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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, 21 Nov 2012 09:32:36 -0500

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/2012/Nov/21/t1353508390in0vseumaoon1is.htm/, Retrieved Sun, 28 Apr 2024 04:14:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=191431, Retrieved Sun, 28 Apr 2024 04:14:46 +0000

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Original text written by user:

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] [standaard deviati...] [2012-11-21 14:32:36] [18a55f974a2e8651a7d8da0218fcbdb6] [Current]

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Dataseries X:

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Histogram

Boxplots

14
14
15
13
8
7
3
3
4
4
0
-4
-14
-18
-8
-1
1
2
0
1
0
-1
-3
-3
-3
-4
-8
-9
-13
-18
-11
-9
-10
-13
-11
-5
-15
-6
-6
-3
-1
-3
-4
-6
0
-4
-2
-2
-6
-7
-6
-6
-3
-2
-5
-11
-11
-11
-10
-14
-8
-9
-5
-1
-2
-5
-4
-6
-2
-2
-2
-2
2
1
-8
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0
-2
-3
1
-2
-1
1
-3
-4
-9
-9
-7
-14
-12
-16
-20
-12
-12
-10
-10
-13
-16

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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191431&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191431&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191431&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	'Gwilym Jenkins' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	14	0.816496580927726	2
2	5.25	2.62995563967658	5
3	1	3.82970843102535	8
4	-10.25	7.41057802513857	17
5	1	0.816496580927726	2
6	-1.75	1.5	3
7	-6	2.94392028877595	6
8	-12.75	3.86221007541882	9
9	-9.75	3.40342964277702	8
10	-7.5	5.19615242270663	12
11	-3.5	2.08166599946613	5
12	-2	1.63299316185545	4
13	-6.25	0.5	1
14	-5.25	4.03112887414927	9
15	-11.5	1.73205080756888	4
16	-5.75	3.5939764421413	8
17	-4.25	1.70782512765993	4
18	-2	0	0
19	-1.5	4.50924975282289	10
20	1	1.4142135623731	3
21	-1	1.4142135623731	3
22	-4.75	2.98607881119482	7
23	-5.5	3	6
24	-11	1.63299316185545	4
25	-21	3.36650164612069	8
26	-22.25	2.3629078131263	5
27	-14.25	3.77491721763537	7
28	-13	2.44948974278318	5
29	-12.25	2.98607881119482	7
30	-6	2.44948974278318	5
31	-1.75	1.25830573921179	3
32	-0.25	1.5	3
33	-6.25	3.20156211871642	6
34	-12.25	3.86221007541882	9
35	-13.5	4.43471156521669	10

