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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, 16 Jan 2011 13:10:31 +0000

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/Jan/16/t1295183294sd095cbti6b8khg.htm/, Retrieved Thu, 16 May 2024 03:45:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117395, Retrieved Thu, 16 May 2024 03:45:55 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

149

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

-       [Standard Deviation-Mean Plot] [] [2011-01-16 13:10:31] [a6954a1d1f0e31732d0acb07eec786a1] [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	'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117395&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117395&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117395&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	'Herman Ole Andreas Wold' @ www.yougetit.org

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	51441.5	1081.76291302669	1965
2	50343.5	242.302152968836	550
3	49011.5	1077.09253703353	2399
4	47221	1091.6889056259	2243
5	46620.25	248.671637573193	516
6	46413.5	423.692105189606	1003
7	48290.75	356.7757232025	807
8	50902.75	727.596213569037	1716
9	53429.5	1283.39458728275	2759
10	57681.75	871.744754309807	2005
11	61875.25	1615.78595426498	3747
12	65748.5	988.02311039098	2420
13	61190.25	2930.3311957297	6247
14	59682.5	224.565506404405	488
15	59297.75	664.659499292683	1428
16	58188.75	2127.79578829047	4280
17	56064	508.047898004378	1115
18	52642.75	1808.18903418125	4177
19	48836.25	2703.72093912568	5652
20	45041.75	525.801214021674	1139
21	42070.5	610.993998879422	1465
22	40709.75	2114.54697669895	4625
23	36976.25	603.556887680579	1370
24	36575.25	933.710652896995	1928
25	38850.25	815.694540458212	1600
26	38912.5	664.869661412421	1472
27	39545.75	1271.71862060756	2940
28	41944.5	533.709971176606	1154
29	44221	1469.04844485583	3282
30	48351.5	1712.48639897275	3817
31	53362.5	1353.85929845017	3071
32	56130	1498.60401707723	3334

