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Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Tue, 16 Aug 2011 08:19:58 -0400

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/2011/Aug/16/t1313497251wk8ej1nzrd4gzjc.htm/, Retrieved Mon, 13 May 2024 23:09:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123848, Retrieved Mon, 13 May 2024 23:09:51 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Standard deviation mean plot - Willem-Jan Carpels

Estimated Impact

137

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

-       [Standard Deviation-Mean Plot] [Standard deviatio...] [2011-08-16 12:19:58] [49802af8bc65831d925aaf5d22a63767] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123848&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]1 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=123848&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123848&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	'Gwilym Jenkins' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	21439.5	127.170489239184	299
2	21956.25	923.387017091606	1916
3	20982	104.188930953981	221
4	21550.25	348.757198253073	813
5	21404	945.261163206585	1988
6	20392.5	253.462028714362	584
7	20721.75	537.398284949502	1175
8	20833.75	1005.70717242479	2066
9	19525.25	149.851871304076	363
10	19820.75	539.85762011849	1182
11	20613.5	1202.38138708149	2280
12	18937.25	651.244641692608	1404
13	17981.25	353.226438232852	812
14	18698.75	923.118401578765	1916
15	17115.25	498.56886852938	1105
16	15662.25	192.825266325068	442
17	16084.25	1269.85730825685	2579
18	13692.25	1064.45334170487	2358
19	10675.5	86.0251901092542	149
20	11097.5	923.300059568936	1767
21	9218.75	1000.18777403712	2358
22	6422.25	193.01014653812	442
23	7288	394.592616927045	813
24	6514.75	1182.33621134881	2800
25	4231.5	718.187765606368	1546
26	5854	460.582963934476	1033
27	5670.75	1004.23947177288	2430
28	4490	886.757012940975	1845
29	6128.5	325.601494673064	663
30	5980.5	950.145778288785	2280

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 21439.5 & 127.170489239184 & 299 \tabularnewline
2 & 21956.25 & 923.387017091606 & 1916 \tabularnewline
3 & 20982 & 104.188930953981 & 221 \tabularnewline
4 & 21550.25 & 348.757198253073 & 813 \tabularnewline
5 & 21404 & 945.261163206585 & 1988 \tabularnewline
6 & 20392.5 & 253.462028714362 & 584 \tabularnewline
7 & 20721.75 & 537.398284949502 & 1175 \tabularnewline
8 & 20833.75 & 1005.70717242479 & 2066 \tabularnewline
9 & 19525.25 & 149.851871304076 & 363 \tabularnewline
10 & 19820.75 & 539.85762011849 & 1182 \tabularnewline
11 & 20613.5 & 1202.38138708149 & 2280 \tabularnewline
12 & 18937.25 & 651.244641692608 & 1404 \tabularnewline
13 & 17981.25 & 353.226438232852 & 812 \tabularnewline
14 & 18698.75 & 923.118401578765 & 1916 \tabularnewline
15 & 17115.25 & 498.56886852938 & 1105 \tabularnewline
16 & 15662.25 & 192.825266325068 & 442 \tabularnewline
17 & 16084.25 & 1269.85730825685 & 2579 \tabularnewline
18 & 13692.25 & 1064.45334170487 & 2358 \tabularnewline
19 & 10675.5 & 86.0251901092542 & 149 \tabularnewline
20 & 11097.5 & 923.300059568936 & 1767 \tabularnewline
21 & 9218.75 & 1000.18777403712 & 2358 \tabularnewline
22 & 6422.25 & 193.01014653812 & 442 \tabularnewline
23 & 7288 & 394.592616927045 & 813 \tabularnewline
24 & 6514.75 & 1182.33621134881 & 2800 \tabularnewline
25 & 4231.5 & 718.187765606368 & 1546 \tabularnewline
26 & 5854 & 460.582963934476 & 1033 \tabularnewline
27 & 5670.75 & 1004.23947177288 & 2430 \tabularnewline
28 & 4490 & 886.757012940975 & 1845 \tabularnewline
29 & 6128.5 & 325.601494673064 & 663 \tabularnewline
30 & 5980.5 & 950.145778288785 & 2280 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123848&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]21439.5[/C][C]127.170489239184[/C][C]299[/C][/ROW]
[ROW][C]2[/C][C]21956.25[/C][C]923.387017091606[/C][C]1916[/C][/ROW]
[ROW][C]3[/C][C]20982[/C][C]104.188930953981[/C][C]221[/C][/ROW]
[ROW][C]4[/C][C]21550.25[/C][C]348.757198253073[/C][C]813[/C][/ROW]
[ROW][C]5[/C][C]21404[/C][C]945.261163206585[/C][C]1988[/C][/ROW]
[ROW][C]6[/C][C]20392.5[/C][C]253.462028714362[/C][C]584[/C][/ROW]
[ROW][C]7[/C][C]20721.75[/C][C]537.398284949502[/C][C]1175[/C][/ROW]
[ROW][C]8[/C][C]20833.75[/C][C]1005.70717242479[/C][C]2066[/C][/ROW]
[ROW][C]9[/C][C]19525.25[/C][C]149.851871304076[/C][C]363[/C][/ROW]
[ROW][C]10[/C][C]19820.75[/C][C]539.85762011849[/C][C]1182[/C][/ROW]
[ROW][C]11[/C][C]20613.5[/C][C]1202.38138708149[/C][C]2280[/C][/ROW]
[ROW][C]12[/C][C]18937.25[/C][C]651.244641692608[/C][C]1404[/C][/ROW]
[ROW][C]13[/C][C]17981.25[/C][C]353.226438232852[/C][C]812[/C][/ROW]
[ROW][C]14[/C][C]18698.75[/C][C]923.118401578765[/C][C]1916[/C][/ROW]
[ROW][C]15[/C][C]17115.25[/C][C]498.56886852938[/C][C]1105[/C][/ROW]
[ROW][C]16[/C][C]15662.25[/C][C]192.825266325068[/C][C]442[/C][/ROW]
[ROW][C]17[/C][C]16084.25[/C][C]1269.85730825685[/C][C]2579[/C][/ROW]
[ROW][C]18[/C][C]13692.25[/C][C]1064.45334170487[/C][C]2358[/C][/ROW]
[ROW][C]19[/C][C]10675.5[/C][C]86.0251901092542[/C][C]149[/C][/ROW]
[ROW][C]20[/C][C]11097.5[/C][C]923.300059568936[/C][C]1767[/C][/ROW]
[ROW][C]21[/C][C]9218.75[/C][C]1000.18777403712[/C][C]2358[/C][/ROW]
[ROW][C]22[/C][C]6422.25[/C][C]193.01014653812[/C][C]442[/C][/ROW]
[ROW][C]23[/C][C]7288[/C][C]394.592616927045[/C][C]813[/C][/ROW]
[ROW][C]24[/C][C]6514.75[/C][C]1182.33621134881[/C][C]2800[/C][/ROW]
[ROW][C]25[/C][C]4231.5[/C][C]718.187765606368[/C][C]1546[/C][/ROW]
[ROW][C]26[/C][C]5854[/C][C]460.582963934476[/C][C]1033[/C][/ROW]
[ROW][C]27[/C][C]5670.75[/C][C]1004.23947177288[/C][C]2430[/C][/ROW]
[ROW][C]28[/C][C]4490[/C][C]886.757012940975[/C][C]1845[/C][/ROW]
[ROW][C]29[/C][C]6128.5[/C][C]325.601494673064[/C][C]663[/C][/ROW]
[ROW][C]30[/C][C]5980.5[/C][C]950.145778288785[/C][C]2280[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123848&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123848&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	21439.5	127.170489239184	299
2	21956.25	923.387017091606	1916
3	20982	104.188930953981	221
4	21550.25	348.757198253073	813
5	21404	945.261163206585	1988
6	20392.5	253.462028714362	584
7	20721.75	537.398284949502	1175
8	20833.75	1005.70717242479	2066
9	19525.25	149.851871304076	363
10	19820.75	539.85762011849	1182
11	20613.5	1202.38138708149	2280
12	18937.25	651.244641692608	1404
13	17981.25	353.226438232852	812
14	18698.75	923.118401578765	1916
15	17115.25	498.56886852938	1105
16	15662.25	192.825266325068	442
17	16084.25	1269.85730825685	2579
18	13692.25	1064.45334170487	2358
19	10675.5	86.0251901092542	149
20	11097.5	923.300059568936	1767
21	9218.75	1000.18777403712	2358
22	6422.25	193.01014653812	442
23	7288	394.592616927045	813
24	6514.75	1182.33621134881	2800
25	4231.5	718.187765606368	1546
26	5854	460.582963934476	1033
27	5670.75	1004.23947177288	2430
28	4490	886.757012940975	1845
29	6128.5	325.601494673064	663
30	5980.5	950.145778288785	2280

