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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

Tue, 13 Dec 2011 10:41:55 -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/13/t13237909536tzrvibmvpbge87.htm/, Retrieved Fri, 03 May 2024 00:53:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154436, Retrieved Fri, 03 May 2024 00:53:34 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

172

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

-       [Standard Deviation-Mean Plot] [] [2011-12-13 15:41:55] [d76b387543b13b5e3afd8ff9e5fdc89f] [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=154436&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=154436&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154436&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	228.166666666667	108.86341177936	336
2	272.583333333333	135.948826156511	404
3	303.333333333333	147.609640811859	431
4	340.666666666667	163.104168239103	441
5	388.833333333333	164.4140191619	463
6	405.833333333333	157.021037000161	436
7	506.833333333333	244.728358996193	737
8	606.666666666667	285.237806155857	854
9	684.583333333333	290.238603513897	842
10	779.75	323.817604384152	934
11	823.666666666667	328.212052665882	977
12	829.25	340.758812331858	1014
13	936.916666666667	340.638827214486	1076
14	1081	413.800127422099	1291
15	1197	430.174805906115	1309
16	1282.33333333333	440.920181053902	1271
17	1351.91666666667	417.880682912617	1251
18	1410.75	435.61244764751	1340
19	1624.16666666667	463.468510911001	1374
20	1835	554.51567729293	1721
21	2020.83333333333	618.383792762646	1814
22	2111	663.71146523991	2326
23	2246.83333333333	680.263028452075	2107
24	2379.16666666667	714.224287834944	2328
25	2523.75	743.009742380763	2368
26	2679.58333333333	721.49169444389	2416
27	2867.58333333333	766.555988387889	2498
28	2917.75	822.147866041361	2609
29	3069.75	866.856507471366	3013
30	2641.25	722.523623394859	2527
31	2651.5	872.318175896846	2994

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 228.166666666667 & 108.86341177936 & 336 \tabularnewline
2 & 272.583333333333 & 135.948826156511 & 404 \tabularnewline
3 & 303.333333333333 & 147.609640811859 & 431 \tabularnewline
4 & 340.666666666667 & 163.104168239103 & 441 \tabularnewline
5 & 388.833333333333 & 164.4140191619 & 463 \tabularnewline
6 & 405.833333333333 & 157.021037000161 & 436 \tabularnewline
7 & 506.833333333333 & 244.728358996193 & 737 \tabularnewline
8 & 606.666666666667 & 285.237806155857 & 854 \tabularnewline
9 & 684.583333333333 & 290.238603513897 & 842 \tabularnewline
10 & 779.75 & 323.817604384152 & 934 \tabularnewline
11 & 823.666666666667 & 328.212052665882 & 977 \tabularnewline
12 & 829.25 & 340.758812331858 & 1014 \tabularnewline
13 & 936.916666666667 & 340.638827214486 & 1076 \tabularnewline
14 & 1081 & 413.800127422099 & 1291 \tabularnewline
15 & 1197 & 430.174805906115 & 1309 \tabularnewline
16 & 1282.33333333333 & 440.920181053902 & 1271 \tabularnewline
17 & 1351.91666666667 & 417.880682912617 & 1251 \tabularnewline
18 & 1410.75 & 435.61244764751 & 1340 \tabularnewline
19 & 1624.16666666667 & 463.468510911001 & 1374 \tabularnewline
20 & 1835 & 554.51567729293 & 1721 \tabularnewline
21 & 2020.83333333333 & 618.383792762646 & 1814 \tabularnewline
22 & 2111 & 663.71146523991 & 2326 \tabularnewline
23 & 2246.83333333333 & 680.263028452075 & 2107 \tabularnewline
24 & 2379.16666666667 & 714.224287834944 & 2328 \tabularnewline
25 & 2523.75 & 743.009742380763 & 2368 \tabularnewline
26 & 2679.58333333333 & 721.49169444389 & 2416 \tabularnewline
27 & 2867.58333333333 & 766.555988387889 & 2498 \tabularnewline
28 & 2917.75 & 822.147866041361 & 2609 \tabularnewline
29 & 3069.75 & 866.856507471366 & 3013 \tabularnewline
30 & 2641.25 & 722.523623394859 & 2527 \tabularnewline
31 & 2651.5 & 872.318175896846 & 2994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154436&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]228.166666666667[/C][C]108.86341177936[/C][C]336[/C][/ROW]
[ROW][C]2[/C][C]272.583333333333[/C][C]135.948826156511[/C][C]404[/C][/ROW]
[ROW][C]3[/C][C]303.333333333333[/C][C]147.609640811859[/C][C]431[/C][/ROW]
[ROW][C]4[/C][C]340.666666666667[/C][C]163.104168239103[/C][C]441[/C][/ROW]
[ROW][C]5[/C][C]388.833333333333[/C][C]164.4140191619[/C][C]463[/C][/ROW]
[ROW][C]6[/C][C]405.833333333333[/C][C]157.021037000161[/C][C]436[/C][/ROW]
[ROW][C]7[/C][C]506.833333333333[/C][C]244.728358996193[/C][C]737[/C][/ROW]
[ROW][C]8[/C][C]606.666666666667[/C][C]285.237806155857[/C][C]854[/C][/ROW]
[ROW][C]9[/C][C]684.583333333333[/C][C]290.238603513897[/C][C]842[/C][/ROW]
[ROW][C]10[/C][C]779.75[/C][C]323.817604384152[/C][C]934[/C][/ROW]
[ROW][C]11[/C][C]823.666666666667[/C][C]328.212052665882[/C][C]977[/C][/ROW]
[ROW][C]12[/C][C]829.25[/C][C]340.758812331858[/C][C]1014[/C][/ROW]
[ROW][C]13[/C][C]936.916666666667[/C][C]340.638827214486[/C][C]1076[/C][/ROW]
[ROW][C]14[/C][C]1081[/C][C]413.800127422099[/C][C]1291[/C][/ROW]
[ROW][C]15[/C][C]1197[/C][C]430.174805906115[/C][C]1309[/C][/ROW]
[ROW][C]16[/C][C]1282.33333333333[/C][C]440.920181053902[/C][C]1271[/C][/ROW]
[ROW][C]17[/C][C]1351.91666666667[/C][C]417.880682912617[/C][C]1251[/C][/ROW]
[ROW][C]18[/C][C]1410.75[/C][C]435.61244764751[/C][C]1340[/C][/ROW]
[ROW][C]19[/C][C]1624.16666666667[/C][C]463.468510911001[/C][C]1374[/C][/ROW]
[ROW][C]20[/C][C]1835[/C][C]554.51567729293[/C][C]1721[/C][/ROW]
[ROW][C]21[/C][C]2020.83333333333[/C][C]618.383792762646[/C][C]1814[/C][/ROW]
[ROW][C]22[/C][C]2111[/C][C]663.71146523991[/C][C]2326[/C][/ROW]
[ROW][C]23[/C][C]2246.83333333333[/C][C]680.263028452075[/C][C]2107[/C][/ROW]
[ROW][C]24[/C][C]2379.16666666667[/C][C]714.224287834944[/C][C]2328[/C][/ROW]
[ROW][C]25[/C][C]2523.75[/C][C]743.009742380763[/C][C]2368[/C][/ROW]
[ROW][C]26[/C][C]2679.58333333333[/C][C]721.49169444389[/C][C]2416[/C][/ROW]
[ROW][C]27[/C][C]2867.58333333333[/C][C]766.555988387889[/C][C]2498[/C][/ROW]
[ROW][C]28[/C][C]2917.75[/C][C]822.147866041361[/C][C]2609[/C][/ROW]
[ROW][C]29[/C][C]3069.75[/C][C]866.856507471366[/C][C]3013[/C][/ROW]
[ROW][C]30[/C][C]2641.25[/C][C]722.523623394859[/C][C]2527[/C][/ROW]
[ROW][C]31[/C][C]2651.5[/C][C]872.318175896846[/C][C]2994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154436&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154436&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	228.166666666667	108.86341177936	336
2	272.583333333333	135.948826156511	404
3	303.333333333333	147.609640811859	431
4	340.666666666667	163.104168239103	441
5	388.833333333333	164.4140191619	463
6	405.833333333333	157.021037000161	436
7	506.833333333333	244.728358996193	737
8	606.666666666667	285.237806155857	854
9	684.583333333333	290.238603513897	842
10	779.75	323.817604384152	934
11	823.666666666667	328.212052665882	977
12	829.25	340.758812331858	1014
13	936.916666666667	340.638827214486	1076
14	1081	413.800127422099	1291
15	1197	430.174805906115	1309
16	1282.33333333333	440.920181053902	1271
17	1351.91666666667	417.880682912617	1251
18	1410.75	435.61244764751	1340
19	1624.16666666667	463.468510911001	1374
20	1835	554.51567729293	1721
21	2020.83333333333	618.383792762646	1814
22	2111	663.71146523991	2326
23	2246.83333333333	680.263028452075	2107
24	2379.16666666667	714.224287834944	2328
25	2523.75	743.009742380763	2368
26	2679.58333333333	721.49169444389	2416
27	2867.58333333333	766.555988387889	2498
28	2917.75	822.147866041361	2609
29	3069.75	866.856507471366	3013
30	2641.25	722.523623394859	2527
31	2651.5	872.318175896846	2994