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 51441.5 & 1081.76291302669 & 1965 \tabularnewline
2 & 50343.5 & 242.302152968836 & 550 \tabularnewline
3 & 49011.5 & 1077.09253703353 & 2399 \tabularnewline
4 & 47221 & 1091.6889056259 & 2243 \tabularnewline
5 & 46620.25 & 248.671637573193 & 516 \tabularnewline
6 & 46413.5 & 423.692105189606 & 1003 \tabularnewline
7 & 48290.75 & 356.7757232025 & 807 \tabularnewline
8 & 50902.75 & 727.596213569037 & 1716 \tabularnewline
9 & 53429.5 & 1283.39458728275 & 2759 \tabularnewline
10 & 57681.75 & 871.744754309807 & 2005 \tabularnewline
11 & 61875.25 & 1615.78595426498 & 3747 \tabularnewline
12 & 65748.5 & 988.02311039098 & 2420 \tabularnewline
13 & 61190.25 & 2930.3311957297 & 6247 \tabularnewline
14 & 59682.5 & 224.565506404405 & 488 \tabularnewline
15 & 59297.75 & 664.659499292683 & 1428 \tabularnewline
16 & 58188.75 & 2127.79578829047 & 4280 \tabularnewline
17 & 56064 & 508.047898004378 & 1115 \tabularnewline
18 & 52642.75 & 1808.18903418125 & 4177 \tabularnewline
19 & 48836.25 & 2703.72093912568 & 5652 \tabularnewline
20 & 45041.75 & 525.801214021674 & 1139 \tabularnewline
21 & 42070.5 & 610.993998879422 & 1465 \tabularnewline
22 & 40709.75 & 2114.54697669895 & 4625 \tabularnewline
23 & 36976.25 & 603.556887680579 & 1370 \tabularnewline
24 & 36575.25 & 933.710652896995 & 1928 \tabularnewline
25 & 38850.25 & 815.694540458212 & 1600 \tabularnewline
26 & 38912.5 & 664.869661412421 & 1472 \tabularnewline
27 & 39545.75 & 1271.71862060756 & 2940 \tabularnewline
28 & 41944.5 & 533.709971176606 & 1154 \tabularnewline
29 & 44221 & 1469.04844485583 & 3282 \tabularnewline
30 & 48351.5 & 1712.48639897275 & 3817 \tabularnewline
31 & 53362.5 & 1353.85929845017 & 3071 \tabularnewline
32 & 56130 & 1498.60401707723 & 3334 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117395&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]51441.5[/C][C]1081.76291302669[/C][C]1965[/C][/ROW]
[ROW][C]2[/C][C]50343.5[/C][C]242.302152968836[/C][C]550[/C][/ROW]
[ROW][C]3[/C][C]49011.5[/C][C]1077.09253703353[/C][C]2399[/C][/ROW]
[ROW][C]4[/C][C]47221[/C][C]1091.6889056259[/C][C]2243[/C][/ROW]
[ROW][C]5[/C][C]46620.25[/C][C]248.671637573193[/C][C]516[/C][/ROW]
[ROW][C]6[/C][C]46413.5[/C][C]423.692105189606[/C][C]1003[/C][/ROW]
[ROW][C]7[/C][C]48290.75[/C][C]356.7757232025[/C][C]807[/C][/ROW]
[ROW][C]8[/C][C]50902.75[/C][C]727.596213569037[/C][C]1716[/C][/ROW]
[ROW][C]9[/C][C]53429.5[/C][C]1283.39458728275[/C][C]2759[/C][/ROW]
[ROW][C]10[/C][C]57681.75[/C][C]871.744754309807[/C][C]2005[/C][/ROW]
[ROW][C]11[/C][C]61875.25[/C][C]1615.78595426498[/C][C]3747[/C][/ROW]
[ROW][C]12[/C][C]65748.5[/C][C]988.02311039098[/C][C]2420[/C][/ROW]
[ROW][C]13[/C][C]61190.25[/C][C]2930.3311957297[/C][C]6247[/C][/ROW]
[ROW][C]14[/C][C]59682.5[/C][C]224.565506404405[/C][C]488[/C][/ROW]
[ROW][C]15[/C][C]59297.75[/C][C]664.659499292683[/C][C]1428[/C][/ROW]
[ROW][C]16[/C][C]58188.75[/C][C]2127.79578829047[/C][C]4280[/C][/ROW]
[ROW][C]17[/C][C]56064[/C][C]508.047898004378[/C][C]1115[/C][/ROW]
[ROW][C]18[/C][C]52642.75[/C][C]1808.18903418125[/C][C]4177[/C][/ROW]
[ROW][C]19[/C][C]48836.25[/C][C]2703.72093912568[/C][C]5652[/C][/ROW]
[ROW][C]20[/C][C]45041.75[/C][C]525.801214021674[/C][C]1139[/C][/ROW]
[ROW][C]21[/C][C]42070.5[/C][C]610.993998879422[/C][C]1465[/C][/ROW]
[ROW][C]22[/C][C]40709.75[/C][C]2114.54697669895[/C][C]4625[/C][/ROW]
[ROW][C]23[/C][C]36976.25[/C][C]603.556887680579[/C][C]1370[/C][/ROW]
[ROW][C]24[/C][C]36575.25[/C][C]933.710652896995[/C][C]1928[/C][/ROW]
[ROW][C]25[/C][C]38850.25[/C][C]815.694540458212[/C][C]1600[/C][/ROW]
[ROW][C]26[/C][C]38912.5[/C][C]664.869661412421[/C][C]1472[/C][/ROW]
[ROW][C]27[/C][C]39545.75[/C][C]1271.71862060756[/C][C]2940[/C][/ROW]
[ROW][C]28[/C][C]41944.5[/C][C]533.709971176606[/C][C]1154[/C][/ROW]
[ROW][C]29[/C][C]44221[/C][C]1469.04844485583[/C][C]3282[/C][/ROW]
[ROW][C]30[/C][C]48351.5[/C][C]1712.48639897275[/C][C]3817[/C][/ROW]
[ROW][C]31[/C][C]53362.5[/C][C]1353.85929845017[/C][C]3071[/C][/ROW]
[ROW][C]32[/C][C]56130[/C][C]1498.60401707723[/C][C]3334[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117395&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117395&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	51441.5	1081.76291302669	1965
2	50343.5	242.302152968836	550
3	49011.5	1077.09253703353	2399
4	47221	1091.6889056259	2243
5	46620.25	248.671637573193	516
6	46413.5	423.692105189606	1003
7	48290.75	356.7757232025	807
8	50902.75	727.596213569037	1716
9	53429.5	1283.39458728275	2759
10	57681.75	871.744754309807	2005
11	61875.25	1615.78595426498	3747
12	65748.5	988.02311039098	2420
13	61190.25	2930.3311957297	6247
14	59682.5	224.565506404405	488
15	59297.75	664.659499292683	1428
16	58188.75	2127.79578829047	4280
17	56064	508.047898004378	1115
18	52642.75	1808.18903418125	4177
19	48836.25	2703.72093912568	5652
20	45041.75	525.801214021674	1139
21	42070.5	610.993998879422	1465
22	40709.75	2114.54697669895	4625
23	36976.25	603.556887680579	1370
24	36575.25	933.710652896995	1928
25	38850.25	815.694540458212	1600
26	38912.5	664.869661412421	1472
27	39545.75	1271.71862060756	2940
28	41944.5	533.709971176606	1154
29	44221	1469.04844485583	3282
30	48351.5	1712.48639897275	3817
31	53362.5	1353.85929845017	3071
32	56130	1498.60401707723	3334

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	103.48737712451
beta	0.0200134639880739
S.D.	0.0156191414552193
T-STAT	1.28134213045278
p-value	0.209889602571648

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 103.48737712451 \tabularnewline
beta & 0.0200134639880739 \tabularnewline
S.D. & 0.0156191414552193 \tabularnewline
T-STAT & 1.28134213045278 \tabularnewline
p-value & 0.209889602571648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117395&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]103.48737712451[/C][/ROW]
[ROW][C]beta[/C][C]0.0200134639880739[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0156191414552193[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.28134213045278[/C][/ROW]
[ROW][C]p-value[/C][C]0.209889602571648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117395&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117395&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	103.48737712451
beta	0.0200134639880739
S.D.	0.0156191414552193
T-STAT	1.28134213045278
p-value	0.209889602571648

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.0122495382604356
beta	0.627832451725583
S.D.	0.765465045726809
T-STAT	0.820197414931542
p-value	0.418573007226473
Lambda	0.372167548274417

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.0122495382604356 \tabularnewline
beta & 0.627832451725583 \tabularnewline
S.D. & 0.765465045726809 \tabularnewline
T-STAT & 0.820197414931542 \tabularnewline
p-value & 0.418573007226473 \tabularnewline
Lambda & 0.372167548274417 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117395&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0122495382604356[/C][/ROW]
[ROW][C]beta[/C][C]0.627832451725583[/C][/ROW]
[ROW][C]S.D.[/C][C]0.765465045726809[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.820197414931542[/C][/ROW]
[ROW][C]p-value[/C][C]0.418573007226473[/C][/ROW]
[ROW][C]Lambda[/C][C]0.372167548274417[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117395&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117395&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	0.0122495382604356
beta	0.627832451725583
S.D.	0.765465045726809
T-STAT	0.820197414931542
p-value	0.418573007226473
Lambda	0.372167548274417

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