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R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Thu, 31 Jan 2019 14:43:41 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2019/Jan/31/t15489422259qabcd224qs6847.htm/, Retrieved Sun, 05 May 2024 17:48:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=317720, Retrieved Sun, 05 May 2024 17:48:58 +0000

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-       [Standard Deviation-Mean Plot] [] [2019-01-31 13:43:41] [9f050f8aed6d13342aa7dd8a5b9f6dd8] [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	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=317720&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=317720&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317720&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	19.75	3.30633001707606	11
2	18.9166666666667	2.57464325272219	8
3	20.4166666666667	5.43487615202764	21
4	20.0833333333333	4.90747728811182	16
5	19.75	5.94099777356081	21
6	20.5833333333333	3.20392751402892	11
7	19.25	4.53521574108463	12
8	19.6666666666667	3.65148371670111	14
9	17.75	6.07715543505497	18
10	21.8333333333333	3.9962103260085	13
11	20.4166666666667	3.47610893576904	10
12	18.6666666666667	5.31436019125767	20
13	19.5	5.21361853052352	18
14	24.0833333333333	3.60450055381106	10
15	22.1666666666667	3.80987552488943	13
16	21.4166666666667	4.73782330790941	16
17	18.75	6.52442961630991	26
18	17.6666666666667	7.17740562565273	25
19	21	4.80530010414637	14
20	16.1666666666667	8.04344265205948	21
21	21.5	3.34392257413628	10
22	20.5833333333333	5.26494985443328	17
23	19.5	6.96092992742676	25

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 19.75 & 3.30633001707606 & 11 \tabularnewline
2 & 18.9166666666667 & 2.57464325272219 & 8 \tabularnewline
3 & 20.4166666666667 & 5.43487615202764 & 21 \tabularnewline
4 & 20.0833333333333 & 4.90747728811182 & 16 \tabularnewline
5 & 19.75 & 5.94099777356081 & 21 \tabularnewline
6 & 20.5833333333333 & 3.20392751402892 & 11 \tabularnewline
7 & 19.25 & 4.53521574108463 & 12 \tabularnewline
8 & 19.6666666666667 & 3.65148371670111 & 14 \tabularnewline
9 & 17.75 & 6.07715543505497 & 18 \tabularnewline
10 & 21.8333333333333 & 3.9962103260085 & 13 \tabularnewline
11 & 20.4166666666667 & 3.47610893576904 & 10 \tabularnewline
12 & 18.6666666666667 & 5.31436019125767 & 20 \tabularnewline
13 & 19.5 & 5.21361853052352 & 18 \tabularnewline
14 & 24.0833333333333 & 3.60450055381106 & 10 \tabularnewline
15 & 22.1666666666667 & 3.80987552488943 & 13 \tabularnewline
16 & 21.4166666666667 & 4.73782330790941 & 16 \tabularnewline
17 & 18.75 & 6.52442961630991 & 26 \tabularnewline
18 & 17.6666666666667 & 7.17740562565273 & 25 \tabularnewline
19 & 21 & 4.80530010414637 & 14 \tabularnewline
20 & 16.1666666666667 & 8.04344265205948 & 21 \tabularnewline
21 & 21.5 & 3.34392257413628 & 10 \tabularnewline
22 & 20.5833333333333 & 5.26494985443328 & 17 \tabularnewline
23 & 19.5 & 6.96092992742676 & 25 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317720&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]19.75[/C][C]3.30633001707606[/C][C]11[/C][/ROW]
[ROW][C]2[/C][C]18.9166666666667[/C][C]2.57464325272219[/C][C]8[/C][/ROW]
[ROW][C]3[/C][C]20.4166666666667[/C][C]5.43487615202764[/C][C]21[/C][/ROW]
[ROW][C]4[/C][C]20.0833333333333[/C][C]4.90747728811182[/C][C]16[/C][/ROW]
[ROW][C]5[/C][C]19.75[/C][C]5.94099777356081[/C][C]21[/C][/ROW]
[ROW][C]6[/C][C]20.5833333333333[/C][C]3.20392751402892[/C][C]11[/C][/ROW]
[ROW][C]7[/C][C]19.25[/C][C]4.53521574108463[/C][C]12[/C][/ROW]
[ROW][C]8[/C][C]19.6666666666667[/C][C]3.65148371670111[/C][C]14[/C][/ROW]
[ROW][C]9[/C][C]17.75[/C][C]6.07715543505497[/C][C]18[/C][/ROW]
[ROW][C]10[/C][C]21.8333333333333[/C][C]3.9962103260085[/C][C]13[/C][/ROW]
[ROW][C]11[/C][C]20.4166666666667[/C][C]3.47610893576904[/C][C]10[/C][/ROW]
[ROW][C]12[/C][C]18.6666666666667[/C][C]5.31436019125767[/C][C]20[/C][/ROW]
[ROW][C]13[/C][C]19.5[/C][C]5.21361853052352[/C][C]18[/C][/ROW]
[ROW][C]14[/C][C]24.0833333333333[/C][C]3.60450055381106[/C][C]10[/C][/ROW]
[ROW][C]15[/C][C]22.1666666666667[/C][C]3.80987552488943[/C][C]13[/C][/ROW]
[ROW][C]16[/C][C]21.4166666666667[/C][C]4.73782330790941[/C][C]16[/C][/ROW]
[ROW][C]17[/C][C]18.75[/C][C]6.52442961630991[/C][C]26[/C][/ROW]
[ROW][C]18[/C][C]17.6666666666667[/C][C]7.17740562565273[/C][C]25[/C][/ROW]
[ROW][C]19[/C][C]21[/C][C]4.80530010414637[/C][C]14[/C][/ROW]
[ROW][C]20[/C][C]16.1666666666667[/C][C]8.04344265205948[/C][C]21[/C][/ROW]
[ROW][C]21[/C][C]21.5[/C][C]3.34392257413628[/C][C]10[/C][/ROW]
[ROW][C]22[/C][C]20.5833333333333[/C][C]5.26494985443328[/C][C]17[/C][/ROW]
[ROW][C]23[/C][C]19.5[/C][C]6.96092992742676[/C][C]25[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317720&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317720&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	19.75	3.30633001707606	11
2	18.9166666666667	2.57464325272219	8
3	20.4166666666667	5.43487615202764	21
4	20.0833333333333	4.90747728811182	16
5	19.75	5.94099777356081	21
6	20.5833333333333	3.20392751402892	11
7	19.25	4.53521574108463	12
8	19.6666666666667	3.65148371670111	14
9	17.75	6.07715543505497	18
10	21.8333333333333	3.9962103260085	13
11	20.4166666666667	3.47610893576904	10
12	18.6666666666667	5.31436019125767	20
13	19.5	5.21361853052352	18
14	24.0833333333333	3.60450055381106	10
15	22.1666666666667	3.80987552488943	13
16	21.4166666666667	4.73782330790941	16
17	18.75	6.52442961630991	26
18	17.6666666666667	7.17740562565273	25
19	21	4.80530010414637	14
20	16.1666666666667	8.04344265205948	21
21	21.5	3.34392257413628	10
22	20.5833333333333	5.26494985443328	17
23	19.5	6.96092992742676	25

