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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

Sun, 03 Jan 2010 14:40:21 -0700

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/2010/Jan/03/t1262554892mt77qly5a5epuoh.htm/, Retrieved Fri, 03 May 2024 04:30:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71573, Retrieved Fri, 03 May 2024 04:30:32 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

114

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

-       [Standard Deviation-Mean Plot] [] [2010-01-03 21:40:21] [46199ea7e385a69efb178ac615a86e3a] [Current]

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Dataseries X:

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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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71573&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71573&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71573&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

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	7783.75	519.547479383101	1109
2	7381.75	107.242326842841	245
3	7948	352.293438296354	816
4	8119.75	520.891783386914	1260
5	7604.75	121.924498495312	278
6	8231.25	456.294038970487	1080
7	8264.75	518.222844601303	1106
8	7956.25	100.071224635257	234
9	8601.25	403.773348138119	929
10	8556	455.703851201633	911
11	8140.75	123.721124577279	289
12	9002	421.08668941205	939
13	8766.25	471.749492138925	955
14	8352.75	166.317718037897	372
15	9158	426.855166693966	1032
16	9084	468.325385460437	997
17	8664.75	188.936276735482	441
18	9336.75	329.704286697438	718
19	9338.75	577.87217444691	1187
20	8931.5	161.287527932778	395
21	9610.5	375.734392002294	859
22	9433.25	543.207986563772	1141
23	9026.75	139.306317157550	341
24	9613.75	422.341390346719	1014
25	9616	621.011540418802	1439
26	9025	94.7945146092325	210
27	9780.75	464.698020223887	1120
28	9876.25	443.678092765464	992
29	9312.25	110.870419860304	230
30	10047	516.651397623839	1247
31	10098.75	664.629408016227	1402
32	9394.5	80.8888125762766	183
33	10186.5	496.833640836313	1216
34	10312	864.100688577437	1794
35	9554.25	179.826536788465	386
36	10207.5	502.675839880932	1213
37	10504.25	739.483321876385	1637
38	9666.5	72.7621696579571	162
39	10522.5	563.263407888944	1325
40	10728	789.651822007649	1905
41	9703.75	69.5910674344536	151
42	10445.25	483.522750240358	1145
43	10271.25	818.076351367442	1991

