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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

Fri, 05 Aug 2011 09:14:39 -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/05/t13125501393ekrwh37v3wfyvy.htm/, Retrieved Mon, 13 May 2024 20:43:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123417, Retrieved Mon, 13 May 2024 20:43:20 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Van Vlaenderen Lynn

Estimated Impact

176

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

-       [Standard Deviation-Mean Plot] [tijdreeksA- stap27] [2011-08-05 13:14:39] [d08a5fa9e4c562ec79e796d78c067f4f] [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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123417&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123417&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	'Gertrude Mary Cox' @ cox.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	447	17.5689119374726	41
2	519.25	129.211390106807	268
3	382.25	14.6144905259586	31
4	398	36.2583323756991	72
5	601.75	113.764010126226	258
6	532.25	52.1432322230476	113
7	503.75	93.6175731366713	228
8	700	151.523375534382	341
9	710.5	117.16228061966	269
10	741.25	123.454107532583	290
11	891.25	105.724090600645	258
12	922.25	130.326193325312	300
13	922.25	94.6057609239522	217
14	1043.75	106.258725131947	258
15	1147	143.487513974794	341
16	1041	172.253688881641	413
17	976.5	128.076799876741	310
18	1108.25	142.31976906483	341
19	1015.25	156.218596844294	382
20	989.5	114.596393195132	279
21	1105.5	147.947062604613	351
22	1098	152.663027613106	372
23	1087.5	108.555669282324	248
24	1263.25	161.487615624233	351
25	1191	196.057814602394	476
26	1090.5	73.7947604282761	155
27	1353.5	182.994535437537	403
28	1296.75	210.083118471396	506
29	1170	76.030695555589	165
30	1377	149.032434948459	320

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 447 & 17.5689119374726 & 41 \tabularnewline
2 & 519.25 & 129.211390106807 & 268 \tabularnewline
3 & 382.25 & 14.6144905259586 & 31 \tabularnewline
4 & 398 & 36.2583323756991 & 72 \tabularnewline
5 & 601.75 & 113.764010126226 & 258 \tabularnewline
6 & 532.25 & 52.1432322230476 & 113 \tabularnewline
7 & 503.75 & 93.6175731366713 & 228 \tabularnewline
8 & 700 & 151.523375534382 & 341 \tabularnewline
9 & 710.5 & 117.16228061966 & 269 \tabularnewline
10 & 741.25 & 123.454107532583 & 290 \tabularnewline
11 & 891.25 & 105.724090600645 & 258 \tabularnewline
12 & 922.25 & 130.326193325312 & 300 \tabularnewline
13 & 922.25 & 94.6057609239522 & 217 \tabularnewline
14 & 1043.75 & 106.258725131947 & 258 \tabularnewline
15 & 1147 & 143.487513974794 & 341 \tabularnewline
16 & 1041 & 172.253688881641 & 413 \tabularnewline
17 & 976.5 & 128.076799876741 & 310 \tabularnewline
18 & 1108.25 & 142.31976906483 & 341 \tabularnewline
19 & 1015.25 & 156.218596844294 & 382 \tabularnewline
20 & 989.5 & 114.596393195132 & 279 \tabularnewline
21 & 1105.5 & 147.947062604613 & 351 \tabularnewline
22 & 1098 & 152.663027613106 & 372 \tabularnewline
23 & 1087.5 & 108.555669282324 & 248 \tabularnewline
24 & 1263.25 & 161.487615624233 & 351 \tabularnewline
25 & 1191 & 196.057814602394 & 476 \tabularnewline
26 & 1090.5 & 73.7947604282761 & 155 \tabularnewline
27 & 1353.5 & 182.994535437537 & 403 \tabularnewline
28 & 1296.75 & 210.083118471396 & 506 \tabularnewline
29 & 1170 & 76.030695555589 & 165 \tabularnewline
30 & 1377 & 149.032434948459 & 320 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123417&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]447[/C][C]17.5689119374726[/C][C]41[/C][/ROW]
[ROW][C]2[/C][C]519.25[/C][C]129.211390106807[/C][C]268[/C][/ROW]
[ROW][C]3[/C][C]382.25[/C][C]14.6144905259586[/C][C]31[/C][/ROW]
[ROW][C]4[/C][C]398[/C][C]36.2583323756991[/C][C]72[/C][/ROW]
[ROW][C]5[/C][C]601.75[/C][C]113.764010126226[/C][C]258[/C][/ROW]
[ROW][C]6[/C][C]532.25[/C][C]52.1432322230476[/C][C]113[/C][/ROW]
[ROW][C]7[/C][C]503.75[/C][C]93.6175731366713[/C][C]228[/C][/ROW]
[ROW][C]8[/C][C]700[/C][C]151.523375534382[/C][C]341[/C][/ROW]
[ROW][C]9[/C][C]710.5[/C][C]117.16228061966[/C][C]269[/C][/ROW]
[ROW][C]10[/C][C]741.25[/C][C]123.454107532583[/C][C]290[/C][/ROW]
[ROW][C]11[/C][C]891.25[/C][C]105.724090600645[/C][C]258[/C][/ROW]
[ROW][C]12[/C][C]922.25[/C][C]130.326193325312[/C][C]300[/C][/ROW]
[ROW][C]13[/C][C]922.25[/C][C]94.6057609239522[/C][C]217[/C][/ROW]
[ROW][C]14[/C][C]1043.75[/C][C]106.258725131947[/C][C]258[/C][/ROW]
[ROW][C]15[/C][C]1147[/C][C]143.487513974794[/C][C]341[/C][/ROW]
[ROW][C]16[/C][C]1041[/C][C]172.253688881641[/C][C]413[/C][/ROW]
[ROW][C]17[/C][C]976.5[/C][C]128.076799876741[/C][C]310[/C][/ROW]
[ROW][C]18[/C][C]1108.25[/C][C]142.31976906483[/C][C]341[/C][/ROW]
[ROW][C]19[/C][C]1015.25[/C][C]156.218596844294[/C][C]382[/C][/ROW]
[ROW][C]20[/C][C]989.5[/C][C]114.596393195132[/C][C]279[/C][/ROW]
[ROW][C]21[/C][C]1105.5[/C][C]147.947062604613[/C][C]351[/C][/ROW]
[ROW][C]22[/C][C]1098[/C][C]152.663027613106[/C][C]372[/C][/ROW]
[ROW][C]23[/C][C]1087.5[/C][C]108.555669282324[/C][C]248[/C][/ROW]
[ROW][C]24[/C][C]1263.25[/C][C]161.487615624233[/C][C]351[/C][/ROW]
[ROW][C]25[/C][C]1191[/C][C]196.057814602394[/C][C]476[/C][/ROW]
[ROW][C]26[/C][C]1090.5[/C][C]73.7947604282761[/C][C]155[/C][/ROW]
[ROW][C]27[/C][C]1353.5[/C][C]182.994535437537[/C][C]403[/C][/ROW]
[ROW][C]28[/C][C]1296.75[/C][C]210.083118471396[/C][C]506[/C][/ROW]
[ROW][C]29[/C][C]1170[/C][C]76.030695555589[/C][C]165[/C][/ROW]
[ROW][C]30[/C][C]1377[/C][C]149.032434948459[/C][C]320[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123417&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	447	17.5689119374726	41
2	519.25	129.211390106807	268
3	382.25	14.6144905259586	31
4	398	36.2583323756991	72
5	601.75	113.764010126226	258
6	532.25	52.1432322230476	113
7	503.75	93.6175731366713	228
8	700	151.523375534382	341
9	710.5	117.16228061966	269
10	741.25	123.454107532583	290
11	891.25	105.724090600645	258
12	922.25	130.326193325312	300
13	922.25	94.6057609239522	217
14	1043.75	106.258725131947	258
15	1147	143.487513974794	341
16	1041	172.253688881641	413
17	976.5	128.076799876741	310
18	1108.25	142.31976906483	341
19	1015.25	156.218596844294	382
20	989.5	114.596393195132	279
21	1105.5	147.947062604613	351
22	1098	152.663027613106	372
23	1087.5	108.555669282324	248
24	1263.25	161.487615624233	351
25	1191	196.057814602394	476
26	1090.5	73.7947604282761	155
27	1353.5	182.994535437537	403
28	1296.75	210.083118471396	506
29	1170	76.030695555589	165
30	1377	149.032434948459	320