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	15.677095985406
beta	-0.541269486050362
S.D.	0.145568192131572
T-STAT	-3.71832251348657
p-value	0.0012715304642033

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 15.677095985406 \tabularnewline
beta & -0.541269486050362 \tabularnewline
S.D. & 0.145568192131572 \tabularnewline
T-STAT & -3.71832251348657 \tabularnewline
p-value & 0.0012715304642033 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317720&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]15.677095985406[/C][/ROW]
[ROW][C]beta[/C][C]-0.541269486050362[/C][/ROW]
[ROW][C]S.D.[/C][C]0.145568192131572[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.71832251348657[/C][/ROW]
[ROW][C]p-value[/C][C]0.0012715304642033[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317720&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317720&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	15.677095985406
beta	-0.541269486050362
S.D.	0.145568192131572
T-STAT	-3.71832251348657
p-value	0.0012715304642033

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	7.59998865302832
beta	-2.02602048918876
S.D.	0.62985118231822
T-STAT	-3.21666537440133
p-value	0.00414019537651543
Lambda	3.02602048918876

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.59998865302832 \tabularnewline
beta & -2.02602048918876 \tabularnewline
S.D. & 0.62985118231822 \tabularnewline
T-STAT & -3.21666537440133 \tabularnewline
p-value & 0.00414019537651543 \tabularnewline
Lambda & 3.02602048918876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317720&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.59998865302832[/C][/ROW]
[ROW][C]beta[/C][C]-2.02602048918876[/C][/ROW]
[ROW][C]S.D.[/C][C]0.62985118231822[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.21666537440133[/C][/ROW]
[ROW][C]p-value[/C][C]0.00414019537651543[/C][/ROW]
[ROW][C]Lambda[/C][C]3.02602048918876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317720&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317720&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	7.59998865302832
beta	-2.02602048918876
S.D.	0.62985118231822
T-STAT	-3.21666537440133
p-value	0.00414019537651543
Lambda	3.02602048918876

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = TRUE ;

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code