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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, 02 Aug 2011 06:38:20 -0400

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/Aug/02/t1312281667go03fm7va549kii.htm/, Retrieved Wed, 15 May 2024 01:42:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123278, Retrieved Wed, 15 May 2024 01:42:08 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Van Laer Axel

Estimated Impact

178

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

-       [Standard Deviation-Mean Plot] [Cijferreeks A, St...] [2011-08-02 10:38:20] [3bbb4c38423daa916cf90d93c467bd86] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123278&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123278&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123278&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' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	34108.5	554.836612586685	1298
2	36395.25	4099.24126109536	8515
3	32057.25	463.070459001651	982
4	35088.5	1105.83106003283	2596
5	44341.75	1878.73350513939	3925
6	45394	1381.20840812191	3293
7	49005	1473.55556393371	2947
8	57585.25	2495.30550901755	5573
9	57498.25	941.690102953195	1965
10	61178.5	1136.03682452052	2626
11	70756	2258.03616741037	4906
12	69697.25	1789.17082750642	4245
13	72140.5	1210.06790443071	2627
14	84822.25	2016.9135454947	4239
15	85883.75	2816.58331730722	6240
16	91770	3652.44402193016	8200
17	105757.75	2051.79618464733	4560
18	108220	2495.66771292441	5888
19	116152	5579.42452229618	12098
20	133565.5	1680.01874989537	3609
21	133652	2848.72989242575	6555
22	142075.25	5540.79310658682	11457
23	161302	1279.44883967017	2942
24	161704.75	2926.17741259822	6240
25	169549.25	5684.28396985935	12445
26	191063.5	2448.13786376503	5889
27	193105.75	2541.08433219626	5889
28	197680.25	5822.61094784805	12444
29	220668	3729.01443637145	8520
30	224190	2891.29763255186	5889

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 34108.5 & 554.836612586685 & 1298 \tabularnewline
2 & 36395.25 & 4099.24126109536 & 8515 \tabularnewline
3 & 32057.25 & 463.070459001651 & 982 \tabularnewline
4 & 35088.5 & 1105.83106003283 & 2596 \tabularnewline
5 & 44341.75 & 1878.73350513939 & 3925 \tabularnewline
6 & 45394 & 1381.20840812191 & 3293 \tabularnewline
7 & 49005 & 1473.55556393371 & 2947 \tabularnewline
8 & 57585.25 & 2495.30550901755 & 5573 \tabularnewline
9 & 57498.25 & 941.690102953195 & 1965 \tabularnewline
10 & 61178.5 & 1136.03682452052 & 2626 \tabularnewline
11 & 70756 & 2258.03616741037 & 4906 \tabularnewline
12 & 69697.25 & 1789.17082750642 & 4245 \tabularnewline
13 & 72140.5 & 1210.06790443071 & 2627 \tabularnewline
14 & 84822.25 & 2016.9135454947 & 4239 \tabularnewline
15 & 85883.75 & 2816.58331730722 & 6240 \tabularnewline
16 & 91770 & 3652.44402193016 & 8200 \tabularnewline
17 & 105757.75 & 2051.79618464733 & 4560 \tabularnewline
18 & 108220 & 2495.66771292441 & 5888 \tabularnewline
19 & 116152 & 5579.42452229618 & 12098 \tabularnewline
20 & 133565.5 & 1680.01874989537 & 3609 \tabularnewline
21 & 133652 & 2848.72989242575 & 6555 \tabularnewline
22 & 142075.25 & 5540.79310658682 & 11457 \tabularnewline
23 & 161302 & 1279.44883967017 & 2942 \tabularnewline
24 & 161704.75 & 2926.17741259822 & 6240 \tabularnewline
25 & 169549.25 & 5684.28396985935 & 12445 \tabularnewline
26 & 191063.5 & 2448.13786376503 & 5889 \tabularnewline
27 & 193105.75 & 2541.08433219626 & 5889 \tabularnewline
28 & 197680.25 & 5822.61094784805 & 12444 \tabularnewline
29 & 220668 & 3729.01443637145 & 8520 \tabularnewline
30 & 224190 & 2891.29763255186 & 5889 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123278&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]34108.5[/C][C]554.836612586685[/C][C]1298[/C][/ROW]
[ROW][C]2[/C][C]36395.25[/C][C]4099.24126109536[/C][C]8515[/C][/ROW]
[ROW][C]3[/C][C]32057.25[/C][C]463.070459001651[/C][C]982[/C][/ROW]
[ROW][C]4[/C][C]35088.5[/C][C]1105.83106003283[/C][C]2596[/C][/ROW]
[ROW][C]5[/C][C]44341.75[/C][C]1878.73350513939[/C][C]3925[/C][/ROW]
[ROW][C]6[/C][C]45394[/C][C]1381.20840812191[/C][C]3293[/C][/ROW]
[ROW][C]7[/C][C]49005[/C][C]1473.55556393371[/C][C]2947[/C][/ROW]
[ROW][C]8[/C][C]57585.25[/C][C]2495.30550901755[/C][C]5573[/C][/ROW]
[ROW][C]9[/C][C]57498.25[/C][C]941.690102953195[/C][C]1965[/C][/ROW]
[ROW][C]10[/C][C]61178.5[/C][C]1136.03682452052[/C][C]2626[/C][/ROW]
[ROW][C]11[/C][C]70756[/C][C]2258.03616741037[/C][C]4906[/C][/ROW]
[ROW][C]12[/C][C]69697.25[/C][C]1789.17082750642[/C][C]4245[/C][/ROW]
[ROW][C]13[/C][C]72140.5[/C][C]1210.06790443071[/C][C]2627[/C][/ROW]
[ROW][C]14[/C][C]84822.25[/C][C]2016.9135454947[/C][C]4239[/C][/ROW]
[ROW][C]15[/C][C]85883.75[/C][C]2816.58331730722[/C][C]6240[/C][/ROW]
[ROW][C]16[/C][C]91770[/C][C]3652.44402193016[/C][C]8200[/C][/ROW]
[ROW][C]17[/C][C]105757.75[/C][C]2051.79618464733[/C][C]4560[/C][/ROW]
[ROW][C]18[/C][C]108220[/C][C]2495.66771292441[/C][C]5888[/C][/ROW]
[ROW][C]19[/C][C]116152[/C][C]5579.42452229618[/C][C]12098[/C][/ROW]
[ROW][C]20[/C][C]133565.5[/C][C]1680.01874989537[/C][C]3609[/C][/ROW]
[ROW][C]21[/C][C]133652[/C][C]2848.72989242575[/C][C]6555[/C][/ROW]
[ROW][C]22[/C][C]142075.25[/C][C]5540.79310658682[/C][C]11457[/C][/ROW]
[ROW][C]23[/C][C]161302[/C][C]1279.44883967017[/C][C]2942[/C][/ROW]
[ROW][C]24[/C][C]161704.75[/C][C]2926.17741259822[/C][C]6240[/C][/ROW]
[ROW][C]25[/C][C]169549.25[/C][C]5684.28396985935[/C][C]12445[/C][/ROW]
[ROW][C]26[/C][C]191063.5[/C][C]2448.13786376503[/C][C]5889[/C][/ROW]
[ROW][C]27[/C][C]193105.75[/C][C]2541.08433219626[/C][C]5889[/C][/ROW]
[ROW][C]28[/C][C]197680.25[/C][C]5822.61094784805[/C][C]12444[/C][/ROW]
[ROW][C]29[/C][C]220668[/C][C]3729.01443637145[/C][C]8520[/C][/ROW]
[ROW][C]30[/C][C]224190[/C][C]2891.29763255186[/C][C]5889[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123278&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123278&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	34108.5	554.836612586685	1298
2	36395.25	4099.24126109536	8515
3	32057.25	463.070459001651	982
4	35088.5	1105.83106003283	2596
5	44341.75	1878.73350513939	3925
6	45394	1381.20840812191	3293
7	49005	1473.55556393371	2947
8	57585.25	2495.30550901755	5573
9	57498.25	941.690102953195	1965
10	61178.5	1136.03682452052	2626
11	70756	2258.03616741037	4906
12	69697.25	1789.17082750642	4245
13	72140.5	1210.06790443071	2627
14	84822.25	2016.9135454947	4239
15	85883.75	2816.58331730722	6240
16	91770	3652.44402193016	8200
17	105757.75	2051.79618464733	4560
18	108220	2495.66771292441	5888
19	116152	5579.42452229618	12098
20	133565.5	1680.01874989537	3609
21	133652	2848.72989242575	6555
22	142075.25	5540.79310658682	11457
23	161302	1279.44883967017	2942
24	161704.75	2926.17741259822	6240
25	169549.25	5684.28396985935	12445
26	191063.5	2448.13786376503	5889
27	193105.75	2541.08433219626	5889
28	197680.25	5822.61094784805	12444
29	220668	3729.01443637145	8520
30	224190	2891.29763255186	5889

