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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, 20 Jul 2010 11:44:27 +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/Jul/20/t1279626263gbq5oqdmjhickaj.htm/, Retrieved Sat, 04 May 2024 03:26:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78045, Retrieved Sat, 04 May 2024 03:26:43 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Vanhille Olivier

Estimated Impact

189

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

-       [Standard Deviation-Mean Plot] [tijdreeks 1 - sta...] [2010-07-20 11:44:27] [ddb1c76c3acba5bf82e5ed3b5a08f68d] [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' @ 72.249.76.132

\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' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78045&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78045&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78045&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' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	566.25	1.70782512765993	4
2	573.25	12.5266382827424	26
3	560	1.41421356237310	3
4	555.5	5.19615242270663	11
5	557.75	15.9033539439537	34
6	547.75	3.30403793359983	7
7	532.25	9.8784276751583	23
8	535	17.2046505340853	38
9	519	2.16024689946929	5
10	492.25	12.3389626792531	27
11	488.75	18.6793111935817	41
12	477.75	4.99165971062398	11
13	450.25	16.3579746097533	37
14	438.25	19.6022957839127	45
15	422.5	5.25991127935317	12
16	394.25	16.5201896679992	38
17	371.75	20.6458228220626	47
18	360.75	8.65544144839919	19
19	325	21.1187120819429	47
20	309	21.5251790546173	49
21	300.5	9.18331820930394	22
22	265.75	18.9626826512847	42
23	247.75	23.7679756535273	53
24	242.25	7.58836829188814	18
25	198.75	21.7159695462425	49
26	179.75	25.0383039894212	57
27	173.5	11.7898261225516	25
28	129.75	27.5484421822118	62
29	98.5	26.5894716006167	60
30	93.5	7.32575365861197	17

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 566.25 & 1.70782512765993 & 4 \tabularnewline
2 & 573.25 & 12.5266382827424 & 26 \tabularnewline
3 & 560 & 1.41421356237310 & 3 \tabularnewline
4 & 555.5 & 5.19615242270663 & 11 \tabularnewline
5 & 557.75 & 15.9033539439537 & 34 \tabularnewline
6 & 547.75 & 3.30403793359983 & 7 \tabularnewline
7 & 532.25 & 9.8784276751583 & 23 \tabularnewline
8 & 535 & 17.2046505340853 & 38 \tabularnewline
9 & 519 & 2.16024689946929 & 5 \tabularnewline
10 & 492.25 & 12.3389626792531 & 27 \tabularnewline
11 & 488.75 & 18.6793111935817 & 41 \tabularnewline
12 & 477.75 & 4.99165971062398 & 11 \tabularnewline
13 & 450.25 & 16.3579746097533 & 37 \tabularnewline
14 & 438.25 & 19.6022957839127 & 45 \tabularnewline
15 & 422.5 & 5.25991127935317 & 12 \tabularnewline
16 & 394.25 & 16.5201896679992 & 38 \tabularnewline
17 & 371.75 & 20.6458228220626 & 47 \tabularnewline
18 & 360.75 & 8.65544144839919 & 19 \tabularnewline
19 & 325 & 21.1187120819429 & 47 \tabularnewline
20 & 309 & 21.5251790546173 & 49 \tabularnewline
21 & 300.5 & 9.18331820930394 & 22 \tabularnewline
22 & 265.75 & 18.9626826512847 & 42 \tabularnewline
23 & 247.75 & 23.7679756535273 & 53 \tabularnewline
24 & 242.25 & 7.58836829188814 & 18 \tabularnewline
25 & 198.75 & 21.7159695462425 & 49 \tabularnewline
26 & 179.75 & 25.0383039894212 & 57 \tabularnewline
27 & 173.5 & 11.7898261225516 & 25 \tabularnewline
28 & 129.75 & 27.5484421822118 & 62 \tabularnewline
29 & 98.5 & 26.5894716006167 & 60 \tabularnewline
30 & 93.5 & 7.32575365861197 & 17 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78045&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]566.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]573.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]560[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]555.5[/C][C]5.19615242270663[/C][C]11[/C][/ROW]
[ROW][C]5[/C][C]557.75[/C][C]15.9033539439537[/C][C]34[/C][/ROW]
[ROW][C]6[/C][C]547.75[/C][C]3.30403793359983[/C][C]7[/C][/ROW]
[ROW][C]7[/C][C]532.25[/C][C]9.8784276751583[/C][C]23[/C][/ROW]
[ROW][C]8[/C][C]535[/C][C]17.2046505340853[/C][C]38[/C][/ROW]
[ROW][C]9[/C][C]519[/C][C]2.16024689946929[/C][C]5[/C][/ROW]
[ROW][C]10[/C][C]492.25[/C][C]12.3389626792531[/C][C]27[/C][/ROW]
[ROW][C]11[/C][C]488.75[/C][C]18.6793111935817[/C][C]41[/C][/ROW]
[ROW][C]12[/C][C]477.75[/C][C]4.99165971062398[/C][C]11[/C][/ROW]
[ROW][C]13[/C][C]450.25[/C][C]16.3579746097533[/C][C]37[/C][/ROW]
[ROW][C]14[/C][C]438.25[/C][C]19.6022957839127[/C][C]45[/C][/ROW]
[ROW][C]15[/C][C]422.5[/C][C]5.25991127935317[/C][C]12[/C][/ROW]
[ROW][C]16[/C][C]394.25[/C][C]16.5201896679992[/C][C]38[/C][/ROW]
[ROW][C]17[/C][C]371.75[/C][C]20.6458228220626[/C][C]47[/C][/ROW]
[ROW][C]18[/C][C]360.75[/C][C]8.65544144839919[/C][C]19[/C][/ROW]
[ROW][C]19[/C][C]325[/C][C]21.1187120819429[/C][C]47[/C][/ROW]
[ROW][C]20[/C][C]309[/C][C]21.5251790546173[/C][C]49[/C][/ROW]
[ROW][C]21[/C][C]300.5[/C][C]9.18331820930394[/C][C]22[/C][/ROW]
[ROW][C]22[/C][C]265.75[/C][C]18.9626826512847[/C][C]42[/C][/ROW]
[ROW][C]23[/C][C]247.75[/C][C]23.7679756535273[/C][C]53[/C][/ROW]
[ROW][C]24[/C][C]242.25[/C][C]7.58836829188814[/C][C]18[/C][/ROW]
[ROW][C]25[/C][C]198.75[/C][C]21.7159695462425[/C][C]49[/C][/ROW]
[ROW][C]26[/C][C]179.75[/C][C]25.0383039894212[/C][C]57[/C][/ROW]
[ROW][C]27[/C][C]173.5[/C][C]11.7898261225516[/C][C]25[/C][/ROW]
[ROW][C]28[/C][C]129.75[/C][C]27.5484421822118[/C][C]62[/C][/ROW]
[ROW][C]29[/C][C]98.5[/C][C]26.5894716006167[/C][C]60[/C][/ROW]
[ROW][C]30[/C][C]93.5[/C][C]7.32575365861197[/C][C]17[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78045&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78045&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	566.25	1.70782512765993	4
2	573.25	12.5266382827424	26
3	560	1.41421356237310	3
4	555.5	5.19615242270663	11
5	557.75	15.9033539439537	34
6	547.75	3.30403793359983	7
7	532.25	9.8784276751583	23
8	535	17.2046505340853	38
9	519	2.16024689946929	5
10	492.25	12.3389626792531	27
11	488.75	18.6793111935817	41
12	477.75	4.99165971062398	11
13	450.25	16.3579746097533	37
14	438.25	19.6022957839127	45
15	422.5	5.25991127935317	12
16	394.25	16.5201896679992	38
17	371.75	20.6458228220626	47
18	360.75	8.65544144839919	19
19	325	21.1187120819429	47
20	309	21.5251790546173	49
21	300.5	9.18331820930394	22
22	265.75	18.9626826512847	42
23	247.75	23.7679756535273	53
24	242.25	7.58836829188814	18
25	198.75	21.7159695462425	49
26	179.75	25.0383039894212	57
27	173.5	11.7898261225516	25
28	129.75	27.5484421822118	62
29	98.5	26.5894716006167	60
30	93.5	7.32575365861197	17

