[/C][/ROW]
[ROW][C]4[/C][C]108.9925[/C][C]1.16939799327118[/C][C]2.5[/C][/ROW]
[ROW][C]5[/C][C]111.7775[/C][C]1.31124304891707[/C][C]2.79000000000001[/C][/ROW]
[ROW][C]6[/C][C]115.3825[/C][C]1.22099344797587[/C][C]2.60000000000001[/C][/ROW]
[ROW][C]7[/C][C]118.875[/C][C]1.55663097746383[/C][C]3.5[/C][/ROW]
[ROW][C]8[/C][C]124.5725[/C][C]2.37227563041622[/C][C]5.44[/C][/ROW]
[ROW][C]9[/C][C]132.0025[/C][C]2.68579442003045[/C][C]6.10000000000002[/C][/ROW]
[ROW][C]10[/C][C]140.785[/C][C]3.15479000885954[/C][C]7.22999999999999[/C][/ROW]
[ROW][C]11[/C][C]150.49[/C][C]3.26709861089826[/C][C]7.43[/C][/ROW]
[ROW][C]12[/C][C]161.0525[/C][C]4.15979466640683[/C][C]9.53[/C][/ROW]
[ROW][C]13[/C][C]173.165[/C][C]4.4142987363038[/C][C]10.13[/C][/ROW]
[ROW][C]14[/C][C]188.2175[/C][C]5.71859758448986[/C][C]13.1400000000000[/C][/ROW]
[ROW][C]15[/C][C]205.9325[/C][C]6.29781642052757[/C][C]14.4200000000000[/C][/ROW]
[ROW][C]16[/C][C]218.34[/C][C]2.34882949572761[/C][C]4.98000000000002[/C][/ROW]
[ROW][C]17[/C][C]221.1125[/C][C]2.86401088219534[/C][C]6.75[/C][/ROW]
[ROW][C]18[/C][C]208.25[/C][C]6.31835949172462[/C][C]13.7700000000000[/C][/ROW]
[ROW][C]19[/C][C]198.455[/C][C]1.98061438279473[/C][C]4.34[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111881&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111881&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	100.515	0.470850294679742	1.14
2	102.84	0.842021377400832	1.81999999999999
3	105.335	1.42832069228167	3.28
4	108.9925	1.16939799327118	2.5
5	111.7775	1.31124304891707	2.79000000000001
6	115.3825	1.22099344797587	2.60000000000001
7	118.875	1.55663097746383	3.5
8	124.5725	2.37227563041622	5.44
9	132.0025	2.68579442003045	6.10000000000002
10	140.785	3.15479000885954	7.22999999999999
11	150.49	3.26709861089826	7.43
12	161.0525	4.15979466640683	9.53
13	173.165	4.4142987363038	10.13
14	188.2175	5.71859758448986	13.1400000000000
15	205.9325	6.29781642052757	14.4200000000000
16	218.34	2.34882949572761	4.98000000000002
17	221.1125	2.86401088219534	6.75
18	208.25	6.31835949172462	13.7700000000000
19	198.455	1.98061438279473	4.34

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-1.66161551264380
beta	0.0295044018521920
S.D.	0.00720623052386016
T-STAT	4.0942905940216
p-value	0.000755997555267205

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.66161551264380 \tabularnewline
beta & 0.0295044018521920 \tabularnewline
S.D. & 0.00720623052386016 \tabularnewline
T-STAT & 4.0942905940216 \tabularnewline
p-value & 0.000755997555267205 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111881&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.66161551264380[/C][/ROW]
[ROW][C]beta[/C][C]0.0295044018521920[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00720623052386016[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.0942905940216[/C][/ROW]
[ROW][C]p-value[/C][C]0.000755997555267205[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111881&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111881&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	-1.66161551264380
beta	0.0295044018521920
S.D.	0.00720623052386016
T-STAT	4.0942905940216
p-value	0.000755997555267205

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-8.94662180693358
beta	1.95947202209655
S.D.	0.379645084015354
T-STAT	5.16132594520125
p-value	7.82961598023542e-05
Lambda	-0.959472022096554

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -8.94662180693358 \tabularnewline
beta & 1.95947202209655 \tabularnewline
S.D. & 0.379645084015354 \tabularnewline
T-STAT & 5.16132594520125 \tabularnewline
p-value & 7.82961598023542e-05 \tabularnewline
Lambda & -0.959472022096554 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111881&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8.94662180693358[/C][/ROW]
[ROW][C]beta[/C][C]1.95947202209655[/C][/ROW]
[ROW][C]S.D.[/C][C]0.379645084015354[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.16132594520125[/C][/ROW]
[ROW][C]p-value[/C][C]7.82961598023542e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.959472022096554[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111881&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111881&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	-8.94662180693358
beta	1.95947202209655
S.D.	0.379645084015354
T-STAT	5.16132594520125
p-value	7.82961598023542e-05
Lambda	-0.959472022096554

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code