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1136.9261049947
beta	0.0133954683594435
S.D.	0.00403428710058345
T-STAT	3.32040532204716
p-value	0.00250614894461325

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1136.9261049947 \tabularnewline
beta & 0.0133954683594435 \tabularnewline
S.D. & 0.00403428710058345 \tabularnewline
T-STAT & 3.32040532204716 \tabularnewline
p-value & 0.00250614894461325 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123278&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1136.9261049947[/C][/ROW]
[ROW][C]beta[/C][C]0.0133954683594435[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00403428710058345[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.32040532204716[/C][/ROW]
[ROW][C]p-value[/C][C]0.00250614894461325[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123278&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123278&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	1136.9261049947
beta	0.0133954683594435
S.D.	0.00403428710058345
T-STAT	3.32040532204716
p-value	0.00250614894461325

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.0854586358697535
beta	0.664861691990468
S.D.	0.152663510023095
T-STAT	4.35507929753409
p-value	0.000161135451335229
Lambda	0.335138308009532

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.0854586358697535 \tabularnewline
beta & 0.664861691990468 \tabularnewline
S.D. & 0.152663510023095 \tabularnewline
T-STAT & 4.35507929753409 \tabularnewline
p-value & 0.000161135451335229 \tabularnewline
Lambda & 0.335138308009532 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123278&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0854586358697535[/C][/ROW]
[ROW][C]beta[/C][C]0.664861691990468[/C][/ROW]
[ROW][C]S.D.[/C][C]0.152663510023095[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.35507929753409[/C][/ROW]
[ROW][C]p-value[/C][C]0.000161135451335229[/C][/ROW]
[ROW][C]Lambda[/C][C]0.335138308009532[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123278&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123278&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	0.0854586358697535
beta	0.664861691990468
S.D.	0.152663510023095
T-STAT	4.35507929753409
p-value	0.000161135451335229
Lambda	0.335138308009532

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