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	24.3515533484539
beta	-0.0277056680474883
S.D.	0.00806211730842057
T-STAT	-3.4365250451703
p-value	0.00185862657440863

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 24.3515533484539 \tabularnewline
beta & -0.0277056680474883 \tabularnewline
S.D. & 0.00806211730842057 \tabularnewline
T-STAT & -3.4365250451703 \tabularnewline
p-value & 0.00185862657440863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78045&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]24.3515533484539[/C][/ROW]
[ROW][C]beta[/C][C]-0.0277056680474883[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00806211730842057[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.4365250451703[/C][/ROW]
[ROW][C]p-value[/C][C]0.00185862657440863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78045&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78045&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	24.3515533484539
beta	-0.0277056680474883
S.D.	0.00806211730842057
T-STAT	-3.4365250451703
p-value	0.00185862657440863

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	6.42450345077569
beta	-0.695149180323769
S.D.	0.263952931541968
T-STAT	-2.63361037993716
p-value	0.0136019657463000
Lambda	1.69514918032377

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 6.42450345077569 \tabularnewline
beta & -0.695149180323769 \tabularnewline
S.D. & 0.263952931541968 \tabularnewline
T-STAT & -2.63361037993716 \tabularnewline
p-value & 0.0136019657463000 \tabularnewline
Lambda & 1.69514918032377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78045&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.42450345077569[/C][/ROW]
[ROW][C]beta[/C][C]-0.695149180323769[/C][/ROW]
[ROW][C]S.D.[/C][C]0.263952931541968[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.63361037993716[/C][/ROW]
[ROW][C]p-value[/C][C]0.0136019657463000[/C][/ROW]
[ROW][C]Lambda[/C][C]1.69514918032377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78045&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78045&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	6.42450345077569
beta	-0.695149180323769
S.D.	0.263952931541968
T-STAT	-2.63361037993716
p-value	0.0136019657463000
Lambda	1.69514918032377

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