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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

Wed, 03 Jun 2009 05:42:04 -0600

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/2009/Jun/03/t1244029361zey2tthbkieni5t.htm/, Retrieved Sun, 12 May 2024 01:13:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41460, Retrieved Sun, 12 May 2024 01:13:36 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

102

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

-       [Standard Deviation-Mean Plot] [Opgave 8, oefenin...] [2009-06-03 11:42:04] [ef3a18d597c5c4b11c910aafede28e07] [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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41460&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41460&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41460&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' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	42.5	5.06622805119022	11
2	40	4.24264068711928	9
3	38	8.40634680861233	20
4	51	13.7840487520902	31
5	54.25	5.61990510002912	13
6	71.5	15.6098259652908	38
7	73.75	18.3007285829463	39
8	109.25	29.1132844820596	69
9	132.5	27.2335577306137	61
10	121.75	13.6717470232106	31
11	110	23.9304547943968	56
12	91.5	9.46924847422786	21
13	101.75	9.74251849711699	22
14	176.5	47.73887304912	111
15	169.25	23.0560910245716	53
16	166.25	14.8632656797444	35
17	217	49.6319789383149	121
18	268	21.4631467093403	49
19	243.75	38.964727639238	81
20	311.5	47.5429630264389	107
21	281	35.1283361405006	75
22	280	26.2678510731274	63
23	324.5	52.924474489597	122
24	340.5	15.0222057856583	27
25	273.25	39.4493345951487	83
26	366.5	71.182863106228	173
27	457.5	48.7476495159852	109
28	375	60.8659729788875	149
29	384.75	48.7399562303182	115

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 42.5 & 5.06622805119022 & 11 \tabularnewline
2 & 40 & 4.24264068711928 & 9 \tabularnewline
3 & 38 & 8.40634680861233 & 20 \tabularnewline
4 & 51 & 13.7840487520902 & 31 \tabularnewline
5 & 54.25 & 5.61990510002912 & 13 \tabularnewline
6 & 71.5 & 15.6098259652908 & 38 \tabularnewline
7 & 73.75 & 18.3007285829463 & 39 \tabularnewline
8 & 109.25 & 29.1132844820596 & 69 \tabularnewline
9 & 132.5 & 27.2335577306137 & 61 \tabularnewline
10 & 121.75 & 13.6717470232106 & 31 \tabularnewline
11 & 110 & 23.9304547943968 & 56 \tabularnewline
12 & 91.5 & 9.46924847422786 & 21 \tabularnewline
13 & 101.75 & 9.74251849711699 & 22 \tabularnewline
14 & 176.5 & 47.73887304912 & 111 \tabularnewline
15 & 169.25 & 23.0560910245716 & 53 \tabularnewline
16 & 166.25 & 14.8632656797444 & 35 \tabularnewline
17 & 217 & 49.6319789383149 & 121 \tabularnewline
18 & 268 & 21.4631467093403 & 49 \tabularnewline
19 & 243.75 & 38.964727639238 & 81 \tabularnewline
20 & 311.5 & 47.5429630264389 & 107 \tabularnewline
21 & 281 & 35.1283361405006 & 75 \tabularnewline
22 & 280 & 26.2678510731274 & 63 \tabularnewline
23 & 324.5 & 52.924474489597 & 122 \tabularnewline
24 & 340.5 & 15.0222057856583 & 27 \tabularnewline
25 & 273.25 & 39.4493345951487 & 83 \tabularnewline
26 & 366.5 & 71.182863106228 & 173 \tabularnewline
27 & 457.5 & 48.7476495159852 & 109 \tabularnewline
28 & 375 & 60.8659729788875 & 149 \tabularnewline
29 & 384.75 & 48.7399562303182 & 115 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41460&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]42.5[/C][C]5.06622805119022[/C][C]11[/C][/ROW]
[ROW][C]2[/C][C]40[/C][C]4.24264068711928[/C][C]9[/C][/ROW]
[ROW][C]3[/C][C]38[/C][C]8.40634680861233[/C][C]20[/C][/ROW]
[ROW][C]4[/C][C]51[/C][C]13.7840487520902[/C][C]31[/C][/ROW]
[ROW][C]5[/C][C]54.25[/C][C]5.61990510002912[/C][C]13[/C][/ROW]
[ROW][C]6[/C][C]71.5[/C][C]15.6098259652908[/C][C]38[/C][/ROW]
[ROW][C]7[/C][C]73.75[/C][C]18.3007285829463[/C][C]39[/C][/ROW]
[ROW][C]8[/C][C]109.25[/C][C]29.1132844820596[/C][C]69[/C][/ROW]
[ROW][C]9[/C][C]132.5[/C][C]27.2335577306137[/C][C]61[/C][/ROW]
[ROW][C]10[/C][C]121.75[/C][C]13.6717470232106[/C][C]31[/C][/ROW]
[ROW][C]11[/C][C]110[/C][C]23.9304547943968[/C][C]56[/C][/ROW]
[ROW][C]12[/C][C]91.5[/C][C]9.46924847422786[/C][C]21[/C][/ROW]
[ROW][C]13[/C][C]101.75[/C][C]9.74251849711699[/C][C]22[/C][/ROW]
[ROW][C]14[/C][C]176.5[/C][C]47.73887304912[/C][C]111[/C][/ROW]
[ROW][C]15[/C][C]169.25[/C][C]23.0560910245716[/C][C]53[/C][/ROW]
[ROW][C]16[/C][C]166.25[/C][C]14.8632656797444[/C][C]35[/C][/ROW]
[ROW][C]17[/C][C]217[/C][C]49.6319789383149[/C][C]121[/C][/ROW]
[ROW][C]18[/C][C]268[/C][C]21.4631467093403[/C][C]49[/C][/ROW]
[ROW][C]19[/C][C]243.75[/C][C]38.964727639238[/C][C]81[/C][/ROW]
[ROW][C]20[/C][C]311.5[/C][C]47.5429630264389[/C][C]107[/C][/ROW]
[ROW][C]21[/C][C]281[/C][C]35.1283361405006[/C][C]75[/C][/ROW]
[ROW][C]22[/C][C]280[/C][C]26.2678510731274[/C][C]63[/C][/ROW]
[ROW][C]23[/C][C]324.5[/C][C]52.924474489597[/C][C]122[/C][/ROW]
[ROW][C]24[/C][C]340.5[/C][C]15.0222057856583[/C][C]27[/C][/ROW]
[ROW][C]25[/C][C]273.25[/C][C]39.4493345951487[/C][C]83[/C][/ROW]
[ROW][C]26[/C][C]366.5[/C][C]71.182863106228[/C][C]173[/C][/ROW]
[ROW][C]27[/C][C]457.5[/C][C]48.7476495159852[/C][C]109[/C][/ROW]
[ROW][C]28[/C][C]375[/C][C]60.8659729788875[/C][C]149[/C][/ROW]
[ROW][C]29[/C][C]384.75[/C][C]48.7399562303182[/C][C]115[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41460&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41460&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	42.5	5.06622805119022	11
2	40	4.24264068711928	9
3	38	8.40634680861233	20
4	51	13.7840487520902	31
5	54.25	5.61990510002912	13
6	71.5	15.6098259652908	38
7	73.75	18.3007285829463	39
8	109.25	29.1132844820596	69
9	132.5	27.2335577306137	61
10	121.75	13.6717470232106	31
11	110	23.9304547943968	56
12	91.5	9.46924847422786	21
13	101.75	9.74251849711699	22
14	176.5	47.73887304912	111
15	169.25	23.0560910245716	53
16	166.25	14.8632656797444	35
17	217	49.6319789383149	121
18	268	21.4631467093403	49
19	243.75	38.964727639238	81
20	311.5	47.5429630264389	107
21	281	35.1283361405006	75
22	280	26.2678510731274	63
23	324.5	52.924474489597	122
24	340.5	15.0222057856583	27
25	273.25	39.4493345951487	83
26	366.5	71.182863106228	173
27	457.5	48.7476495159852	109
28	375	60.8659729788875	149
29	384.75	48.7399562303182	115

