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Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Mon, 05 Dec 2011 17:33:44 -0500

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/Dec/05/t1323124446maw65v2abk7m452.htm/, Retrieved Fri, 03 May 2024 10:50:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151311, Retrieved Fri, 03 May 2024 10:50:38 +0000

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Estimated Impact

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

-       [Standard Deviation-Mean Plot] [WS9 - SMP] [2011-12-05 22:33:44] [8aedcf735e397266388b06f47fe45218] [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	2 seconds
R Server	'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151311&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151311&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151311&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	'George Udny Yule' @ yule.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	2253.16666666667	810.782880176856	2239
2	2039.33333333333	247.108122574763	767
3	2306.08333333333	275.82354647107	948
4	2294.08333333333	237.446054479494	827
5	2557.91666666667	379.968529398598	1383
6	2626.5	226.707861675449	687
7	2360.91666666667	294.065997024581	958
8	2100.16666666667	203.019404954006	553
9	1983.75	206.167242349947	683
10	2068.75	327.297230774608	931
11	2217.25	300.385245067972	1008
12	2449.08333333333	308.458471739518	1112
13	2082.25	440.271429709199	1856
14	2871.5	764.284513896375	2831
15	2814.5	506.012845686747	1782
16	2431.08333333333	304.580921724897	861
17	3031.91666666667	419.096313151249	1337
18	2889.41666666667	504.041026168115	1648
19	2783	379.846859094078	1249
20	2524.33333333333	332.343560828614	1214
21	2803.16666666667	438.98039577957	1173

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2253.16666666667 & 810.782880176856 & 2239 \tabularnewline
2 & 2039.33333333333 & 247.108122574763 & 767 \tabularnewline
3 & 2306.08333333333 & 275.82354647107 & 948 \tabularnewline
4 & 2294.08333333333 & 237.446054479494 & 827 \tabularnewline
5 & 2557.91666666667 & 379.968529398598 & 1383 \tabularnewline
6 & 2626.5 & 226.707861675449 & 687 \tabularnewline
7 & 2360.91666666667 & 294.065997024581 & 958 \tabularnewline
8 & 2100.16666666667 & 203.019404954006 & 553 \tabularnewline
9 & 1983.75 & 206.167242349947 & 683 \tabularnewline
10 & 2068.75 & 327.297230774608 & 931 \tabularnewline
11 & 2217.25 & 300.385245067972 & 1008 \tabularnewline
12 & 2449.08333333333 & 308.458471739518 & 1112 \tabularnewline
13 & 2082.25 & 440.271429709199 & 1856 \tabularnewline
14 & 2871.5 & 764.284513896375 & 2831 \tabularnewline
15 & 2814.5 & 506.012845686747 & 1782 \tabularnewline
16 & 2431.08333333333 & 304.580921724897 & 861 \tabularnewline
17 & 3031.91666666667 & 419.096313151249 & 1337 \tabularnewline
18 & 2889.41666666667 & 504.041026168115 & 1648 \tabularnewline
19 & 2783 & 379.846859094078 & 1249 \tabularnewline
20 & 2524.33333333333 & 332.343560828614 & 1214 \tabularnewline
21 & 2803.16666666667 & 438.98039577957 & 1173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151311&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]2253.16666666667[/C][C]810.782880176856[/C][C]2239[/C][/ROW]
[ROW][C]2[/C][C]2039.33333333333[/C][C]247.108122574763[/C][C]767[/C][/ROW]
[ROW][C]3[/C][C]2306.08333333333[/C][C]275.82354647107[/C][C]948[/C][/ROW]
[ROW][C]4[/C][C]2294.08333333333[/C][C]237.446054479494[/C][C]827[/C][/ROW]
[ROW][C]5[/C][C]2557.91666666667[/C][C]379.968529398598[/C][C]1383[/C][/ROW]
[ROW][C]6[/C][C]2626.5[/C][C]226.707861675449[/C][C]687[/C][/ROW]
[ROW][C]7[/C][C]2360.91666666667[/C][C]294.065997024581[/C][C]958[/C][/ROW]
[ROW][C]8[/C][C]2100.16666666667[/C][C]203.019404954006[/C][C]553[/C][/ROW]
[ROW][C]9[/C][C]1983.75[/C][C]206.167242349947[/C][C]683[/C][/ROW]
[ROW][C]10[/C][C]2068.75[/C][C]327.297230774608[/C][C]931[/C][/ROW]
[ROW][C]11[/C][C]2217.25[/C][C]300.385245067972[/C][C]1008[/C][/ROW]
[ROW][C]12[/C][C]2449.08333333333[/C][C]308.458471739518[/C][C]1112[/C][/ROW]
[ROW][C]13[/C][C]2082.25[/C][C]440.271429709199[/C][C]1856[/C][/ROW]
[ROW][C]14[/C][C]2871.5[/C][C]764.284513896375[/C][C]2831[/C][/ROW]
[ROW][C]15[/C][C]2814.5[/C][C]506.012845686747[/C][C]1782[/C][/ROW]
[ROW][C]16[/C][C]2431.08333333333[/C][C]304.580921724897[/C][C]861[/C][/ROW]
[ROW][C]17[/C][C]3031.91666666667[/C][C]419.096313151249[/C][C]1337[/C][/ROW]
[ROW][C]18[/C][C]2889.41666666667[/C][C]504.041026168115[/C][C]1648[/C][/ROW]
[ROW][C]19[/C][C]2783[/C][C]379.846859094078[/C][C]1249[/C][/ROW]
[ROW][C]20[/C][C]2524.33333333333[/C][C]332.343560828614[/C][C]1214[/C][/ROW]
[ROW][C]21[/C][C]2803.16666666667[/C][C]438.98039577957[/C][C]1173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151311&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151311&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	2253.16666666667	810.782880176856	2239
2	2039.33333333333	247.108122574763	767
3	2306.08333333333	275.82354647107	948
4	2294.08333333333	237.446054479494	827
5	2557.91666666667	379.968529398598	1383
6	2626.5	226.707861675449	687
7	2360.91666666667	294.065997024581	958
8	2100.16666666667	203.019404954006	553
9	1983.75	206.167242349947	683
10	2068.75	327.297230774608	931
11	2217.25	300.385245067972	1008
12	2449.08333333333	308.458471739518	1112
13	2082.25	440.271429709199	1856
14	2871.5	764.284513896375	2831
15	2814.5	506.012845686747	1782
16	2431.08333333333	304.580921724897	861
17	3031.91666666667	419.096313151249	1337
18	2889.41666666667	504.041026168115	1648
19	2783	379.846859094078	1249
20	2524.33333333333	332.343560828614	1214
21	2803.16666666667	438.98039577957	1173

