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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, 20 Dec 2012 12:58:59 -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/2012/Dec/20/t1356026356vo9f34c6k9z3jw1.htm/, Retrieved Fri, 26 Apr 2024 09:19:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=202969, Retrieved Fri, 26 Apr 2024 09:19:44 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-     [Standard Deviation-Mean Plot] [sdmp] [2011-12-21 13:30:50] [26f9350dcf28f408b6e37deed68b781e]
- R  D    [Standard Deviation-Mean Plot] [lambda bepalen] [2012-12-20 17:58:59] [3d604e7f846c7f85ca2541c807d08ff8] [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	3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202969&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]3 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=202969&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202969&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	56.8333333333333	8.03213243884534	27
2	95.6666666666667	7.73813852801744	25
3	92.3333333333333	6.19872909750397	17
4	82.5	5.66488385502378	20
5	102.333333333333	6.52733181369391	22
6	125.75	8.97597804242979	28
7	193.333333333333	48.1953097177296	154
8	374.75	34.5704156232412	96
9	356	16.8846352963548	59
10	348.666666666667	55.4343728833447	145
11	437.583333333333	24.1527650716447	92
12	424.583333333333	10.4050541332158	35
13	391.166666666667	24.54618405201	78
14	348.083333333333	17.1488580766573	55
15	365.666666666667	18.23749052381	57
16	349.666666666667	14.760717729121	45
17	322.083333333333	8.8570293946091	25
18	281.666666666667	19.4437806524504	58
19	276.666666666667	17.2591653297252	58
20	253.583333333333	13.1111218113293	45
21	306.666666666667	30.0403768688784	91
22	318.25	10.9554884543195	37
23	290.666666666667	4.49915817041636	16
24	300.083333333333	7.89082704886829	25
25	292	15.015143870591	44
26	264.666666666667	15.5641390459744	40
27	264.833333333333	18.0546309009544	51
28	301.25	8.54001277410158	23
29	304.5	12.0943262430252	38
30	330	12.3361995031622	39
31	322.083333333333	15.1505075422535	41
32	329	8.75941052396066	26
33	363.5	37.7924956475849	111
34	484.166666666667	14.6028224752075	45
35	510	27.2363393615622	88
36	600	30.4421955963638	83
37	702.916666666667	40.9288925140205	121
38	934.416666666667	94.5106615759045	287
39	1121.41666666667	111.127656596394	329

