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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

Thu, 05 Aug 2010 13:59:58 +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/05/t1281016796zsagqg3c8n4u6gw.htm/, Retrieved Sun, 05 May 2024 14:24:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78411, Retrieved Sun, 05 May 2024 14:24:31 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Philippe De Vocht

Estimated Impact

140

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

-       [Standard Deviation-Mean Plot] [Omzet product X] [2010-08-05 13:59:58] [181f2439255053cc457d7672472fa443] [Current]
-   P     [Standard Deviation-Mean Plot] [Omzet product X] [2010-08-16 13:39:48] [74be16979710d4c4e7c6647856088456] 

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Dataseries X:

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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	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=78411&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=78411&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78411&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	71.25	1.70782512765993	4
2	78.25	12.5266382827424	26
3	65	1.41421356237310	3
4	70.5	1.29099444873581	3
5	79.25	7.88986691902975	18
6	75.5	4.12310562561766	10
7	85.5	4.20317340430616	10
8	100.25	5.18812747209113	11
9	114.5	6.2449979983984	14
10	115.75	6.23832242407097	13
11	122	8.98146239020499	19
12	128	6.21825270205921	14
13	121.25	5.85234995535981	14
14	128.5	12.5830573921179	26
15	142.5	11.0302614051829	26
16	145	5.35412613473634	11
17	148.75	12.5266382827424	27
18	172.5	11.9023807142381	28
19	180.75	6.13052471924984	12
20	183.5	15.8429795177549	33
21	189.75	8.0156097709407	18
22	191.25	4.78713553878169	10
23	187.25	20.3039405042470	42
24	186.5	4.65474668125631	11
25	179.5	5.56776436283002	13
26	171.25	16.2557682070089	38
27	189.75	6.9462219947249	15
28	186.5	9.1104335791443	20
29	175.25	14.7507061977837	32
30	186.75	9.9121138007995	23