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7783.75 & 519.547479383101 & 1109 \tabularnewline
2 & 7381.75 & 107.242326842841 & 245 \tabularnewline
3 & 7948 & 352.293438296354 & 816 \tabularnewline
4 & 8119.75 & 520.891783386914 & 1260 \tabularnewline
5 & 7604.75 & 121.924498495312 & 278 \tabularnewline
6 & 8231.25 & 456.294038970487 & 1080 \tabularnewline
7 & 8264.75 & 518.222844601303 & 1106 \tabularnewline
8 & 7956.25 & 100.071224635257 & 234 \tabularnewline
9 & 8601.25 & 403.773348138119 & 929 \tabularnewline
10 & 8556 & 455.703851201633 & 911 \tabularnewline
11 & 8140.75 & 123.721124577279 & 289 \tabularnewline
12 & 9002 & 421.08668941205 & 939 \tabularnewline
13 & 8766.25 & 471.749492138925 & 955 \tabularnewline
14 & 8352.75 & 166.317718037897 & 372 \tabularnewline
15 & 9158 & 426.855166693966 & 1032 \tabularnewline
16 & 9084 & 468.325385460437 & 997 \tabularnewline
17 & 8664.75 & 188.936276735482 & 441 \tabularnewline
18 & 9336.75 & 329.704286697438 & 718 \tabularnewline
19 & 9338.75 & 577.87217444691 & 1187 \tabularnewline
20 & 8931.5 & 161.287527932778 & 395 \tabularnewline
21 & 9610.5 & 375.734392002294 & 859 \tabularnewline
22 & 9433.25 & 543.207986563772 & 1141 \tabularnewline
23 & 9026.75 & 139.306317157550 & 341 \tabularnewline
24 & 9613.75 & 422.341390346719 & 1014 \tabularnewline
25 & 9616 & 621.011540418802 & 1439 \tabularnewline
26 & 9025 & 94.7945146092325 & 210 \tabularnewline
27 & 9780.75 & 464.698020223887 & 1120 \tabularnewline
28 & 9876.25 & 443.678092765464 & 992 \tabularnewline
29 & 9312.25 & 110.870419860304 & 230 \tabularnewline
30 & 10047 & 516.651397623839 & 1247 \tabularnewline
31 & 10098.75 & 664.629408016227 & 1402 \tabularnewline
32 & 9394.5 & 80.8888125762766 & 183 \tabularnewline
33 & 10186.5 & 496.833640836313 & 1216 \tabularnewline
34 & 10312 & 864.100688577437 & 1794 \tabularnewline
35 & 9554.25 & 179.826536788465 & 386 \tabularnewline
36 & 10207.5 & 502.675839880932 & 1213 \tabularnewline
37 & 10504.25 & 739.483321876385 & 1637 \tabularnewline
38 & 9666.5 & 72.7621696579571 & 162 \tabularnewline
39 & 10522.5 & 563.263407888944 & 1325 \tabularnewline
40 & 10728 & 789.651822007649 & 1905 \tabularnewline
41 & 9703.75 & 69.5910674344536 & 151 \tabularnewline
42 & 10445.25 & 483.522750240358 & 1145 \tabularnewline
43 & 10271.25 & 818.076351367442 & 1991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71573&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]7783.75[/C][C]519.547479383101[/C][C]1109[/C][/ROW]
[ROW][C]2[/C][C]7381.75[/C][C]107.242326842841[/C][C]245[/C][/ROW]
[ROW][C]3[/C][C]7948[/C][C]352.293438296354[/C][C]816[/C][/ROW]
[ROW][C]4[/C][C]8119.75[/C][C]520.891783386914[/C][C]1260[/C][/ROW]
[ROW][C]5[/C][C]7604.75[/C][C]121.924498495312[/C][C]278[/C][/ROW]
[ROW][C]6[/C][C]8231.25[/C][C]456.294038970487[/C][C]1080[/C][/ROW]
[ROW][C]7[/C][C]8264.75[/C][C]518.222844601303[/C][C]1106[/C][/ROW]
[ROW][C]8[/C][C]7956.25[/C][C]100.071224635257[/C][C]234[/C][/ROW]
[ROW][C]9[/C][C]8601.25[/C][C]403.773348138119[/C][C]929[/C][/ROW]
[ROW][C]10[/C][C]8556[/C][C]455.703851201633[/C][C]911[/C][/ROW]
[ROW][C]11[/C][C]8140.75[/C][C]123.721124577279[/C][C]289[/C][/ROW]
[ROW][C]12[/C][C]9002[/C][C]421.08668941205[/C][C]939[/C][/ROW]
[ROW][C]13[/C][C]8766.25[/C][C]471.749492138925[/C][C]955[/C][/ROW]
[ROW][C]14[/C][C]8352.75[/C][C]166.317718037897[/C][C]372[/C][/ROW]
[ROW][C]15[/C][C]9158[/C][C]426.855166693966[/C][C]1032[/C][/ROW]
[ROW][C]16[/C][C]9084[/C][C]468.325385460437[/C][C]997[/C][/ROW]
[ROW][C]17[/C][C]8664.75[/C][C]188.936276735482[/C][C]441[/C][/ROW]
[ROW][C]18[/C][C]9336.75[/C][C]329.704286697438[/C][C]718[/C][/ROW]
[ROW][C]19[/C][C]9338.75[/C][C]577.87217444691[/C][C]1187[/C][/ROW]
[ROW][C]20[/C][C]8931.5[/C][C]161.287527932778[/C][C]395[/C][/ROW]
[ROW][C]21[/C][C]9610.5[/C][C]375.734392002294[/C][C]859[/C][/ROW]
[ROW][C]22[/C][C]9433.25[/C][C]543.207986563772[/C][C]1141[/C][/ROW]
[ROW][C]23[/C][C]9026.75[/C][C]139.306317157550[/C][C]341[/C][/ROW]
[ROW][C]24[/C][C]9613.75[/C][C]422.341390346719[/C][C]1014[/C][/ROW]
[ROW][C]25[/C][C]9616[/C][C]621.011540418802[/C][C]1439[/C][/ROW]
[ROW][C]26[/C][C]9025[/C][C]94.7945146092325[/C][C]210[/C][/ROW]
[ROW][C]27[/C][C]9780.75[/C][C]464.698020223887[/C][C]1120[/C][/ROW]
[ROW][C]28[/C][C]9876.25[/C][C]443.678092765464[/C][C]992[/C][/ROW]
[ROW][C]29[/C][C]9312.25[/C][C]110.870419860304[/C][C]230[/C][/ROW]
[ROW][C]30[/C][C]10047[/C][C]516.651397623839[/C][C]1247[/C][/ROW]
[ROW][C]31[/C][C]10098.75[/C][C]664.629408016227[/C][C]1402[/C][/ROW]
[ROW][C]32[/C][C]9394.5[/C][C]80.8888125762766[/C][C]183[/C][/ROW]
[ROW][C]33[/C][C]10186.5[/C][C]496.833640836313[/C][C]1216[/C][/ROW]
[ROW][C]34[/C][C]10312[/C][C]864.100688577437[/C][C]1794[/C][/ROW]
[ROW][C]35[/C][C]9554.25[/C][C]179.826536788465[/C][C]386[/C][/ROW]
[ROW][C]36[/C][C]10207.5[/C][C]502.675839880932[/C][C]1213[/C][/ROW]
[ROW][C]37[/C][C]10504.25[/C][C]739.483321876385[/C][C]1637[/C][/ROW]
[ROW][C]38[/C][C]9666.5[/C][C]72.7621696579571[/C][C]162[/C][/ROW]
[ROW][C]39[/C][C]10522.5[/C][C]563.263407888944[/C][C]1325[/C][/ROW]
[ROW][C]40[/C][C]10728[/C][C]789.651822007649[/C][C]1905[/C][/ROW]
[ROW][C]41[/C][C]9703.75[/C][C]69.5910674344536[/C][C]151[/C][/ROW]
[ROW][C]42[/C][C]10445.25[/C][C]483.522750240358[/C][C]1145[/C][/ROW]
[ROW][C]43[/C][C]10271.25[/C][C]818.076351367442[/C][C]1991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71573&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71573&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	7783.75	519.547479383101	1109
2	7381.75	107.242326842841	245
3	7948	352.293438296354	816
4	8119.75	520.891783386914	1260
5	7604.75	121.924498495312	278
6	8231.25	456.294038970487	1080
7	8264.75	518.222844601303	1106
8	7956.25	100.071224635257	234
9	8601.25	403.773348138119	929
10	8556	455.703851201633	911
11	8140.75	123.721124577279	289
12	9002	421.08668941205	939
13	8766.25	471.749492138925	955
14	8352.75	166.317718037897	372
15	9158	426.855166693966	1032
16	9084	468.325385460437	997
17	8664.75	188.936276735482	441
18	9336.75	329.704286697438	718
19	9338.75	577.87217444691	1187
20	8931.5	161.287527932778	395
21	9610.5	375.734392002294	859
22	9433.25	543.207986563772	1141
23	9026.75	139.306317157550	341
24	9613.75	422.341390346719	1014
25	9616	621.011540418802	1439
26	9025	94.7945146092325	210
27	9780.75	464.698020223887	1120
28	9876.25	443.678092765464	992
29	9312.25	110.870419860304	230
30	10047	516.651397623839	1247
31	10098.75	664.629408016227	1402
32	9394.5	80.8888125762766	183
33	10186.5	496.833640836313	1216
34	10312	864.100688577437	1794
35	9554.25	179.826536788465	386
36	10207.5	502.675839880932	1213
37	10504.25	739.483321876385	1637
38	9666.5	72.7621696579571	162
39	10522.5	563.263407888944	1325
40	10728	789.651822007649	1905
41	9703.75	69.5910674344536	151
42	10445.25	483.522750240358	1145
43	10271.25	818.076351367442	1991

