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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

Sun, 15 Aug 2010 20:19:41 +0000

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/2010/Aug/15/t1281903576pysdo7tm499f6iy.htm/, Retrieved Sat, 27 Apr 2024 20:49:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78915, Retrieved Sat, 27 Apr 2024 20:49:11 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

De Cock Nicola

Estimated Impact

121

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

-       [Standard Deviation-Mean Plot] [TIJDREEKS A - STA...] [2010-08-15 20:19:41] [c2fbba04702f7f714f5f9c5d7ee07bac] [Current]

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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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78915&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78915&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78915&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	250.25	1.70782512765993	4
2	257.25	12.5266382827424	26
3	244	1.4142135623731	3
4	239	2.16024689946929	5
5	240.75	12.0104121494643	24
6	222.75	1.5	3
7	221.5	4.72581562625261	10
8	231.75	5.18812747209113	11
9	221.75	5.1234753829798	11
10	210.75	4.64578662158878	10
11	210.75	10.2428837085396	23
12	200.25	9.21502396451939	22
13	205.75	5.7373048260195	12
14	200.5	9.9498743710662	21
15	190.75	10.3722385883344	24
16	191.25	7.63216876123687	17
17	201.75	7.41057802513857	17
18	184	9.41629792788369	20
19	188.25	8.73212459828649	19
20	200.5	8.18535277187245	17
21	177.75	9.9121138007995	21
22	178.5	6.13731754650732	15
23	197.5	8.88819441731559	19
24	163	4.83045891539648	11
25	159	7.34846922834953	16
26	182.5	9.03696114115064	19
27	139.75	7.08872343937891	15
28	118.25	4.11298755975102	10
29	136.25	8.34166250416147	18
30	94.25	7.67571929311297	17

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 250.25 & 1.70782512765993 & 4 \tabularnewline
2 & 257.25 & 12.5266382827424 & 26 \tabularnewline
3 & 244 & 1.4142135623731 & 3 \tabularnewline
4 & 239 & 2.16024689946929 & 5 \tabularnewline
5 & 240.75 & 12.0104121494643 & 24 \tabularnewline
6 & 222.75 & 1.5 & 3 \tabularnewline
7 & 221.5 & 4.72581562625261 & 10 \tabularnewline
8 & 231.75 & 5.18812747209113 & 11 \tabularnewline
9 & 221.75 & 5.1234753829798 & 11 \tabularnewline
10 & 210.75 & 4.64578662158878 & 10 \tabularnewline
11 & 210.75 & 10.2428837085396 & 23 \tabularnewline
12 & 200.25 & 9.21502396451939 & 22 \tabularnewline
13 & 205.75 & 5.7373048260195 & 12 \tabularnewline
14 & 200.5 & 9.9498743710662 & 21 \tabularnewline
15 & 190.75 & 10.3722385883344 & 24 \tabularnewline
16 & 191.25 & 7.63216876123687 & 17 \tabularnewline
17 & 201.75 & 7.41057802513857 & 17 \tabularnewline
18 & 184 & 9.41629792788369 & 20 \tabularnewline
19 & 188.25 & 8.73212459828649 & 19 \tabularnewline
20 & 200.5 & 8.18535277187245 & 17 \tabularnewline
21 & 177.75 & 9.9121138007995 & 21 \tabularnewline
22 & 178.5 & 6.13731754650732 & 15 \tabularnewline
23 & 197.5 & 8.88819441731559 & 19 \tabularnewline
24 & 163 & 4.83045891539648 & 11 \tabularnewline
25 & 159 & 7.34846922834953 & 16 \tabularnewline
26 & 182.5 & 9.03696114115064 & 19 \tabularnewline
27 & 139.75 & 7.08872343937891 & 15 \tabularnewline
28 & 118.25 & 4.11298755975102 & 10 \tabularnewline
29 & 136.25 & 8.34166250416147 & 18 \tabularnewline
30 & 94.25 & 7.67571929311297 & 17 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78915&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]250.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]257.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]244[/C][C]1.4142135623731[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]239[/C][C]2.16024689946929[/C][C]5[/C][/ROW]
[ROW][C]5[/C][C]240.75[/C][C]12.0104121494643[/C][C]24[/C][/ROW]
[ROW][C]6[/C][C]222.75[/C][C]1.5[/C][C]3[/C][/ROW]
[ROW][C]7[/C][C]221.5[/C][C]4.72581562625261[/C][C]10[/C][/ROW]
[ROW][C]8[/C][C]231.75[/C][C]5.18812747209113[/C][C]11[/C][/ROW]
[ROW][C]9[/C][C]221.75[/C][C]5.1234753829798[/C][C]11[/C][/ROW]
[ROW][C]10[/C][C]210.75[/C][C]4.64578662158878[/C][C]10[/C][/ROW]
[ROW][C]11[/C][C]210.75[/C][C]10.2428837085396[/C][C]23[/C][/ROW]
[ROW][C]12[/C][C]200.25[/C][C]9.21502396451939[/C][C]22[/C][/ROW]
[ROW][C]13[/C][C]205.75[/C][C]5.7373048260195[/C][C]12[/C][/ROW]
[ROW][C]14[/C][C]200.5[/C][C]9.9498743710662[/C][C]21[/C][/ROW]
[ROW][C]15[/C][C]190.75[/C][C]10.3722385883344[/C][C]24[/C][/ROW]
[ROW][C]16[/C][C]191.25[/C][C]7.63216876123687[/C][C]17[/C][/ROW]
[ROW][C]17[/C][C]201.75[/C][C]7.41057802513857[/C][C]17[/C][/ROW]
[ROW][C]18[/C][C]184[/C][C]9.41629792788369[/C][C]20[/C][/ROW]
[ROW][C]19[/C][C]188.25[/C][C]8.73212459828649[/C][C]19[/C][/ROW]
[ROW][C]20[/C][C]200.5[/C][C]8.18535277187245[/C][C]17[/C][/ROW]
[ROW][C]21[/C][C]177.75[/C][C]9.9121138007995[/C][C]21[/C][/ROW]
[ROW][C]22[/C][C]178.5[/C][C]6.13731754650732[/C][C]15[/C][/ROW]
[ROW][C]23[/C][C]197.5[/C][C]8.88819441731559[/C][C]19[/C][/ROW]
[ROW][C]24[/C][C]163[/C][C]4.83045891539648[/C][C]11[/C][/ROW]
[ROW][C]25[/C][C]159[/C][C]7.34846922834953[/C][C]16[/C][/ROW]
[ROW][C]26[/C][C]182.5[/C][C]9.03696114115064[/C][C]19[/C][/ROW]
[ROW][C]27[/C][C]139.75[/C][C]7.08872343937891[/C][C]15[/C][/ROW]
[ROW][C]28[/C][C]118.25[/C][C]4.11298755975102[/C][C]10[/C][/ROW]
[ROW][C]29[/C][C]136.25[/C][C]8.34166250416147[/C][C]18[/C][/ROW]
[ROW][C]30[/C][C]94.25[/C][C]7.67571929311297[/C][C]17[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78915&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78915&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	250.25	1.70782512765993	4
2	257.25	12.5266382827424	26
3	244	1.4142135623731	3
4	239	2.16024689946929	5
5	240.75	12.0104121494643	24
6	222.75	1.5	3
7	221.5	4.72581562625261	10
8	231.75	5.18812747209113	11
9	221.75	5.1234753829798	11
10	210.75	4.64578662158878	10
11	210.75	10.2428837085396	23
12	200.25	9.21502396451939	22
13	205.75	5.7373048260195	12
14	200.5	9.9498743710662	21
15	190.75	10.3722385883344	24
16	191.25	7.63216876123687	17
17	201.75	7.41057802513857	17
18	184	9.41629792788369	20
19	188.25	8.73212459828649	19
20	200.5	8.18535277187245	17
21	177.75	9.9121138007995	21
22	178.5	6.13731754650732	15
23	197.5	8.88819441731559	19
24	163	4.83045891539648	11
25	159	7.34846922834953	16
26	182.5	9.03696114115064	19
27	139.75	7.08872343937891	15
28	118.25	4.11298755975102	10
29	136.25	8.34166250416147	18
30	94.25	7.67571929311297	17