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 71.25 & 1.70782512765993 & 4 \tabularnewline
2 & 78.25 & 12.5266382827424 & 26 \tabularnewline
3 & 65 & 1.41421356237310 & 3 \tabularnewline
4 & 70.5 & 1.29099444873581 & 3 \tabularnewline
5 & 79.25 & 7.88986691902975 & 18 \tabularnewline
6 & 75.5 & 4.12310562561766 & 10 \tabularnewline
7 & 85.5 & 4.20317340430616 & 10 \tabularnewline
8 & 100.25 & 5.18812747209113 & 11 \tabularnewline
9 & 114.5 & 6.2449979983984 & 14 \tabularnewline
10 & 115.75 & 6.23832242407097 & 13 \tabularnewline
11 & 122 & 8.98146239020499 & 19 \tabularnewline
12 & 128 & 6.21825270205921 & 14 \tabularnewline
13 & 121.25 & 5.85234995535981 & 14 \tabularnewline
14 & 128.5 & 12.5830573921179 & 26 \tabularnewline
15 & 142.5 & 11.0302614051829 & 26 \tabularnewline
16 & 145 & 5.35412613473634 & 11 \tabularnewline
17 & 148.75 & 12.5266382827424 & 27 \tabularnewline
18 & 172.5 & 11.9023807142381 & 28 \tabularnewline
19 & 180.75 & 6.13052471924984 & 12 \tabularnewline
20 & 183.5 & 15.8429795177549 & 33 \tabularnewline
21 & 189.75 & 8.0156097709407 & 18 \tabularnewline
22 & 191.25 & 4.78713553878169 & 10 \tabularnewline
23 & 187.25 & 20.3039405042470 & 42 \tabularnewline
24 & 186.5 & 4.65474668125631 & 11 \tabularnewline
25 & 179.5 & 5.56776436283002 & 13 \tabularnewline
26 & 171.25 & 16.2557682070089 & 38 \tabularnewline
27 & 189.75 & 6.9462219947249 & 15 \tabularnewline
28 & 186.5 & 9.1104335791443 & 20 \tabularnewline
29 & 175.25 & 14.7507061977837 & 32 \tabularnewline
30 & 186.75 & 9.9121138007995 & 23 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78411&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]71.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]78.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]65[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]70.5[/C][C]1.29099444873581[/C][C]3[/C][/ROW]
[ROW][C]5[/C][C]79.25[/C][C]7.88986691902975[/C][C]18[/C][/ROW]
[ROW][C]6[/C][C]75.5[/C][C]4.12310562561766[/C][C]10[/C][/ROW]
[ROW][C]7[/C][C]85.5[/C][C]4.20317340430616[/C][C]10[/C][/ROW]
[ROW][C]8[/C][C]100.25[/C][C]5.18812747209113[/C][C]11[/C][/ROW]
[ROW][C]9[/C][C]114.5[/C][C]6.2449979983984[/C][C]14[/C][/ROW]
[ROW][C]10[/C][C]115.75[/C][C]6.23832242407097[/C][C]13[/C][/ROW]
[ROW][C]11[/C][C]122[/C][C]8.98146239020499[/C][C]19[/C][/ROW]
[ROW][C]12[/C][C]128[/C][C]6.21825270205921[/C][C]14[/C][/ROW]
[ROW][C]13[/C][C]121.25[/C][C]5.85234995535981[/C][C]14[/C][/ROW]
[ROW][C]14[/C][C]128.5[/C][C]12.5830573921179[/C][C]26[/C][/ROW]
[ROW][C]15[/C][C]142.5[/C][C]11.0302614051829[/C][C]26[/C][/ROW]
[ROW][C]16[/C][C]145[/C][C]5.35412613473634[/C][C]11[/C][/ROW]
[ROW][C]17[/C][C]148.75[/C][C]12.5266382827424[/C][C]27[/C][/ROW]
[ROW][C]18[/C][C]172.5[/C][C]11.9023807142381[/C][C]28[/C][/ROW]
[ROW][C]19[/C][C]180.75[/C][C]6.13052471924984[/C][C]12[/C][/ROW]
[ROW][C]20[/C][C]183.5[/C][C]15.8429795177549[/C][C]33[/C][/ROW]
[ROW][C]21[/C][C]189.75[/C][C]8.0156097709407[/C][C]18[/C][/ROW]
[ROW][C]22[/C][C]191.25[/C][C]4.78713553878169[/C][C]10[/C][/ROW]
[ROW][C]23[/C][C]187.25[/C][C]20.3039405042470[/C][C]42[/C][/ROW]
[ROW][C]24[/C][C]186.5[/C][C]4.65474668125631[/C][C]11[/C][/ROW]
[ROW][C]25[/C][C]179.5[/C][C]5.56776436283002[/C][C]13[/C][/ROW]
[ROW][C]26[/C][C]171.25[/C][C]16.2557682070089[/C][C]38[/C][/ROW]
[ROW][C]27[/C][C]189.75[/C][C]6.9462219947249[/C][C]15[/C][/ROW]
[ROW][C]28[/C][C]186.5[/C][C]9.1104335791443[/C][C]20[/C][/ROW]
[ROW][C]29[/C][C]175.25[/C][C]14.7507061977837[/C][C]32[/C][/ROW]
[ROW][C]30[/C][C]186.75[/C][C]9.9121138007995[/C][C]23[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78411&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78411&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	71.25	1.70782512765993	4
2	78.25	12.5266382827424	26
3	65	1.41421356237310	3
4	70.5	1.29099444873581	3
5	79.25	7.88986691902975	18
6	75.5	4.12310562561766	10
7	85.5	4.20317340430616	10
8	100.25	5.18812747209113	11
9	114.5	6.2449979983984	14
10	115.75	6.23832242407097	13
11	122	8.98146239020499	19
12	128	6.21825270205921	14
13	121.25	5.85234995535981	14
14	128.5	12.5830573921179	26
15	142.5	11.0302614051829	26
16	145	5.35412613473634	11
17	148.75	12.5266382827424	27
18	172.5	11.9023807142381	28
19	180.75	6.13052471924984	12
20	183.5	15.8429795177549	33
21	189.75	8.0156097709407	18
22	191.25	4.78713553878169	10
23	187.25	20.3039405042470	42
24	186.5	4.65474668125631	11
25	179.5	5.56776436283002	13
26	171.25	16.2557682070089	38
27	189.75	6.9462219947249	15
28	186.5	9.1104335791443	20
29	175.25	14.7507061977837	32
30	186.75	9.9121138007995	23

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.22218343569408
beta	0.050545445753578
S.D.	0.0172465529832396
T-STAT	2.93075641275672
p-value	0.0066621118425517

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.22218343569408 \tabularnewline
beta & 0.050545445753578 \tabularnewline
S.D. & 0.0172465529832396 \tabularnewline
T-STAT & 2.93075641275672 \tabularnewline
p-value & 0.0066621118425517 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78411&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.22218343569408[/C][/ROW]
[ROW][C]beta[/C][C]0.050545445753578[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0172465529832396[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.93075641275672[/C][/ROW]
[ROW][C]p-value[/C][C]0.0066621118425517[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78411&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78411&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	1.22218343569408
beta	0.050545445753578
S.D.	0.0172465529832396
T-STAT	2.93075641275672
p-value	0.0066621118425517

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.70232509239089
beta	1.15385168298121
S.D.	0.276041845956774
T-STAT	4.17998828757977
p-value	0.000258879975489120
Lambda	-0.153851682981214

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.70232509239089 \tabularnewline
beta & 1.15385168298121 \tabularnewline
S.D. & 0.276041845956774 \tabularnewline
T-STAT & 4.17998828757977 \tabularnewline
p-value & 0.000258879975489120 \tabularnewline
Lambda & -0.153851682981214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78411&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.70232509239089[/C][/ROW]
[ROW][C]beta[/C][C]1.15385168298121[/C][/ROW]
[ROW][C]S.D.[/C][C]0.276041845956774[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.17998828757977[/C][/ROW]
[ROW][C]p-value[/C][C]0.000258879975489120[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.153851682981214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78411&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78411&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	-3.70232509239089
beta	1.15385168298121
S.D.	0.276041845956774
T-STAT	4.17998828757977
p-value	0.000258879975489120
Lambda	-0.153851682981214

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