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 56.8333333333333 & 8.03213243884534 & 27 \tabularnewline
2 & 95.6666666666667 & 7.73813852801744 & 25 \tabularnewline
3 & 92.3333333333333 & 6.19872909750397 & 17 \tabularnewline
4 & 82.5 & 5.66488385502378 & 20 \tabularnewline
5 & 102.333333333333 & 6.52733181369391 & 22 \tabularnewline
6 & 125.75 & 8.97597804242979 & 28 \tabularnewline
7 & 193.333333333333 & 48.1953097177296 & 154 \tabularnewline
8 & 374.75 & 34.5704156232412 & 96 \tabularnewline
9 & 356 & 16.8846352963548 & 59 \tabularnewline
10 & 348.666666666667 & 55.4343728833447 & 145 \tabularnewline
11 & 437.583333333333 & 24.1527650716447 & 92 \tabularnewline
12 & 424.583333333333 & 10.4050541332158 & 35 \tabularnewline
13 & 391.166666666667 & 24.54618405201 & 78 \tabularnewline
14 & 348.083333333333 & 17.1488580766573 & 55 \tabularnewline
15 & 365.666666666667 & 18.23749052381 & 57 \tabularnewline
16 & 349.666666666667 & 14.760717729121 & 45 \tabularnewline
17 & 322.083333333333 & 8.8570293946091 & 25 \tabularnewline
18 & 281.666666666667 & 19.4437806524504 & 58 \tabularnewline
19 & 276.666666666667 & 17.2591653297252 & 58 \tabularnewline
20 & 253.583333333333 & 13.1111218113293 & 45 \tabularnewline
21 & 306.666666666667 & 30.0403768688784 & 91 \tabularnewline
22 & 318.25 & 10.9554884543195 & 37 \tabularnewline
23 & 290.666666666667 & 4.49915817041636 & 16 \tabularnewline
24 & 300.083333333333 & 7.89082704886829 & 25 \tabularnewline
25 & 292 & 15.015143870591 & 44 \tabularnewline
26 & 264.666666666667 & 15.5641390459744 & 40 \tabularnewline
27 & 264.833333333333 & 18.0546309009544 & 51 \tabularnewline
28 & 301.25 & 8.54001277410158 & 23 \tabularnewline
29 & 304.5 & 12.0943262430252 & 38 \tabularnewline
30 & 330 & 12.3361995031622 & 39 \tabularnewline
31 & 322.083333333333 & 15.1505075422535 & 41 \tabularnewline
32 & 329 & 8.75941052396066 & 26 \tabularnewline
33 & 363.5 & 37.7924956475849 & 111 \tabularnewline
34 & 484.166666666667 & 14.6028224752075 & 45 \tabularnewline
35 & 510 & 27.2363393615622 & 88 \tabularnewline
36 & 600 & 30.4421955963638 & 83 \tabularnewline
37 & 702.916666666667 & 40.9288925140205 & 121 \tabularnewline
38 & 934.416666666667 & 94.5106615759045 & 287 \tabularnewline
39 & 1121.41666666667 & 111.127656596394 & 329 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202969&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]56.8333333333333[/C][C]8.03213243884534[/C][C]27[/C][/ROW]
[ROW][C]2[/C][C]95.6666666666667[/C][C]7.73813852801744[/C][C]25[/C][/ROW]
[ROW][C]3[/C][C]92.3333333333333[/C][C]6.19872909750397[/C][C]17[/C][/ROW]
[ROW][C]4[/C][C]82.5[/C][C]5.66488385502378[/C][C]20[/C][/ROW]
[ROW][C]5[/C][C]102.333333333333[/C][C]6.52733181369391[/C][C]22[/C][/ROW]
[ROW][C]6[/C][C]125.75[/C][C]8.97597804242979[/C][C]28[/C][/ROW]
[ROW][C]7[/C][C]193.333333333333[/C][C]48.1953097177296[/C][C]154[/C][/ROW]
[ROW][C]8[/C][C]374.75[/C][C]34.5704156232412[/C][C]96[/C][/ROW]
[ROW][C]9[/C][C]356[/C][C]16.8846352963548[/C][C]59[/C][/ROW]
[ROW][C]10[/C][C]348.666666666667[/C][C]55.4343728833447[/C][C]145[/C][/ROW]
[ROW][C]11[/C][C]437.583333333333[/C][C]24.1527650716447[/C][C]92[/C][/ROW]
[ROW][C]12[/C][C]424.583333333333[/C][C]10.4050541332158[/C][C]35[/C][/ROW]
[ROW][C]13[/C][C]391.166666666667[/C][C]24.54618405201[/C][C]78[/C][/ROW]
[ROW][C]14[/C][C]348.083333333333[/C][C]17.1488580766573[/C][C]55[/C][/ROW]
[ROW][C]15[/C][C]365.666666666667[/C][C]18.23749052381[/C][C]57[/C][/ROW]
[ROW][C]16[/C][C]349.666666666667[/C][C]14.760717729121[/C][C]45[/C][/ROW]
[ROW][C]17[/C][C]322.083333333333[/C][C]8.8570293946091[/C][C]25[/C][/ROW]
[ROW][C]18[/C][C]281.666666666667[/C][C]19.4437806524504[/C][C]58[/C][/ROW]
[ROW][C]19[/C][C]276.666666666667[/C][C]17.2591653297252[/C][C]58[/C][/ROW]
[ROW][C]20[/C][C]253.583333333333[/C][C]13.1111218113293[/C][C]45[/C][/ROW]
[ROW][C]21[/C][C]306.666666666667[/C][C]30.0403768688784[/C][C]91[/C][/ROW]
[ROW][C]22[/C][C]318.25[/C][C]10.9554884543195[/C][C]37[/C][/ROW]
[ROW][C]23[/C][C]290.666666666667[/C][C]4.49915817041636[/C][C]16[/C][/ROW]
[ROW][C]24[/C][C]300.083333333333[/C][C]7.89082704886829[/C][C]25[/C][/ROW]
[ROW][C]25[/C][C]292[/C][C]15.015143870591[/C][C]44[/C][/ROW]
[ROW][C]26[/C][C]264.666666666667[/C][C]15.5641390459744[/C][C]40[/C][/ROW]
[ROW][C]27[/C][C]264.833333333333[/C][C]18.0546309009544[/C][C]51[/C][/ROW]
[ROW][C]28[/C][C]301.25[/C][C]8.54001277410158[/C][C]23[/C][/ROW]
[ROW][C]29[/C][C]304.5[/C][C]12.0943262430252[/C][C]38[/C][/ROW]
[ROW][C]30[/C][C]330[/C][C]12.3361995031622[/C][C]39[/C][/ROW]
[ROW][C]31[/C][C]322.083333333333[/C][C]15.1505075422535[/C][C]41[/C][/ROW]
[ROW][C]32[/C][C]329[/C][C]8.75941052396066[/C][C]26[/C][/ROW]
[ROW][C]33[/C][C]363.5[/C][C]37.7924956475849[/C][C]111[/C][/ROW]
[ROW][C]34[/C][C]484.166666666667[/C][C]14.6028224752075[/C][C]45[/C][/ROW]
[ROW][C]35[/C][C]510[/C][C]27.2363393615622[/C][C]88[/C][/ROW]
[ROW][C]36[/C][C]600[/C][C]30.4421955963638[/C][C]83[/C][/ROW]
[ROW][C]37[/C][C]702.916666666667[/C][C]40.9288925140205[/C][C]121[/C][/ROW]
[ROW][C]38[/C][C]934.416666666667[/C][C]94.5106615759045[/C][C]287[/C][/ROW]
[ROW][C]39[/C][C]1121.41666666667[/C][C]111.127656596394[/C][C]329[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202969&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202969&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	56.8333333333333	8.03213243884534	27
2	95.6666666666667	7.73813852801744	25
3	92.3333333333333	6.19872909750397	17
4	82.5	5.66488385502378	20
5	102.333333333333	6.52733181369391	22
6	125.75	8.97597804242979	28
7	193.333333333333	48.1953097177296	154
8	374.75	34.5704156232412	96
9	356	16.8846352963548	59
10	348.666666666667	55.4343728833447	145
11	437.583333333333	24.1527650716447	92
12	424.583333333333	10.4050541332158	35
13	391.166666666667	24.54618405201	78
14	348.083333333333	17.1488580766573	55
15	365.666666666667	18.23749052381	57
16	349.666666666667	14.760717729121	45
17	322.083333333333	8.8570293946091	25
18	281.666666666667	19.4437806524504	58
19	276.666666666667	17.2591653297252	58
20	253.583333333333	13.1111218113293	45
21	306.666666666667	30.0403768688784	91
22	318.25	10.9554884543195	37
23	290.666666666667	4.49915817041636	16
24	300.083333333333	7.89082704886829	25
25	292	15.015143870591	44
26	264.666666666667	15.5641390459744	40
27	264.833333333333	18.0546309009544	51
28	301.25	8.54001277410158	23
29	304.5	12.0943262430252	38
30	330	12.3361995031622	39
31	322.083333333333	15.1505075422535	41
32	329	8.75941052396066	26
33	363.5	37.7924956475849	111
34	484.166666666667	14.6028224752075	45
35	510	27.2363393615622	88
36	600	30.4421955963638	83
37	702.916666666667	40.9288925140205	121
38	934.416666666667	94.5106615759045	287
39	1121.41666666667	111.127656596394	329