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14 & 0.816496580927726 & 2 \tabularnewline
2 & 5.25 & 2.62995563967658 & 5 \tabularnewline
3 & 1 & 3.82970843102535 & 8 \tabularnewline
4 & -10.25 & 7.41057802513857 & 17 \tabularnewline
5 & 1 & 0.816496580927726 & 2 \tabularnewline
6 & -1.75 & 1.5 & 3 \tabularnewline
7 & -6 & 2.94392028877595 & 6 \tabularnewline
8 & -12.75 & 3.86221007541882 & 9 \tabularnewline
9 & -9.75 & 3.40342964277702 & 8 \tabularnewline
10 & -7.5 & 5.19615242270663 & 12 \tabularnewline
11 & -3.5 & 2.08166599946613 & 5 \tabularnewline
12 & -2 & 1.63299316185545 & 4 \tabularnewline
13 & -6.25 & 0.5 & 1 \tabularnewline
14 & -5.25 & 4.03112887414927 & 9 \tabularnewline
15 & -11.5 & 1.73205080756888 & 4 \tabularnewline
16 & -5.75 & 3.5939764421413 & 8 \tabularnewline
17 & -4.25 & 1.70782512765993 & 4 \tabularnewline
18 & -2 & 0 & 0 \tabularnewline
19 & -1.5 & 4.50924975282289 & 10 \tabularnewline
20 & 1 & 1.4142135623731 & 3 \tabularnewline
21 & -1 & 1.4142135623731 & 3 \tabularnewline
22 & -4.75 & 2.98607881119482 & 7 \tabularnewline
23 & -5.5 & 3 & 6 \tabularnewline
24 & -11 & 1.63299316185545 & 4 \tabularnewline
25 & -21 & 3.36650164612069 & 8 \tabularnewline
26 & -22.25 & 2.3629078131263 & 5 \tabularnewline
27 & -14.25 & 3.77491721763537 & 7 \tabularnewline
28 & -13 & 2.44948974278318 & 5 \tabularnewline
29 & -12.25 & 2.98607881119482 & 7 \tabularnewline
30 & -6 & 2.44948974278318 & 5 \tabularnewline
31 & -1.75 & 1.25830573921179 & 3 \tabularnewline
32 & -0.25 & 1.5 & 3 \tabularnewline
33 & -6.25 & 3.20156211871642 & 6 \tabularnewline
34 & -12.25 & 3.86221007541882 & 9 \tabularnewline
35 & -13.5 & 4.43471156521669 & 10 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191431&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]14[/C][C]0.816496580927726[/C][C]2[/C][/ROW]
[ROW][C]2[/C][C]5.25[/C][C]2.62995563967658[/C][C]5[/C][/ROW]
[ROW][C]3[/C][C]1[/C][C]3.82970843102535[/C][C]8[/C][/ROW]
[ROW][C]4[/C][C]-10.25[/C][C]7.41057802513857[/C][C]17[/C][/ROW]
[ROW][C]5[/C][C]1[/C][C]0.816496580927726[/C][C]2[/C][/ROW]
[ROW][C]6[/C][C]-1.75[/C][C]1.5[/C][C]3[/C][/ROW]
[ROW][C]7[/C][C]-6[/C][C]2.94392028877595[/C][C]6[/C][/ROW]
[ROW][C]8[/C][C]-12.75[/C][C]3.86221007541882[/C][C]9[/C][/ROW]
[ROW][C]9[/C][C]-9.75[/C][C]3.40342964277702[/C][C]8[/C][/ROW]
[ROW][C]10[/C][C]-7.5[/C][C]5.19615242270663[/C][C]12[/C][/ROW]
[ROW][C]11[/C][C]-3.5[/C][C]2.08166599946613[/C][C]5[/C][/ROW]
[ROW][C]12[/C][C]-2[/C][C]1.63299316185545[/C][C]4[/C][/ROW]
[ROW][C]13[/C][C]-6.25[/C][C]0.5[/C][C]1[/C][/ROW]
[ROW][C]14[/C][C]-5.25[/C][C]4.03112887414927[/C][C]9[/C][/ROW]
[ROW][C]15[/C][C]-11.5[/C][C]1.73205080756888[/C][C]4[/C][/ROW]
[ROW][C]16[/C][C]-5.75[/C][C]3.5939764421413[/C][C]8[/C][/ROW]
[ROW][C]17[/C][C]-4.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]18[/C][C]-2[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-1.5[/C][C]4.50924975282289[/C][C]10[/C][/ROW]
[ROW][C]20[/C][C]1[/C][C]1.4142135623731[/C][C]3[/C][/ROW]
[ROW][C]21[/C][C]-1[/C][C]1.4142135623731[/C][C]3[/C][/ROW]
[ROW][C]22[/C][C]-4.75[/C][C]2.98607881119482[/C][C]7[/C][/ROW]
[ROW][C]23[/C][C]-5.5[/C][C]3[/C][C]6[/C][/ROW]
[ROW][C]24[/C][C]-11[/C][C]1.63299316185545[/C][C]4[/C][/ROW]
[ROW][C]25[/C][C]-21[/C][C]3.36650164612069[/C][C]8[/C][/ROW]
[ROW][C]26[/C][C]-22.25[/C][C]2.3629078131263[/C][C]5[/C][/ROW]
[ROW][C]27[/C][C]-14.25[/C][C]3.77491721763537[/C][C]7[/C][/ROW]
[ROW][C]28[/C][C]-13[/C][C]2.44948974278318[/C][C]5[/C][/ROW]
[ROW][C]29[/C][C]-12.25[/C][C]2.98607881119482[/C][C]7[/C][/ROW]
[ROW][C]30[/C][C]-6[/C][C]2.44948974278318[/C][C]5[/C][/ROW]
[ROW][C]31[/C][C]-1.75[/C][C]1.25830573921179[/C][C]3[/C][/ROW]
[ROW][C]32[/C][C]-0.25[/C][C]1.5[/C][C]3[/C][/ROW]
[ROW][C]33[/C][C]-6.25[/C][C]3.20156211871642[/C][C]6[/C][/ROW]
[ROW][C]34[/C][C]-12.25[/C][C]3.86221007541882[/C][C]9[/C][/ROW]
[ROW][C]35[/C][C]-13.5[/C][C]4.43471156521669[/C][C]10[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191431&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191431&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	14	0.816496580927726	2
2	5.25	2.62995563967658	5
3	1	3.82970843102535	8
4	-10.25	7.41057802513857	17
5	1	0.816496580927726	2
6	-1.75	1.5	3
7	-6	2.94392028877595	6
8	-12.75	3.86221007541882	9
9	-9.75	3.40342964277702	8
10	-7.5	5.19615242270663	12
11	-3.5	2.08166599946613	5
12	-2	1.63299316185545	4
13	-6.25	0.5	1
14	-5.25	4.03112887414927	9
15	-11.5	1.73205080756888	4
16	-5.75	3.5939764421413	8
17	-4.25	1.70782512765993	4
18	-2	0	0
19	-1.5	4.50924975282289	10
20	1	1.4142135623731	3
21	-1	1.4142135623731	3
22	-4.75	2.98607881119482	7
23	-5.5	3	6
24	-11	1.63299316185545	4
25	-21	3.36650164612069	8
26	-22.25	2.3629078131263	5
27	-14.25	3.77491721763537	7
28	-13	2.44948974278318	5
29	-12.25	2.98607881119482	7
30	-6	2.44948974278318	5
31	-1.75	1.25830573921179	3
32	-0.25	1.5	3
33	-6.25	3.20156211871642	6
34	-12.25	3.86221007541882	9
35	-13.5	4.43471156521669	10

