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Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Thu, 21 May 2009 07:26:19 -0600

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/2009/May/21/t12429125879ionij6oh54i5x9.htm/, Retrieved Tue, 07 May 2024 00:15:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40260, Retrieved Tue, 07 May 2024 00:15:41 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

133

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

-       [Standard Deviation-Mean Plot] [Kempeneers Liesbe...] [2009-05-21 13:26:19] [866e757444a60b1c09d57e14cc8533e4] [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	'Gwilym Jenkins' @ 72.249.127.135
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40260&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40260&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40260&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	'Gwilym Jenkins' @ 72.249.127.135
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	214.983333333333	19.0928750791461	57.8
2	252.375	10.1116606854750	35.5
3	265.241666666667	12.5741768813081	44.3
4	287.466666666667	17.6427339323037	64.2
5	312.75	18.2249329715690	63.1
6	328.916666666667	28.4394359147912	97
7	353.091666666667	16.4530438373923	56.1
8	387.783333333333	27.9378802258717	97
9	420.616666666667	21.6254409659016	76.5
10	454.916666666667	40.9665236578119	118.4
11	490.816666666667	42.5723946693017	142.2
12	522.116666666667	33.5124626298210	98.8
13	541.775	31.6760915001721	115.9
14	584.708333333333	27.5586798184045	94.1
15	568.45	35.7575548279343	113.8
16	561.383333333333	43.4351100824988	148.1
17	561.116666666667	62.2513356312842	154.4
18	640.2	68.5249523232895	232.1
19	646.241666666667	80.409276469971	223.3
20	653.625	48.0277027065914	161.9
21	647.825	51.0115517220453	179.2
22	609.391666666667	37.7984477394926	121.4
23	632.383333333333	49.5234349178306	155.3
24	677.1	42.7675110334936	152.7
25	632.741666666667	77.9145622791498	275.1
26	636.183333333333	77.6536814479793	225.8
27	530.9	111.942793831980	292.6
28	461.466666666667	55.6051229381763	136
29	525.583333333333	30.6400164174337	97
30	548.083333333333	44.1720980079534	147
31	558.583333333333	27.4638881354252	88
32	510.75	40.2720859788875	117
33	533.25	56.3045694900027	183
34	561.25	31.072130160761	89
35	555.5	43.0929228528305	175
36	501.416666666667	68.6883056519327	194
37	538.416666666667	26.8986594236196	88

