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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, 10 May 2011 16:37:22 +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/2011/May/10/t1305045271o7pkzwyxep3epzq.htm/, Retrieved Sun, 12 May 2024 15:09:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121420, Retrieved Sun, 12 May 2024 15:09:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

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

-       [Standard Deviation-Mean Plot] [standard deviatio...] [2011-05-10 16:37:22] [93a9440e82e53db41c1ce1bc7dd7ea5d] [Current]

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Dataseries X:

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Histogram

Boxplots

17.1
13.4
15.3
14
9.7
13.7
13.7
12.5
9.8
7
-1.9
-2.9
-6.8
-10.4
-17.2
-19.8
-16.8
-23.2
-21.7
-17.6
-13
-12.6
-4
-0.2
3.1
6.5
19.2
26.6
26.6
31.4
31.2
26.4
20.7
20.7
15
13.3
8.7
10.2
4.3
-0.1
-4.6
-3.9
-3.5
-3.4
-2.5
-1.1
0.3
-0.9
3.6
2.7
-0.2
-1
5.8
6.4
9.6
13.2
10.6
10.9
12.9
15.9
12.2
9.1
9
17.4
14.7
17
13.7
9.5
14.8
13.6
12.6
8.9
10.2
12.7
16
10.4
9.9
9.5
8.6
10
3.5
-4.2
-4.4
-1.5
-0.1
0.8
-2.4
-1.2
0.2
-1.9
-1.6
-4.2
-2.2
6.2
5.7
3.1
1.1
-0.9
0.1
-4
-4
-5.3
-8
-6.3
-3.6
-3.5
-5.1
-3.3

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	'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121420&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121420&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121420&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	'Herman Ole Andreas Wold' @ www.yougetit.org

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	14.95	1.63808831670742	3.7
2	12.4	1.88679622641132	4
3	3	6.3524273575802	12.7
4	-13.55	5.99638780155742	13
5	-19.825	3.10952836723942	6.4
6	-7.45	6.37155135478532	12.8
7	13.85	10.9661600693527	23.5
8	28.9	2.77368587502863	5
9	17.425	3.84480168539289	7.4
10	5.775	4.64856608715706	10.3
11	-3.85	0.544671154612273	1.2
12	-1.05	1.1474609652039	2.8
13	1.275	2.22017266595791	4.6
14	8.75	3.40342964277702	7.4
15	12.575	2.44045760736247	5.3
16	11.925	3.94070636646105	8.4
17	13.725	3.1372758884102	7.5
18	12.475	2.54738427934748	5.9
19	12.325	2.69984567460191	5.8
20	9.5	0.637704215656967	1.4
21	-1.65	3.67922093202714	7.9
22	-0.725	1.38413631313297	3.2
23	-1.875	1.80623918681884	4.4
24	3.2	3.84794317352357	8.4
25	-0.925	2.20661883130428	5.1
26	-5.9	1.68720676464584	4
27	-3.875	0.826135582092915	1.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14.95 & 1.63808831670742 & 3.7 \tabularnewline
2 & 12.4 & 1.88679622641132 & 4 \tabularnewline
3 & 3 & 6.3524273575802 & 12.7 \tabularnewline
4 & -13.55 & 5.99638780155742 & 13 \tabularnewline
5 & -19.825 & 3.10952836723942 & 6.4 \tabularnewline
6 & -7.45 & 6.37155135478532 & 12.8 \tabularnewline
7 & 13.85 & 10.9661600693527 & 23.5 \tabularnewline
8 & 28.9 & 2.77368587502863 & 5 \tabularnewline
9 & 17.425 & 3.84480168539289 & 7.4 \tabularnewline
10 & 5.775 & 4.64856608715706 & 10.3 \tabularnewline
11 & -3.85 & 0.544671154612273 & 1.2 \tabularnewline
12 & -1.05 & 1.1474609652039 & 2.8 \tabularnewline
13 & 1.275 & 2.22017266595791 & 4.6 \tabularnewline
14 & 8.75 & 3.40342964277702 & 7.4 \tabularnewline
15 & 12.575 & 2.44045760736247 & 5.3 \tabularnewline
16 & 11.925 & 3.94070636646105 & 8.4 \tabularnewline
17 & 13.725 & 3.1372758884102 & 7.5 \tabularnewline
18 & 12.475 & 2.54738427934748 & 5.9 \tabularnewline
19 & 12.325 & 2.69984567460191 & 5.8 \tabularnewline
20 & 9.5 & 0.637704215656967 & 1.4 \tabularnewline
21 & -1.65 & 3.67922093202714 & 7.9 \tabularnewline
22 & -0.725 & 1.38413631313297 & 3.2 \tabularnewline
23 & -1.875 & 1.80623918681884 & 4.4 \tabularnewline
24 & 3.2 & 3.84794317352357 & 8.4 \tabularnewline
25 & -0.925 & 2.20661883130428 & 5.1 \tabularnewline
26 & -5.9 & 1.68720676464584 & 4 \tabularnewline
27 & -3.875 & 0.826135582092915 & 1.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121420&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]14.95[/C][C]1.63808831670742[/C][C]3.7[/C][/ROW]
[ROW][C]2[/C][C]12.4[/C][C]1.88679622641132[/C][C]4[/C][/ROW]
[ROW][C]3[/C][C]3[/C][C]6.3524273575802[/C][C]12.7[/C][/ROW]
[ROW][C]4[/C][C]-13.55[/C][C]5.99638780155742[/C][C]13[/C][/ROW]
[ROW][C]5[/C][C]-19.825[/C][C]3.10952836723942[/C][C]6.4[/C][/ROW]
[ROW][C]6[/C][C]-7.45[/C][C]6.37155135478532[/C][C]12.8[/C][/ROW]
[ROW][C]7[/C][C]13.85[/C][C]10.9661600693527[/C][C]23.5[/C][/ROW]
[ROW][C]8[/C][C]28.9[/C][C]2.77368587502863[/C][C]5[/C][/ROW]
[ROW][C]9[/C][C]17.425[/C][C]3.84480168539289[/C][C]7.4[/C][/ROW]
[ROW][C]10[/C][C]5.775[/C][C]4.64856608715706[/C][C]10.3[/C][/ROW]
[ROW][C]11[/C][C]-3.85[/C][C]0.544671154612273[/C][C]1.2[/C][/ROW]
[ROW][C]12[/C][C]-1.05[/C][C]1.1474609652039[/C][C]2.8[/C][/ROW]
[ROW][C]13[/C][C]1.275[/C][C]2.22017266595791[/C][C]4.6[/C][/ROW]
[ROW][C]14[/C][C]8.75[/C][C]3.40342964277702[/C][C]7.4[/C][/ROW]
[ROW][C]15[/C][C]12.575[/C][C]2.44045760736247[/C][C]5.3[/C][/ROW]
[ROW][C]16[/C][C]11.925[/C][C]3.94070636646105[/C][C]8.4[/C][/ROW]
[ROW][C]17[/C][C]13.725[/C][C]3.1372758884102[/C][C]7.5[/C][/ROW]
[ROW][C]18[/C][C]12.475[/C][C]2.54738427934748[/C][C]5.9[/C][/ROW]
[ROW][C]19[/C][C]12.325[/C][C]2.69984567460191[/C][C]5.8[/C][/ROW]
[ROW][C]20[/C][C]9.5[/C][C]0.637704215656967[/C][C]1.4[/C][/ROW]
[ROW][C]21[/C][C]-1.65[/C][C]3.67922093202714[/C][C]7.9[/C][/ROW]
[ROW][C]22[/C][C]-0.725[/C][C]1.38413631313297[/C][C]3.2[/C][/ROW]
[ROW][C]23[/C][C]-1.875[/C][C]1.80623918681884[/C][C]4.4[/C][/ROW]
[ROW][C]24[/C][C]3.2[/C][C]3.84794317352357[/C][C]8.4[/C][/ROW]
[ROW][C]25[/C][C]-0.925[/C][C]2.20661883130428[/C][C]5.1[/C][/ROW]
[ROW][C]26[/C][C]-5.9[/C][C]1.68720676464584[/C][C]4[/C][/ROW]
[ROW][C]27[/C][C]-3.875[/C][C]0.826135582092915[/C][C]1.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121420&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121420&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	14.95	1.63808831670742	3.7
2	12.4	1.88679622641132	4
3	3	6.3524273575802	12.7
4	-13.55	5.99638780155742	13
5	-19.825	3.10952836723942	6.4
6	-7.45	6.37155135478532	12.8
7	13.85	10.9661600693527	23.5
8	28.9	2.77368587502863	5
9	17.425	3.84480168539289	7.4
10	5.775	4.64856608715706	10.3
11	-3.85	0.544671154612273	1.2
12	-1.05	1.1474609652039	2.8
13	1.275	2.22017266595791	4.6
14	8.75	3.40342964277702	7.4
15	12.575	2.44045760736247	5.3
16	11.925	3.94070636646105	8.4
17	13.725	3.1372758884102	7.5
18	12.475	2.54738427934748	5.9
19	12.325	2.69984567460191	5.8
20	9.5	0.637704215656967	1.4
21	-1.65	3.67922093202714	7.9
22	-0.725	1.38413631313297	3.2
23	-1.875	1.80623918681884	4.4
24	3.2	3.84794317352357	8.4
25	-0.925	2.20661883130428	5.1
26	-5.9	1.68720676464584	4
27	-3.875	0.826135582092915	1.8