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	5.31031908779098
beta	0.118417234511755
S.D.	0.0175210711376911
T-STAT	6.75856136769043
p-value	2.94493500097904e-07

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.31031908779098 \tabularnewline
beta & 0.118417234511755 \tabularnewline
S.D. & 0.0175210711376911 \tabularnewline
T-STAT & 6.75856136769043 \tabularnewline
p-value & 2.94493500097904e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41460&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.31031908779098[/C][/ROW]
[ROW][C]beta[/C][C]0.118417234511755[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0175210711376911[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.75856136769043[/C][/ROW]
[ROW][C]p-value[/C][C]2.94493500097904e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41460&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41460&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	5.31031908779098
beta	0.118417234511755
S.D.	0.0175210711376911
T-STAT	6.75856136769043
p-value	2.94493500097904e-07

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.23184308619977
beta	0.860215036497359
S.D.	0.105720773816344
T-STAT	8.13666988468797
p-value	9.69500129041493e-09
Lambda	0.139784963502641

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.23184308619977 \tabularnewline
beta & 0.860215036497359 \tabularnewline
S.D. & 0.105720773816344 \tabularnewline
T-STAT & 8.13666988468797 \tabularnewline
p-value & 9.69500129041493e-09 \tabularnewline
Lambda & 0.139784963502641 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41460&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.23184308619977[/C][/ROW]
[ROW][C]beta[/C][C]0.860215036497359[/C][/ROW]
[ROW][C]S.D.[/C][C]0.105720773816344[/C][/ROW]
[ROW][C]T-STAT[/C][C]8.13666988468797[/C][/ROW]
[ROW][C]p-value[/C][C]9.69500129041493e-09[/C][/ROW]
[ROW][C]Lambda[/C][C]0.139784963502641[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41460&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41460&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	-1.23184308619977
beta	0.860215036497359
S.D.	0.105720773816344
T-STAT	8.13666988468797
p-value	9.69500129041493e-09
Lambda	0.139784963502641

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

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