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Author's title

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

Thu, 22 Dec 2011 12:16:57 -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/22/t1324574246fki1b7bjy6yjg6n.htm/, Retrieved Fri, 03 May 2024 11:23:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159750, Retrieved Fri, 03 May 2024 11:23:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

170

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

-     [(Partial) Autocorrelation Function] [] [2011-12-06 13:49:56] [ad2d4c5ace9fa07b356a7b5098237581]
- RMP   [Spectral Analysis] [] [2011-12-06 14:18:39] [ad2d4c5ace9fa07b356a7b5098237581]
- RMP     [Standard Deviation-Mean Plot] [] [2011-12-06 14:41:16] [ad2d4c5ace9fa07b356a7b5098237581]
- R PD        [Standard Deviation-Mean Plot] [] [2011-12-22 17:16:57] [daf26cf00f2f7a7ee0a1368c8ac8117e] [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	'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159750&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159750&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159750&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	'Gertrude Mary Cox' @ cox.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	315.364166666667	1.66762464892342	4.89999999999998
2	316.093333333333	1.64916691549144	5.03000000000003
3	317.009166666667	2.0469554257852	6.19
4	317.793333333333	1.79797529224267	5.77999999999997
5	318.561666666667	1.84826126317945	5.58999999999997
6	319.145833333333	2.07148369459422	6.25
7	319.640833333333	1.93007987744894	5.54000000000002
8	320.2375	1.72675799746756	4.86000000000001
9	321.579166666667	1.99934743141735	5.90999999999997
10	322.253333333333	1.8772433044873	5.69
11	323.27	1.87280538230751	5.31999999999999
12	324.841666666667	1.84862520579893	5.56
13	325.833333333333	1.80117301845887	5.03999999999996
14	326.448333333333	1.83353525058874	5.56
15	327.7625	1.75548555831558	5.13999999999999
16	329.84	1.75849625842908	5.30000000000001
17	330.343333333333	1.99715858765457	5.94
18	331.275833333333	1.91820208591907	5.56
19	332.179166666667	2.11728581972871	6.02000000000004
20	334.150833333333	1.93990373863022	5.63
21	335.615833333333	2.04101337723706	5.67000000000002
22	337.0525	1.89539213980546	5.26999999999998
23	338.995	1.94230182094245	5.42000000000002
24	340.339166666667	2.11011183819649	6.05000000000001
25	341.346666666667	2.1885085553796	6.31999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 315.364166666667 & 1.66762464892342 & 4.89999999999998 \tabularnewline
2 & 316.093333333333 & 1.64916691549144 & 5.03000000000003 \tabularnewline
3 & 317.009166666667 & 2.0469554257852 & 6.19 \tabularnewline
4 & 317.793333333333 & 1.79797529224267 & 5.77999999999997 \tabularnewline
5 & 318.561666666667 & 1.84826126317945 & 5.58999999999997 \tabularnewline
6 & 319.145833333333 & 2.07148369459422 & 6.25 \tabularnewline
7 & 319.640833333333 & 1.93007987744894 & 5.54000000000002 \tabularnewline
8 & 320.2375 & 1.72675799746756 & 4.86000000000001 \tabularnewline
9 & 321.579166666667 & 1.99934743141735 & 5.90999999999997 \tabularnewline
10 & 322.253333333333 & 1.8772433044873 & 5.69 \tabularnewline
11 & 323.27 & 1.87280538230751 & 5.31999999999999 \tabularnewline
12 & 324.841666666667 & 1.84862520579893 & 5.56 \tabularnewline
13 & 325.833333333333 & 1.80117301845887 & 5.03999999999996 \tabularnewline
14 & 326.448333333333 & 1.83353525058874 & 5.56 \tabularnewline
15 & 327.7625 & 1.75548555831558 & 5.13999999999999 \tabularnewline
16 & 329.84 & 1.75849625842908 & 5.30000000000001 \tabularnewline
17 & 330.343333333333 & 1.99715858765457 & 5.94 \tabularnewline
18 & 331.275833333333 & 1.91820208591907 & 5.56 \tabularnewline
19 & 332.179166666667 & 2.11728581972871 & 6.02000000000004 \tabularnewline
20 & 334.150833333333 & 1.93990373863022 & 5.63 \tabularnewline
21 & 335.615833333333 & 2.04101337723706 & 5.67000000000002 \tabularnewline
22 & 337.0525 & 1.89539213980546 & 5.26999999999998 \tabularnewline
23 & 338.995 & 1.94230182094245 & 5.42000000000002 \tabularnewline
24 & 340.339166666667 & 2.11011183819649 & 6.05000000000001 \tabularnewline
25 & 341.346666666667 & 2.1885085553796 & 6.31999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159750&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]315.364166666667[/C][C]1.66762464892342[/C][C]4.89999999999998[/C][/ROW]
[ROW][C]2[/C][C]316.093333333333[/C][C]1.64916691549144[/C][C]5.03000000000003[/C][/ROW]
[ROW][C]3[/C][C]317.009166666667[/C][C]2.0469554257852[/C][C]6.19[/C][/ROW]
[ROW][C]4[/C][C]317.793333333333[/C][C]1.79797529224267[/C][C]5.77999999999997[/C][/ROW]
[ROW][C]5[/C][C]318.561666666667[/C][C]1.84826126317945[/C][C]5.58999999999997[/C][/ROW]
[ROW][C]6[/C][C]319.145833333333[/C][C]2.07148369459422[/C][C]6.25[/C][/ROW]
[ROW][C]7[/C][C]319.640833333333[/C][C]1.93007987744894[/C][C]5.54000000000002[/C][/ROW]
[ROW][C]8[/C][C]320.2375[/C][C]1.72675799746756[/C][C]4.86000000000001[/C][/ROW]
[ROW][C]9[/C][C]321.579166666667[/C][C]1.99934743141735[/C][C]5.90999999999997[/C][/ROW]
[ROW][C]10[/C][C]322.253333333333[/C][C]1.8772433044873[/C][C]5.69[/C][/ROW]
[ROW][C]11[/C][C]323.27[/C][C]1.87280538230751[/C][C]5.31999999999999[/C][/ROW]
[ROW][C]12[/C][C]324.841666666667[/C][C]1.84862520579893[/C][C]5.56[/C][/ROW]
[ROW][C]13[/C][C]325.833333333333[/C][C]1.80117301845887[/C][C]5.03999999999996[/C][/ROW]
[ROW][C]14[/C][C]326.448333333333[/C][C]1.83353525058874[/C][C]5.56[/C][/ROW]
[ROW][C]15[/C][C]327.7625[/C][C]1.75548555831558[/C][C]5.13999999999999[/C][/ROW]
[ROW][C]16[/C][C]329.84[/C][C]1.75849625842908[/C][C]5.30000000000001[/C][/ROW]
[ROW][C]17[/C][C]330.343333333333[/C][C]1.99715858765457[/C][C]5.94[/C][/ROW]
[ROW][C]18[/C][C]331.275833333333[/C][C]1.91820208591907[/C][C]5.56[/C][/ROW]
[ROW][C]19[/C][C]332.179166666667[/C][C]2.11728581972871[/C][C]6.02000000000004[/C][/ROW]
[ROW][C]20[/C][C]334.150833333333[/C][C]1.93990373863022[/C][C]5.63[/C][/ROW]
[ROW][C]21[/C][C]335.615833333333[/C][C]2.04101337723706[/C][C]5.67000000000002[/C][/ROW]
[ROW][C]22[/C][C]337.0525[/C][C]1.89539213980546[/C][C]5.26999999999998[/C][/ROW]
[ROW][C]23[/C][C]338.995[/C][C]1.94230182094245[/C][C]5.42000000000002[/C][/ROW]
[ROW][C]24[/C][C]340.339166666667[/C][C]2.11011183819649[/C][C]6.05000000000001[/C][/ROW]
[ROW][C]25[/C][C]341.346666666667[/C][C]2.1885085553796[/C][C]6.31999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159750&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159750&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	315.364166666667	1.66762464892342	4.89999999999998
2	316.093333333333	1.64916691549144	5.03000000000003
3	317.009166666667	2.0469554257852	6.19
4	317.793333333333	1.79797529224267	5.77999999999997
5	318.561666666667	1.84826126317945	5.58999999999997
6	319.145833333333	2.07148369459422	6.25
7	319.640833333333	1.93007987744894	5.54000000000002
8	320.2375	1.72675799746756	4.86000000000001
9	321.579166666667	1.99934743141735	5.90999999999997
10	322.253333333333	1.8772433044873	5.69
11	323.27	1.87280538230751	5.31999999999999
12	324.841666666667	1.84862520579893	5.56
13	325.833333333333	1.80117301845887	5.03999999999996
14	326.448333333333	1.83353525058874	5.56
15	327.7625	1.75548555831558	5.13999999999999
16	329.84	1.75849625842908	5.30000000000001
17	330.343333333333	1.99715858765457	5.94
18	331.275833333333	1.91820208591907	5.56
19	332.179166666667	2.11728581972871	6.02000000000004
20	334.150833333333	1.93990373863022	5.63
21	335.615833333333	2.04101337723706	5.67000000000002
22	337.0525	1.89539213980546	5.26999999999998
23	338.995	1.94230182094245	5.42000000000002
24	340.339166666667	2.11011183819649	6.05000000000001
25	341.346666666667	2.1885085553796	6.31999999999999