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-159.973947732975
beta	0.218810303114013
S.D.	0.105709409472666
T-STAT	2.0699226701346
p-value	0.0523324334395047

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -159.973947732975 \tabularnewline
beta & 0.218810303114013 \tabularnewline
S.D. & 0.105709409472666 \tabularnewline
T-STAT & 2.0699226701346 \tabularnewline
p-value & 0.0523324334395047 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151311&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-159.973947732975[/C][/ROW]
[ROW][C]beta[/C][C]0.218810303114013[/C][/ROW]
[ROW][C]S.D.[/C][C]0.105709409472666[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.0699226701346[/C][/ROW]
[ROW][C]p-value[/C][C]0.0523324334395047[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151311&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151311&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	-159.973947732975
beta	0.218810303114013
S.D.	0.105709409472666
T-STAT	2.0699226701346
p-value	0.0523324334395047

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-5.84038969412889
beta	1.50022962222457
S.D.	0.576621262492703
T-STAT	2.601759109158
p-value	0.0175193337687202
Lambda	-0.500229622224574

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.84038969412889 \tabularnewline
beta & 1.50022962222457 \tabularnewline
S.D. & 0.576621262492703 \tabularnewline
T-STAT & 2.601759109158 \tabularnewline
p-value & 0.0175193337687202 \tabularnewline
Lambda & -0.500229622224574 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151311&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.84038969412889[/C][/ROW]
[ROW][C]beta[/C][C]1.50022962222457[/C][/ROW]
[ROW][C]S.D.[/C][C]0.576621262492703[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.601759109158[/C][/ROW]
[ROW][C]p-value[/C][C]0.0175193337687202[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.500229622224574[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151311&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151311&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	-5.84038969412889
beta	1.50022962222457
S.D.	0.576621262492703
T-STAT	2.601759109158
p-value	0.0175193337687202
Lambda	-0.500229622224574

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code