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-797.482276027966
beta	0.129344767534308
S.D.	0.0337922706790445
T-STAT	3.82764356863767
p-value	0.00043428168114996

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -797.482276027966 \tabularnewline
beta & 0.129344767534308 \tabularnewline
S.D. & 0.0337922706790445 \tabularnewline
T-STAT & 3.82764356863767 \tabularnewline
p-value & 0.00043428168114996 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71573&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-797.482276027966[/C][/ROW]
[ROW][C]beta[/C][C]0.129344767534308[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0337922706790445[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.82764356863767[/C][/ROW]
[ROW][C]p-value[/C][C]0.00043428168114996[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71573&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71573&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	-797.482276027966
beta	0.129344767534308
S.D.	0.0337922706790445
T-STAT	3.82764356863767
p-value	0.00043428168114996

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-22.6746541298514
beta	3.11597244280131
S.D.	1.09812567438796
T-STAT	2.83753719221435
p-value	0.00703666515493814
Lambda	-2.11597244280131

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -22.6746541298514 \tabularnewline
beta & 3.11597244280131 \tabularnewline
S.D. & 1.09812567438796 \tabularnewline
T-STAT & 2.83753719221435 \tabularnewline
p-value & 0.00703666515493814 \tabularnewline
Lambda & -2.11597244280131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71573&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-22.6746541298514[/C][/ROW]
[ROW][C]beta[/C][C]3.11597244280131[/C][/ROW]
[ROW][C]S.D.[/C][C]1.09812567438796[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.83753719221435[/C][/ROW]
[ROW][C]p-value[/C][C]0.00703666515493814[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.11597244280131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71573&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71573&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	-22.6746541298514
beta	3.11597244280131
S.D.	1.09812567438796
T-STAT	2.83753719221435
p-value	0.00703666515493814
Lambda	-2.11597244280131

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