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-1.20313899316904
beta	0.00951556642533766
S.D.	0.00310702142494558
T-STAT	3.06260083980732
p-value	0.00551450083557781

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.20313899316904 \tabularnewline
beta & 0.00951556642533766 \tabularnewline
S.D. & 0.00310702142494558 \tabularnewline
T-STAT & 3.06260083980732 \tabularnewline
p-value & 0.00551450083557781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159750&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.20313899316904[/C][/ROW]
[ROW][C]beta[/C][C]0.00951556642533766[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00310702142494558[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.06260083980732[/C][/ROW]
[ROW][C]p-value[/C][C]0.00551450083557781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159750&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159750&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	-1.20313899316904
beta	0.00951556642533766
S.D.	0.00310702142494558
T-STAT	3.06260083980732
p-value	0.00551450083557781

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-8.83172909537602
beta	1.63659378558557
S.D.	0.535686736861663
T-STAT	3.05513217514699
p-value	0.00561259381068688
Lambda	-0.636593785585568

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -8.83172909537602 \tabularnewline
beta & 1.63659378558557 \tabularnewline
S.D. & 0.535686736861663 \tabularnewline
T-STAT & 3.05513217514699 \tabularnewline
p-value & 0.00561259381068688 \tabularnewline
Lambda & -0.636593785585568 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159750&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8.83172909537602[/C][/ROW]
[ROW][C]beta[/C][C]1.63659378558557[/C][/ROW]
[ROW][C]S.D.[/C][C]0.535686736861663[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.05513217514699[/C][/ROW]
[ROW][C]p-value[/C][C]0.00561259381068688[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.636593785585568[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159750&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159750&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	-8.83172909537602
beta	1.63659378558557
S.D.	0.535686736861663
T-STAT	3.05513217514699
p-value	0.00561259381068688
Lambda	-0.636593785585568

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code