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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

Wed, 24 Jan 2018 10:29:17 +0100

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/2018/Jan/24/t1516786232hc4tyib1bz52cxf.htm/, Retrieved Mon, 06 May 2024 02:31:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=312258, Retrieved Mon, 06 May 2024 02:31:37 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Standard Deviation-Mean Plot] [RG Perceived usef...] [2018-01-24 09:29:17] [9cf7a9c8199d28657b6a757635af2182] [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	2 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312258&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=312258&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312258&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	Big Analytics Cloud Computing Center

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	10.5	2.64575131106459	8
2	11.0833333333333	1.88092498199125	8
3	11.5	2.02259958738973	6
4	10.5	1.88293774338254	6
5	9.91666666666667	1.72986249234563	6
6	10.75	1.81533868615599	6
7	10.3333333333333	2.96443566094439	9
8	10.75	2.56284642891099	9
9	10.4166666666667	1.97522534195852	6
10	11.0833333333333	2.15146180044822	7
11	10.4166666666667	2.50302846870576	9
12	9.16666666666667	1.80067327475704	6
13	10.25	2.92714567764944	10
14	10.5833333333333	3.17542648054294	9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 10.5 & 2.64575131106459 & 8 \tabularnewline
2 & 11.0833333333333 & 1.88092498199125 & 8 \tabularnewline
3 & 11.5 & 2.02259958738973 & 6 \tabularnewline
4 & 10.5 & 1.88293774338254 & 6 \tabularnewline
5 & 9.91666666666667 & 1.72986249234563 & 6 \tabularnewline
6 & 10.75 & 1.81533868615599 & 6 \tabularnewline
7 & 10.3333333333333 & 2.96443566094439 & 9 \tabularnewline
8 & 10.75 & 2.56284642891099 & 9 \tabularnewline
9 & 10.4166666666667 & 1.97522534195852 & 6 \tabularnewline
10 & 11.0833333333333 & 2.15146180044822 & 7 \tabularnewline
11 & 10.4166666666667 & 2.50302846870576 & 9 \tabularnewline
12 & 9.16666666666667 & 1.80067327475704 & 6 \tabularnewline
13 & 10.25 & 2.92714567764944 & 10 \tabularnewline
14 & 10.5833333333333 & 3.17542648054294 & 9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312258&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]10.5[/C][C]2.64575131106459[/C][C]8[/C][/ROW]
[ROW][C]2[/C][C]11.0833333333333[/C][C]1.88092498199125[/C][C]8[/C][/ROW]
[ROW][C]3[/C][C]11.5[/C][C]2.02259958738973[/C][C]6[/C][/ROW]
[ROW][C]4[/C][C]10.5[/C][C]1.88293774338254[/C][C]6[/C][/ROW]
[ROW][C]5[/C][C]9.91666666666667[/C][C]1.72986249234563[/C][C]6[/C][/ROW]
[ROW][C]6[/C][C]10.75[/C][C]1.81533868615599[/C][C]6[/C][/ROW]
[ROW][C]7[/C][C]10.3333333333333[/C][C]2.96443566094439[/C][C]9[/C][/ROW]
[ROW][C]8[/C][C]10.75[/C][C]2.56284642891099[/C][C]9[/C][/ROW]
[ROW][C]9[/C][C]10.4166666666667[/C][C]1.97522534195852[/C][C]6[/C][/ROW]
[ROW][C]10[/C][C]11.0833333333333[/C][C]2.15146180044822[/C][C]7[/C][/ROW]
[ROW][C]11[/C][C]10.4166666666667[/C][C]2.50302846870576[/C][C]9[/C][/ROW]
[ROW][C]12[/C][C]9.16666666666667[/C][C]1.80067327475704[/C][C]6[/C][/ROW]
[ROW][C]13[/C][C]10.25[/C][C]2.92714567764944[/C][C]10[/C][/ROW]
[ROW][C]14[/C][C]10.5833333333333[/C][C]3.17542648054294[/C][C]9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312258&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312258&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	10.5	2.64575131106459	8
2	11.0833333333333	1.88092498199125	8
3	11.5	2.02259958738973	6
4	10.5	1.88293774338254	6
5	9.91666666666667	1.72986249234563	6
6	10.75	1.81533868615599	6
7	10.3333333333333	2.96443566094439	9
8	10.75	2.56284642891099	9
9	10.4166666666667	1.97522534195852	6
10	11.0833333333333	2.15146180044822	7
11	10.4166666666667	2.50302846870576	9
12	9.16666666666667	1.80067327475704	6
13	10.25	2.92714567764944	10
14	10.5833333333333	3.17542648054294	9

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.88948623384136
beta	0.0379276785227025
S.D.	0.256691475861227
T-STAT	0.14775589409602
p-value	0.88498905765608

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.88948623384136 \tabularnewline
beta & 0.0379276785227025 \tabularnewline
S.D. & 0.256691475861227 \tabularnewline
T-STAT & 0.14775589409602 \tabularnewline
p-value & 0.88498905765608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312258&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.88948623384136[/C][/ROW]
[ROW][C]beta[/C][C]0.0379276785227025[/C][/ROW]
[ROW][C]S.D.[/C][C]0.256691475861227[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.14775589409602[/C][/ROW]
[ROW][C]p-value[/C][C]0.88498905765608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312258&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312258&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	1.88948623384136
beta	0.0379276785227025
S.D.	0.256691475861227
T-STAT	0.14775589409602
p-value	0.88498905765608

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.0400063044628192
beta	0.36010160530421
S.D.	1.12083926732036
T-STAT	0.321278541717334
p-value	0.753526099874779
Lambda	0.639898394695789

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.0400063044628192 \tabularnewline
beta & 0.36010160530421 \tabularnewline
S.D. & 1.12083926732036 \tabularnewline
T-STAT & 0.321278541717334 \tabularnewline
p-value & 0.753526099874779 \tabularnewline
Lambda & 0.639898394695789 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312258&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0400063044628192[/C][/ROW]
[ROW][C]beta[/C][C]0.36010160530421[/C][/ROW]
[ROW][C]S.D.[/C][C]1.12083926732036[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.321278541717334[/C][/ROW]
[ROW][C]p-value[/C][C]0.753526099874779[/C][/ROW]
[ROW][C]Lambda[/C][C]0.639898394695789[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312258&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312258&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	-0.0400063044628192
beta	0.36010160530421
S.D.	1.12083926732036
T-STAT	0.321278541717334
p-value	0.753526099874779
Lambda	0.639898394695789

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

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