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	3.13704755941345
beta	0.00860406410699007
S.D.	0.0424877546717445
T-STAT	0.202506914603138
p-value	0.841159467920293

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.13704755941345 \tabularnewline
beta & 0.00860406410699007 \tabularnewline
S.D. & 0.0424877546717445 \tabularnewline
T-STAT & 0.202506914603138 \tabularnewline
p-value & 0.841159467920293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121420&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.13704755941345[/C][/ROW]
[ROW][C]beta[/C][C]0.00860406410699007[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0424877546717445[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.202506914603138[/C][/ROW]
[ROW][C]p-value[/C][C]0.841159467920293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121420&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121420&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	3.13704755941345
beta	0.00860406410699007
S.D.	0.0424877546717445
T-STAT	0.202506914603138
p-value	0.841159467920293

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	1.25396092511956
beta	-0.0715120252052902
S.D.	0.211350769269943
T-STAT	-0.33835706135497
p-value	0.740114845299968
Lambda	1.07151202520529

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.25396092511956 \tabularnewline
beta & -0.0715120252052902 \tabularnewline
S.D. & 0.211350769269943 \tabularnewline
T-STAT & -0.33835706135497 \tabularnewline
p-value & 0.740114845299968 \tabularnewline
Lambda & 1.07151202520529 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121420&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.25396092511956[/C][/ROW]
[ROW][C]beta[/C][C]-0.0715120252052902[/C][/ROW]
[ROW][C]S.D.[/C][C]0.211350769269943[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.33835706135497[/C][/ROW]
[ROW][C]p-value[/C][C]0.740114845299968[/C][/ROW]
[ROW][C]Lambda[/C][C]1.07151202520529[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121420&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121420&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	1.25396092511956
beta	-0.0715120252052902
S.D.	0.211350769269943
T-STAT	-0.33835706135497
p-value	0.740114845299968
Lambda	1.07151202520529

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