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-7.87351958652492
beta	0.0872842020651113
S.D.	0.0102962449665075
T-STAT	8.47728490814243
p-value	3.37965543220944e-10

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -7.87351958652492 \tabularnewline
beta & 0.0872842020651113 \tabularnewline
S.D. & 0.0102962449665075 \tabularnewline
T-STAT & 8.47728490814243 \tabularnewline
p-value & 3.37965543220944e-10 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202969&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.87351958652492[/C][/ROW]
[ROW][C]beta[/C][C]0.0872842020651113[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0102962449665075[/C][/ROW]
[ROW][C]T-STAT[/C][C]8.47728490814243[/C][/ROW]
[ROW][C]p-value[/C][C]3.37965543220944e-10[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202969&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202969&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	-7.87351958652492
beta	0.0872842020651113
S.D.	0.0102962449665075
T-STAT	8.47728490814243
p-value	3.37965543220944e-10

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.88660545665165
beta	0.825349173616136
S.D.	0.14428633714742
T-STAT	5.72021710394422
p-value	1.50267745907885e-06
Lambda	0.174650826383864

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.88660545665165 \tabularnewline
beta & 0.825349173616136 \tabularnewline
S.D. & 0.14428633714742 \tabularnewline
T-STAT & 5.72021710394422 \tabularnewline
p-value & 1.50267745907885e-06 \tabularnewline
Lambda & 0.174650826383864 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202969&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.88660545665165[/C][/ROW]
[ROW][C]beta[/C][C]0.825349173616136[/C][/ROW]
[ROW][C]S.D.[/C][C]0.14428633714742[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.72021710394422[/C][/ROW]
[ROW][C]p-value[/C][C]1.50267745907885e-06[/C][/ROW]
[ROW][C]Lambda[/C][C]0.174650826383864[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202969&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202969&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	-1.88660545665165
beta	0.825349173616136
S.D.	0.14428633714742
T-STAT	5.72021710394422
p-value	1.50267745907885e-06
Lambda	0.174650826383864

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