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	13.3108112881255
beta	0.11592368174408
S.D.	0.0217275349949884
T-STAT	5.33533517588712
p-value	1.10953944042437e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 13.3108112881255 \tabularnewline
beta & 0.11592368174408 \tabularnewline
S.D. & 0.0217275349949884 \tabularnewline
T-STAT & 5.33533517588712 \tabularnewline
p-value & 1.10953944042437e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123417&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]13.3108112881255[/C][/ROW]
[ROW][C]beta[/C][C]0.11592368174408[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0217275349949884[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.33533517588712[/C][/ROW]
[ROW][C]p-value[/C][C]1.10953944042437e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123417&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123417&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	13.3108112881255
beta	0.11592368174408
S.D.	0.0217275349949884
T-STAT	5.33533517588712
p-value	1.10953944042437e-05

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.78668445658898
beta	1.24768186124492
S.D.	0.210485190233045
T-STAT	5.92764678533204
p-value	2.22373946848878e-06
Lambda	-0.247681861244915

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.78668445658898 \tabularnewline
beta & 1.24768186124492 \tabularnewline
S.D. & 0.210485190233045 \tabularnewline
T-STAT & 5.92764678533204 \tabularnewline
p-value & 2.22373946848878e-06 \tabularnewline
Lambda & -0.247681861244915 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123417&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.78668445658898[/C][/ROW]
[ROW][C]beta[/C][C]1.24768186124492[/C][/ROW]
[ROW][C]S.D.[/C][C]0.210485190233045[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.92764678533204[/C][/ROW]
[ROW][C]p-value[/C][C]2.22373946848878e-06[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.247681861244915[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123417&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123417&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	-3.78668445658898
beta	1.24768186124492
S.D.	0.210485190233045
T-STAT	5.92764678533204
p-value	2.22373946848878e-06
Lambda	-0.247681861244915

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = grey ;

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