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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

Sun, 21 Dec 2008 09:21:43 -0700

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/2008/Dec/21/t12298766472zte5w6dlvg4uxq.htm/, Retrieved Sun, 19 May 2024 11:37:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35664, Retrieved Sun, 19 May 2024 11:37:07 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

148

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

-       [Standard Deviation-Mean Plot] [] [2008-12-21 16:21:43] [a2d5a6282476ec2b5afae6fb53d308f8] [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=35664&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=35664&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35664&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	101.4	12.3328828746567	28.2
2	96.125	7.50216635379408	16.6
3	100.45	4.17013189239861	9.9
4	106.975	3.73575070545845	7.8
5	123.325	6.50659921413125	14.00
6	147.575	12.8593351305579	31.3
7	149	8.09238325011036	19.1000000000000
8	180.6	8.66871770602011	21.2
9	210.05	9.28672888229937	18.7
10	205.925	11.427561711348	25.3
11	234.575	12.9445934659996	27
12	232.575	25.6811701446799	51.7
13	203.15	11.1906210730236	27.1
14	228.825	11.1290535686254	27
15	266.85	17.7903531911726	41.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 101.4 & 12.3328828746567 & 28.2 \tabularnewline
2 & 96.125 & 7.50216635379408 & 16.6 \tabularnewline
3 & 100.45 & 4.17013189239861 & 9.9 \tabularnewline
4 & 106.975 & 3.73575070545845 & 7.8 \tabularnewline
5 & 123.325 & 6.50659921413125 & 14.00 \tabularnewline
6 & 147.575 & 12.8593351305579 & 31.3 \tabularnewline
7 & 149 & 8.09238325011036 & 19.1000000000000 \tabularnewline
8 & 180.6 & 8.66871770602011 & 21.2 \tabularnewline
9 & 210.05 & 9.28672888229937 & 18.7 \tabularnewline
10 & 205.925 & 11.427561711348 & 25.3 \tabularnewline
11 & 234.575 & 12.9445934659996 & 27 \tabularnewline
12 & 232.575 & 25.6811701446799 & 51.7 \tabularnewline
13 & 203.15 & 11.1906210730236 & 27.1 \tabularnewline
14 & 228.825 & 11.1290535686254 & 27 \tabularnewline
15 & 266.85 & 17.7903531911726 & 41.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35664&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]101.4[/C][C]12.3328828746567[/C][C]28.2[/C][/ROW]
[ROW][C]2[/C][C]96.125[/C][C]7.50216635379408[/C][C]16.6[/C][/ROW]
[ROW][C]3[/C][C]100.45[/C][C]4.17013189239861[/C][C]9.9[/C][/ROW]
[ROW][C]4[/C][C]106.975[/C][C]3.73575070545845[/C][C]7.8[/C][/ROW]
[ROW][C]5[/C][C]123.325[/C][C]6.50659921413125[/C][C]14.00[/C][/ROW]
[ROW][C]6[/C][C]147.575[/C][C]12.8593351305579[/C][C]31.3[/C][/ROW]
[ROW][C]7[/C][C]149[/C][C]8.09238325011036[/C][C]19.1000000000000[/C][/ROW]
[ROW][C]8[/C][C]180.6[/C][C]8.66871770602011[/C][C]21.2[/C][/ROW]
[ROW][C]9[/C][C]210.05[/C][C]9.28672888229937[/C][C]18.7[/C][/ROW]
[ROW][C]10[/C][C]205.925[/C][C]11.427561711348[/C][C]25.3[/C][/ROW]
[ROW][C]11[/C][C]234.575[/C][C]12.9445934659996[/C][C]27[/C][/ROW]
[ROW][C]12[/C][C]232.575[/C][C]25.6811701446799[/C][C]51.7[/C][/ROW]
[ROW][C]13[/C][C]203.15[/C][C]11.1906210730236[/C][C]27.1[/C][/ROW]
[ROW][C]14[/C][C]228.825[/C][C]11.1290535686254[/C][C]27[/C][/ROW]
[ROW][C]15[/C][C]266.85[/C][C]17.7903531911726[/C][C]41.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35664&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35664&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	101.4	12.3328828746567	28.2
2	96.125	7.50216635379408	16.6
3	100.45	4.17013189239861	9.9
4	106.975	3.73575070545845	7.8
5	123.325	6.50659921413125	14.00
6	147.575	12.8593351305579	31.3
7	149	8.09238325011036	19.1000000000000
8	180.6	8.66871770602011	21.2
9	210.05	9.28672888229937	18.7
10	205.925	11.427561711348	25.3
11	234.575	12.9445934659996	27
12	232.575	25.6811701446799	51.7
13	203.15	11.1906210730236	27.1
14	228.825	11.1290535686254	27
15	266.85	17.7903531911726	41.9

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-0.00784592089822007
beta	0.063166011431456
S.D.	0.0194669472494940
T-STAT	3.24478258567726
p-value	0.00639210308943549

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.00784592089822007 \tabularnewline
beta & 0.063166011431456 \tabularnewline
S.D. & 0.0194669472494940 \tabularnewline
T-STAT & 3.24478258567726 \tabularnewline
p-value & 0.00639210308943549 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35664&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.00784592089822007[/C][/ROW]
[ROW][C]beta[/C][C]0.063166011431456[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0194669472494940[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.24478258567726[/C][/ROW]
[ROW][C]p-value[/C][C]0.00639210308943549[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35664&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35664&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	-0.00784592089822007
beta	0.063166011431456
S.D.	0.0194669472494940
T-STAT	3.24478258567726
p-value	0.00639210308943549

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-2.73122656854836
beta	0.983006374439033
S.D.	0.273178409733374
T-STAT	3.59840433729174
p-value	0.00324173743080089
Lambda	0.0169936255609667

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.73122656854836 \tabularnewline
beta & 0.983006374439033 \tabularnewline
S.D. & 0.273178409733374 \tabularnewline
T-STAT & 3.59840433729174 \tabularnewline
p-value & 0.00324173743080089 \tabularnewline
Lambda & 0.0169936255609667 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35664&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.73122656854836[/C][/ROW]
[ROW][C]beta[/C][C]0.983006374439033[/C][/ROW]
[ROW][C]S.D.[/C][C]0.273178409733374[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.59840433729174[/C][/ROW]
[ROW][C]p-value[/C][C]0.00324173743080089[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0169936255609667[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35664&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35664&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	-2.73122656854836
beta	0.983006374439033
S.D.	0.273178409733374
T-STAT	3.59840433729174
p-value	0.00324173743080089
Lambda	0.0169936255609667

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