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 214.983333333333 & 19.0928750791461 & 57.8 \tabularnewline
2 & 252.375 & 10.1116606854750 & 35.5 \tabularnewline
3 & 265.241666666667 & 12.5741768813081 & 44.3 \tabularnewline
4 & 287.466666666667 & 17.6427339323037 & 64.2 \tabularnewline
5 & 312.75 & 18.2249329715690 & 63.1 \tabularnewline
6 & 328.916666666667 & 28.4394359147912 & 97 \tabularnewline
7 & 353.091666666667 & 16.4530438373923 & 56.1 \tabularnewline
8 & 387.783333333333 & 27.9378802258717 & 97 \tabularnewline
9 & 420.616666666667 & 21.6254409659016 & 76.5 \tabularnewline
10 & 454.916666666667 & 40.9665236578119 & 118.4 \tabularnewline
11 & 490.816666666667 & 42.5723946693017 & 142.2 \tabularnewline
12 & 522.116666666667 & 33.5124626298210 & 98.8 \tabularnewline
13 & 541.775 & 31.6760915001721 & 115.9 \tabularnewline
14 & 584.708333333333 & 27.5586798184045 & 94.1 \tabularnewline
15 & 568.45 & 35.7575548279343 & 113.8 \tabularnewline
16 & 561.383333333333 & 43.4351100824988 & 148.1 \tabularnewline
17 & 561.116666666667 & 62.2513356312842 & 154.4 \tabularnewline
18 & 640.2 & 68.5249523232895 & 232.1 \tabularnewline
19 & 646.241666666667 & 80.409276469971 & 223.3 \tabularnewline
20 & 653.625 & 48.0277027065914 & 161.9 \tabularnewline
21 & 647.825 & 51.0115517220453 & 179.2 \tabularnewline
22 & 609.391666666667 & 37.7984477394926 & 121.4 \tabularnewline
23 & 632.383333333333 & 49.5234349178306 & 155.3 \tabularnewline
24 & 677.1 & 42.7675110334936 & 152.7 \tabularnewline
25 & 632.741666666667 & 77.9145622791498 & 275.1 \tabularnewline
26 & 636.183333333333 & 77.6536814479793 & 225.8 \tabularnewline
27 & 530.9 & 111.942793831980 & 292.6 \tabularnewline
28 & 461.466666666667 & 55.6051229381763 & 136 \tabularnewline
29 & 525.583333333333 & 30.6400164174337 & 97 \tabularnewline
30 & 548.083333333333 & 44.1720980079534 & 147 \tabularnewline
31 & 558.583333333333 & 27.4638881354252 & 88 \tabularnewline
32 & 510.75 & 40.2720859788875 & 117 \tabularnewline
33 & 533.25 & 56.3045694900027 & 183 \tabularnewline
34 & 561.25 & 31.072130160761 & 89 \tabularnewline
35 & 555.5 & 43.0929228528305 & 175 \tabularnewline
36 & 501.416666666667 & 68.6883056519327 & 194 \tabularnewline
37 & 538.416666666667 & 26.8986594236196 & 88 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40260&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]214.983333333333[/C][C]19.0928750791461[/C][C]57.8[/C][/ROW]
[ROW][C]2[/C][C]252.375[/C][C]10.1116606854750[/C][C]35.5[/C][/ROW]
[ROW][C]3[/C][C]265.241666666667[/C][C]12.5741768813081[/C][C]44.3[/C][/ROW]
[ROW][C]4[/C][C]287.466666666667[/C][C]17.6427339323037[/C][C]64.2[/C][/ROW]
[ROW][C]5[/C][C]312.75[/C][C]18.2249329715690[/C][C]63.1[/C][/ROW]
[ROW][C]6[/C][C]328.916666666667[/C][C]28.4394359147912[/C][C]97[/C][/ROW]
[ROW][C]7[/C][C]353.091666666667[/C][C]16.4530438373923[/C][C]56.1[/C][/ROW]
[ROW][C]8[/C][C]387.783333333333[/C][C]27.9378802258717[/C][C]97[/C][/ROW]
[ROW][C]9[/C][C]420.616666666667[/C][C]21.6254409659016[/C][C]76.5[/C][/ROW]
[ROW][C]10[/C][C]454.916666666667[/C][C]40.9665236578119[/C][C]118.4[/C][/ROW]
[ROW][C]11[/C][C]490.816666666667[/C][C]42.5723946693017[/C][C]142.2[/C][/ROW]
[ROW][C]12[/C][C]522.116666666667[/C][C]33.5124626298210[/C][C]98.8[/C][/ROW]
[ROW][C]13[/C][C]541.775[/C][C]31.6760915001721[/C][C]115.9[/C][/ROW]
[ROW][C]14[/C][C]584.708333333333[/C][C]27.5586798184045[/C][C]94.1[/C][/ROW]
[ROW][C]15[/C][C]568.45[/C][C]35.7575548279343[/C][C]113.8[/C][/ROW]
[ROW][C]16[/C][C]561.383333333333[/C][C]43.4351100824988[/C][C]148.1[/C][/ROW]
[ROW][C]17[/C][C]561.116666666667[/C][C]62.2513356312842[/C][C]154.4[/C][/ROW]
[ROW][C]18[/C][C]640.2[/C][C]68.5249523232895[/C][C]232.1[/C][/ROW]
[ROW][C]19[/C][C]646.241666666667[/C][C]80.409276469971[/C][C]223.3[/C][/ROW]
[ROW][C]20[/C][C]653.625[/C][C]48.0277027065914[/C][C]161.9[/C][/ROW]
[ROW][C]21[/C][C]647.825[/C][C]51.0115517220453[/C][C]179.2[/C][/ROW]
[ROW][C]22[/C][C]609.391666666667[/C][C]37.7984477394926[/C][C]121.4[/C][/ROW]
[ROW][C]23[/C][C]632.383333333333[/C][C]49.5234349178306[/C][C]155.3[/C][/ROW]
[ROW][C]24[/C][C]677.1[/C][C]42.7675110334936[/C][C]152.7[/C][/ROW]
[ROW][C]25[/C][C]632.741666666667[/C][C]77.9145622791498[/C][C]275.1[/C][/ROW]
[ROW][C]26[/C][C]636.183333333333[/C][C]77.6536814479793[/C][C]225.8[/C][/ROW]
[ROW][C]27[/C][C]530.9[/C][C]111.942793831980[/C][C]292.6[/C][/ROW]
[ROW][C]28[/C][C]461.466666666667[/C][C]55.6051229381763[/C][C]136[/C][/ROW]
[ROW][C]29[/C][C]525.583333333333[/C][C]30.6400164174337[/C][C]97[/C][/ROW]
[ROW][C]30[/C][C]548.083333333333[/C][C]44.1720980079534[/C][C]147[/C][/ROW]
[ROW][C]31[/C][C]558.583333333333[/C][C]27.4638881354252[/C][C]88[/C][/ROW]
[ROW][C]32[/C][C]510.75[/C][C]40.2720859788875[/C][C]117[/C][/ROW]
[ROW][C]33[/C][C]533.25[/C][C]56.3045694900027[/C][C]183[/C][/ROW]
[ROW][C]34[/C][C]561.25[/C][C]31.072130160761[/C][C]89[/C][/ROW]
[ROW][C]35[/C][C]555.5[/C][C]43.0929228528305[/C][C]175[/C][/ROW]
[ROW][C]36[/C][C]501.416666666667[/C][C]68.6883056519327[/C][C]194[/C][/ROW]
[ROW][C]37[/C][C]538.416666666667[/C][C]26.8986594236196[/C][C]88[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40260&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40260&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	214.983333333333	19.0928750791461	57.8
2	252.375	10.1116606854750	35.5
3	265.241666666667	12.5741768813081	44.3
4	287.466666666667	17.6427339323037	64.2
5	312.75	18.2249329715690	63.1
6	328.916666666667	28.4394359147912	97
7	353.091666666667	16.4530438373923	56.1
8	387.783333333333	27.9378802258717	97
9	420.616666666667	21.6254409659016	76.5
10	454.916666666667	40.9665236578119	118.4
11	490.816666666667	42.5723946693017	142.2
12	522.116666666667	33.5124626298210	98.8
13	541.775	31.6760915001721	115.9
14	584.708333333333	27.5586798184045	94.1
15	568.45	35.7575548279343	113.8
16	561.383333333333	43.4351100824988	148.1
17	561.116666666667	62.2513356312842	154.4
18	640.2	68.5249523232895	232.1
19	646.241666666667	80.409276469971	223.3
20	653.625	48.0277027065914	161.9
21	647.825	51.0115517220453	179.2
22	609.391666666667	37.7984477394926	121.4
23	632.383333333333	49.5234349178306	155.3
24	677.1	42.7675110334936	152.7
25	632.741666666667	77.9145622791498	275.1
26	636.183333333333	77.6536814479793	225.8
27	530.9	111.942793831980	292.6
28	461.466666666667	55.6051229381763	136
29	525.583333333333	30.6400164174337	97
30	548.083333333333	44.1720980079534	147
31	558.583333333333	27.4638881354252	88
32	510.75	40.2720859788875	117
33	533.25	56.3045694900027	183
34	561.25	31.072130160761	89
35	555.5	43.0929228528305	175
36	501.416666666667	68.6883056519327	194
37	538.416666666667	26.8986594236196	88