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	2.18618574326997
beta	-0.0835488150815177
S.D.	0.0337839225271371
T-STAT	-2.47303477014567
p-value	0.0187192399144044

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.18618574326997 \tabularnewline
beta & -0.0835488150815177 \tabularnewline
S.D. & 0.0337839225271371 \tabularnewline
T-STAT & -2.47303477014567 \tabularnewline
p-value & 0.0187192399144044 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191431&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.18618574326997[/C][/ROW]
[ROW][C]beta[/C][C]-0.0835488150815177[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0337839225271371[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.47303477014567[/C][/ROW]
[ROW][C]p-value[/C][C]0.0187192399144044[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191431&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191431&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	2.18618574326997
beta	-0.0835488150815177
S.D.	0.0337839225271371
T-STAT	-2.47303477014567
p-value	0.0187192399144044

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.573801394689685
beta	-0.143844958203777
S.D.	0.315899906876232
T-STAT	-0.455349796162285
p-value	0.679792935863251
Lambda	1.14384495820378

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.573801394689685 \tabularnewline
beta & -0.143844958203777 \tabularnewline
S.D. & 0.315899906876232 \tabularnewline
T-STAT & -0.455349796162285 \tabularnewline
p-value & 0.679792935863251 \tabularnewline
Lambda & 1.14384495820378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191431&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.573801394689685[/C][/ROW]
[ROW][C]beta[/C][C]-0.143844958203777[/C][/ROW]
[ROW][C]S.D.[/C][C]0.315899906876232[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.455349796162285[/C][/ROW]
[ROW][C]p-value[/C][C]0.679792935863251[/C][/ROW]
[ROW][C]Lambda[/C][C]1.14384495820378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191431&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191431&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	0.573801394689685
beta	-0.143844958203777
S.D.	0.315899906876232
T-STAT	-0.455349796162285
p-value	0.679792935863251
Lambda	1.14384495820378

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 <- '12'
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