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	9.21629157118917
beta	-0.0111291754826557
S.D.	0.0146463319648786
T-STAT	-0.759860933737066
p-value	0.453688476853477

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.21629157118917 \tabularnewline
beta & -0.0111291754826557 \tabularnewline
S.D. & 0.0146463319648786 \tabularnewline
T-STAT & -0.759860933737066 \tabularnewline
p-value & 0.453688476853477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78915&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.21629157118917[/C][/ROW]
[ROW][C]beta[/C][C]-0.0111291754826557[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0146463319648786[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.759860933737066[/C][/ROW]
[ROW][C]p-value[/C][C]0.453688476853477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78915&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78915&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	9.21629157118917
beta	-0.0111291754826557
S.D.	0.0146463319648786
T-STAT	-0.759860933737066
p-value	0.453688476853477

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	5.26865910768464
beta	-0.657139620211465
S.D.	0.48489294429476
T-STAT	-1.35522619568578
p-value	0.186178361977016
Lambda	1.65713962021147

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.26865910768464 \tabularnewline
beta & -0.657139620211465 \tabularnewline
S.D. & 0.48489294429476 \tabularnewline
T-STAT & -1.35522619568578 \tabularnewline
p-value & 0.186178361977016 \tabularnewline
Lambda & 1.65713962021147 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78915&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.26865910768464[/C][/ROW]
[ROW][C]beta[/C][C]-0.657139620211465[/C][/ROW]
[ROW][C]S.D.[/C][C]0.48489294429476[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.35522619568578[/C][/ROW]
[ROW][C]p-value[/C][C]0.186178361977016[/C][/ROW]
[ROW][C]Lambda[/C][C]1.65713962021147[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78915&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78915&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	5.26865910768464
beta	-0.657139620211465
S.D.	0.48489294429476
T-STAT	-1.35522619568578
p-value	0.186178361977016
Lambda	1.65713962021147

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