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	95.14897252333
beta	0.253983957723705
S.D.	0.00705856718156638
T-STAT	35.9823674111922
p-value	1.28875564730472e-25

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 95.14897252333 \tabularnewline
beta & 0.253983957723705 \tabularnewline
S.D. & 0.00705856718156638 \tabularnewline
T-STAT & 35.9823674111922 \tabularnewline
p-value & 1.28875564730472e-25 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154436&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]95.14897252333[/C][/ROW]
[ROW][C]beta[/C][C]0.253983957723705[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00705856718156638[/C][/ROW]
[ROW][C]T-STAT[/C][C]35.9823674111922[/C][/ROW]
[ROW][C]p-value[/C][C]1.28875564730472e-25[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154436&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154436&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	95.14897252333
beta	0.253983957723705
S.D.	0.00705856718156638
T-STAT	35.9823674111922
p-value	1.28875564730472e-25

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.649159289620702
beta	0.759728802400252
S.D.	0.0166051244745235
T-STAT	45.7526713254015
p-value	1.36723704309177e-28
Lambda	0.240271197599748

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.649159289620702 \tabularnewline
beta & 0.759728802400252 \tabularnewline
S.D. & 0.0166051244745235 \tabularnewline
T-STAT & 45.7526713254015 \tabularnewline
p-value & 1.36723704309177e-28 \tabularnewline
Lambda & 0.240271197599748 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154436&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.649159289620702[/C][/ROW]
[ROW][C]beta[/C][C]0.759728802400252[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0166051244745235[/C][/ROW]
[ROW][C]T-STAT[/C][C]45.7526713254015[/C][/ROW]
[ROW][C]p-value[/C][C]1.36723704309177e-28[/C][/ROW]
[ROW][C]Lambda[/C][C]0.240271197599748[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154436&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154436&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	0.649159289620702
beta	0.759728802400252
S.D.	0.0166051244745235
T-STAT	45.7526713254015
p-value	1.36723704309177e-28
Lambda	0.240271197599748

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code