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Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Sat, 22 Nov 2014 16:54:16 +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/2014/Nov/22/t1416675469fh03p4ej289n4ai.htm/, Retrieved Sun, 19 May 2024 20:47:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=257896, Retrieved Sun, 19 May 2024 20:47:01 +0000

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-       [Standard Deviation-Mean Plot] [] [2014-11-22 16:54:16] [ba3f7115fe3efa85f8b130de707d46eb] [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	2 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257896&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257896&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257896&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	2 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	1164.5	17.019596548293	41
2	1187	12.5698050899765	29
3	1173	4.54606056566195	11
4	1126.75	3.86221007541882	9
5	1127.25	10.2753750945322	25
6	1130	9.55684745788763	23
7	1124.75	14.2916059279565	34
8	1115.5	12.2882057274445	27
9	1127.75	17.9513230710162	38
10	1146.5	13.2790561913614	31
11	1164.5	21.142374511866	51
12	1181.5	9.98331942124796	24
13	1180.25	12.5797456254091	30
14	1182.5	8.88819441731559	21
15	1192.5	1	2
16	1214.25	10.9658560997307	24
17	1252.25	11.6153633893506	25
18	1292.25	23.0126776654377	56

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1164.5 & 17.019596548293 & 41 \tabularnewline
2 & 1187 & 12.5698050899765 & 29 \tabularnewline
3 & 1173 & 4.54606056566195 & 11 \tabularnewline
4 & 1126.75 & 3.86221007541882 & 9 \tabularnewline
5 & 1127.25 & 10.2753750945322 & 25 \tabularnewline
6 & 1130 & 9.55684745788763 & 23 \tabularnewline
7 & 1124.75 & 14.2916059279565 & 34 \tabularnewline
8 & 1115.5 & 12.2882057274445 & 27 \tabularnewline
9 & 1127.75 & 17.9513230710162 & 38 \tabularnewline
10 & 1146.5 & 13.2790561913614 & 31 \tabularnewline
11 & 1164.5 & 21.142374511866 & 51 \tabularnewline
12 & 1181.5 & 9.98331942124796 & 24 \tabularnewline
13 & 1180.25 & 12.5797456254091 & 30 \tabularnewline
14 & 1182.5 & 8.88819441731559 & 21 \tabularnewline
15 & 1192.5 & 1 & 2 \tabularnewline
16 & 1214.25 & 10.9658560997307 & 24 \tabularnewline
17 & 1252.25 & 11.6153633893506 & 25 \tabularnewline
18 & 1292.25 & 23.0126776654377 & 56 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257896&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]1164.5[/C][C]17.019596548293[/C][C]41[/C][/ROW]
[ROW][C]2[/C][C]1187[/C][C]12.5698050899765[/C][C]29[/C][/ROW]
[ROW][C]3[/C][C]1173[/C][C]4.54606056566195[/C][C]11[/C][/ROW]
[ROW][C]4[/C][C]1126.75[/C][C]3.86221007541882[/C][C]9[/C][/ROW]
[ROW][C]5[/C][C]1127.25[/C][C]10.2753750945322[/C][C]25[/C][/ROW]
[ROW][C]6[/C][C]1130[/C][C]9.55684745788763[/C][C]23[/C][/ROW]
[ROW][C]7[/C][C]1124.75[/C][C]14.2916059279565[/C][C]34[/C][/ROW]
[ROW][C]8[/C][C]1115.5[/C][C]12.2882057274445[/C][C]27[/C][/ROW]
[ROW][C]9[/C][C]1127.75[/C][C]17.9513230710162[/C][C]38[/C][/ROW]
[ROW][C]10[/C][C]1146.5[/C][C]13.2790561913614[/C][C]31[/C][/ROW]
[ROW][C]11[/C][C]1164.5[/C][C]21.142374511866[/C][C]51[/C][/ROW]
[ROW][C]12[/C][C]1181.5[/C][C]9.98331942124796[/C][C]24[/C][/ROW]
[ROW][C]13[/C][C]1180.25[/C][C]12.5797456254091[/C][C]30[/C][/ROW]
[ROW][C]14[/C][C]1182.5[/C][C]8.88819441731559[/C][C]21[/C][/ROW]
[ROW][C]15[/C][C]1192.5[/C][C]1[/C][C]2[/C][/ROW]
[ROW][C]16[/C][C]1214.25[/C][C]10.9658560997307[/C][C]24[/C][/ROW]
[ROW][C]17[/C][C]1252.25[/C][C]11.6153633893506[/C][C]25[/C][/ROW]
[ROW][C]18[/C][C]1292.25[/C][C]23.0126776654377[/C][C]56[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257896&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257896&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	1164.5	17.019596548293	41
2	1187	12.5698050899765	29
3	1173	4.54606056566195	11
4	1126.75	3.86221007541882	9
5	1127.25	10.2753750945322	25
6	1130	9.55684745788763	23
7	1124.75	14.2916059279565	34
8	1115.5	12.2882057274445	27
9	1127.75	17.9513230710162	38
10	1146.5	13.2790561913614	31
11	1164.5	21.142374511866	51
12	1181.5	9.98331942124796	24
13	1180.25	12.5797456254091	30
14	1182.5	8.88819441731559	21
15	1192.5	1	2
16	1214.25	10.9658560997307	24
17	1252.25	11.6153633893506	25
18	1292.25	23.0126776654377	56

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-19.2166829156442
beta	0.0265962106607931
S.D.	0.0292254939706268
T-STAT	0.910034598132842
p-value	0.376310124581781

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -19.2166829156442 \tabularnewline
beta & 0.0265962106607931 \tabularnewline
S.D. & 0.0292254939706268 \tabularnewline
T-STAT & 0.910034598132842 \tabularnewline
p-value & 0.376310124581781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257896&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-19.2166829156442[/C][/ROW]
[ROW][C]beta[/C][C]0.0265962106607931[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0292254939706268[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.910034598132842[/C][/ROW]
[ROW][C]p-value[/C][C]0.376310124581781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257896&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257896&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	-19.2166829156442
beta	0.0265962106607931
S.D.	0.0292254939706268
T-STAT	0.910034598132842
p-value	0.376310124581781

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-6.72732835467071
beta	1.27861846845596
S.D.	4.63477538960069
T-STAT	0.275874958541652
p-value	0.786175503262478
Lambda	-0.278618468455958

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.72732835467071 \tabularnewline
beta & 1.27861846845596 \tabularnewline
S.D. & 4.63477538960069 \tabularnewline
T-STAT & 0.275874958541652 \tabularnewline
p-value & 0.786175503262478 \tabularnewline
Lambda & -0.278618468455958 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257896&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.72732835467071[/C][/ROW]
[ROW][C]beta[/C][C]1.27861846845596[/C][/ROW]
[ROW][C]S.D.[/C][C]4.63477538960069[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.275874958541652[/C][/ROW]
[ROW][C]p-value[/C][C]0.786175503262478[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.278618468455958[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257896&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257896&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	-6.72732835467071
beta	1.27861846845596
S.D.	4.63477538960069
T-STAT	0.275874958541652
p-value	0.786175503262478
Lambda	-0.278618468455958

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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Figures (Output of Computation)

Input Parameters & R Code