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-11.8476387906605
beta	0.106790099206510
S.D.	0.0233894254527159
T-STAT	4.56574272943971
p-value	5.91121258955702e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -11.8476387906605 \tabularnewline
beta & 0.106790099206510 \tabularnewline
S.D. & 0.0233894254527159 \tabularnewline
T-STAT & 4.56574272943971 \tabularnewline
p-value & 5.91121258955702e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40260&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.8476387906605[/C][/ROW]
[ROW][C]beta[/C][C]0.106790099206510[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0233894254527159[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.56574272943971[/C][/ROW]
[ROW][C]p-value[/C][C]5.91121258955702e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40260&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40260&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	-11.8476387906605
beta	0.106790099206510
S.D.	0.0233894254527159
T-STAT	4.56574272943971
p-value	5.91121258955702e-05

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-4.94246727240051
beta	1.38172371111577
S.D.	0.198874168275516
T-STAT	6.94772842092576
p-value	4.46287364559361e-08
Lambda	-0.381723711115773

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.94246727240051 \tabularnewline
beta & 1.38172371111577 \tabularnewline
S.D. & 0.198874168275516 \tabularnewline
T-STAT & 6.94772842092576 \tabularnewline
p-value & 4.46287364559361e-08 \tabularnewline
Lambda & -0.381723711115773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40260&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.94246727240051[/C][/ROW]
[ROW][C]beta[/C][C]1.38172371111577[/C][/ROW]
[ROW][C]S.D.[/C][C]0.198874168275516[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.94772842092576[/C][/ROW]
[ROW][C]p-value[/C][C]4.46287364559361e-08[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.381723711115773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40260&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40260&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	-4.94246727240051
beta	1.38172371111577
S.D.	0.198874168275516
T-STAT	6.94772842092576
p-value	4.46287364559361e-08
Lambda	-0.381723711115773

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