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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, 20 Dec 2017 08:56:41 +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/2017/Dec/20/t15137602292xyjg8af8vmnnz8.htm/, Retrieved Mon, 13 May 2024 21:46:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310448, Retrieved Mon, 13 May 2024 21:46:20 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

110

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

-       [Standard Deviation-Mean Plot] [] [2017-12-20 07:56:41] [1ea4e9c673228daef4af35aa2d91fd76] [Current]

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Dataseries X:

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Histogram

Boxplots

15,4
17,3
19,2
14,5
11,1
7,1
5,1
2,1
1,4
3
9
11,1
15,8
20,2
18,6
14,8
12,8
6,4
6,1
6,1
6,6
9,3
12,4
13,5
16,5
19,3
16,2
16,5
13,6
8,8
4,3
3,5
3,3
6,6
10,3
13,1
16,5
19
19,4
13.5
10.2
10.1
9.6
4.8
4.5
5.3
8.5
14.2
16
18.3
18,1
17.5
9.7
6.1
4.7
1.1
6.1
9.6
8.8
15.5
19.2

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	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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310448&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]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310448&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310448&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	Big Analytics Cloud Computing Center

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	9.69166666666667	6.08581933429649	17.8
2	11.8833333333333	4.98540293499356	14.1
3	11	5.66263671318005	16
4	11.3	5.24889598781583	14.9
5	10.9583333333333	5.91906908118826	17.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.69166666666667 & 6.08581933429649 & 17.8 \tabularnewline
2 & 11.8833333333333 & 4.98540293499356 & 14.1 \tabularnewline
3 & 11 & 5.66263671318005 & 16 \tabularnewline
4 & 11.3 & 5.24889598781583 & 14.9 \tabularnewline
5 & 10.9583333333333 & 5.91906908118826 & 17.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310448&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]9.69166666666667[/C][C]6.08581933429649[/C][C]17.8[/C][/ROW]
[ROW][C]2[/C][C]11.8833333333333[/C][C]4.98540293499356[/C][C]14.1[/C][/ROW]
[ROW][C]3[/C][C]11[/C][C]5.66263671318005[/C][C]16[/C][/ROW]
[ROW][C]4[/C][C]11.3[/C][C]5.24889598781583[/C][C]14.9[/C][/ROW]
[ROW][C]5[/C][C]10.9583333333333[/C][C]5.91906908118826[/C][C]17.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310448&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310448&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	9.69166666666667	6.08581933429649	17.8
2	11.8833333333333	4.98540293499356	14.1
3	11	5.66263671318005	16
4	11.3	5.24889598781583	14.9
5	10.9583333333333	5.91906908118826	17.2

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	11.1118013482009
beta	-0.50438631044736
S.D.	0.154621845712918
T-STAT	-3.26206370207117
p-value	0.0470581329296753

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 11.1118013482009 \tabularnewline
beta & -0.50438631044736 \tabularnewline
S.D. & 0.154621845712918 \tabularnewline
T-STAT & -3.26206370207117 \tabularnewline
p-value & 0.0470581329296753 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310448&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]11.1118013482009[/C][/ROW]
[ROW][C]beta[/C][C]-0.50438631044736[/C][/ROW]
[ROW][C]S.D.[/C][C]0.154621845712918[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.26206370207117[/C][/ROW]
[ROW][C]p-value[/C][C]0.0470581329296753[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310448&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310448&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	11.1118013482009
beta	-0.50438631044736
S.D.	0.154621845712918
T-STAT	-3.26206370207117
p-value	0.0470581329296753

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.00644033173782
beta	-0.957071525254358
S.D.	0.319568716621267
T-STAT	-2.99488490417108
p-value	0.0579044962095528
Lambda	1.95707152525436

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.00644033173782 \tabularnewline
beta & -0.957071525254358 \tabularnewline
S.D. & 0.319568716621267 \tabularnewline
T-STAT & -2.99488490417108 \tabularnewline
p-value & 0.0579044962095528 \tabularnewline
Lambda & 1.95707152525436 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310448&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.00644033173782[/C][/ROW]
[ROW][C]beta[/C][C]-0.957071525254358[/C][/ROW]
[ROW][C]S.D.[/C][C]0.319568716621267[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.99488490417108[/C][/ROW]
[ROW][C]p-value[/C][C]0.0579044962095528[/C][/ROW]
[ROW][C]Lambda[/C][C]1.95707152525436[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310448&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310448&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	4.00644033173782
beta	-0.957071525254358
S.D.	0.319568716621267
T-STAT	-2.99488490417108
p-value	0.0579044962095528
Lambda	1.95707152525436

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