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	752.078487651688
beta	-0.00776520803709032
S.D.	0.0107841138595858
T-STAT	-0.720059908324126
p-value	0.477456378585242

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 752.078487651688 \tabularnewline
beta & -0.00776520803709032 \tabularnewline
S.D. & 0.0107841138595858 \tabularnewline
T-STAT & -0.720059908324126 \tabularnewline
p-value & 0.477456378585242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123848&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]752.078487651688[/C][/ROW]
[ROW][C]beta[/C][C]-0.00776520803709032[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0107841138595858[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.720059908324126[/C][/ROW]
[ROW][C]p-value[/C][C]0.477456378585242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123848&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123848&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	752.078487651688
beta	-0.00776520803709032
S.D.	0.0107841138595858
T-STAT	-0.720059908324126
p-value	0.477456378585242

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	8.42460658823753
beta	-0.234026730897555
S.D.	0.262732568172009
T-STAT	-0.890741229859023
p-value	0.380658316329005
Lambda	1.23402673089755

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 8.42460658823753 \tabularnewline
beta & -0.234026730897555 \tabularnewline
S.D. & 0.262732568172009 \tabularnewline
T-STAT & -0.890741229859023 \tabularnewline
p-value & 0.380658316329005 \tabularnewline
Lambda & 1.23402673089755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123848&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.42460658823753[/C][/ROW]
[ROW][C]beta[/C][C]-0.234026730897555[/C][/ROW]
[ROW][C]S.D.[/C][C]0.262732568172009[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.890741229859023[/C][/ROW]
[ROW][C]p-value[/C][C]0.380658316329005[/C][/ROW]
[ROW][C]Lambda[/C][C]1.23402673089755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123848&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123848&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	8.42460658823753
beta	-0.234026730897555
S.D.	0.262732568172009
T-STAT	-0.890741229859023
p-value	0.380658316329005
Lambda	1.23402673089755

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code