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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

Wed, 03 Aug 2011 12:22:03 -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/03/t1312388598w9spy84kxxd2awe.htm/, Retrieved Tue, 14 May 2024 15:31:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123369, Retrieved Tue, 14 May 2024 15:31:54 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Marin Peeters

Estimated Impact

122

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

-       [Standard Deviation-Mean Plot] [Tijdreeks 1 - Sta...] [2011-08-03 16:22:03] [3f8170910ab21fde7eba151af40022ac] [Current]

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Dataseries X:

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Boxplots

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' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123369&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' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123369&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123369&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' @ wold.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	5563.25	172.490337893653	404
2	6279.25	1283.15272538645	2662
3	4922.75	148.032372585639	314
4	3799.5	533.912289925352	1124
5	4282.75	1512.73645534618	3280
6	3642.25	561.104491160069	1134
7	3645	433.724182709088	1033
8	3796.5	1515.25850379839	3280
9	3566.5	436.071477321475	1022
10	2926.25	291.966179548248	708
11	4819	950.438846007464	1741
12	4953.5	807.979166398078	1842
13	4872.25	981.992320065013	2258
14	6796	244.198007089875	517
15	6975.5	796.862807096261	1944
16	7231.25	861.604462616113	2055
17	10253	441.93061295487	1022
18	10766.75	944.238802775371	2156
19	10764	1087.13415302191	2561
20	13611.25	757.852393279852	1741
21	14431.75	906.820958072761	1843
22	13763.25	762.750887686581	1742
23	15815.75	754.891327719869	1741
24	16403	1151.5424438552	2359
25	16273.75	644.984948144787	1539
26	17865.5	403.677676700938	820
27	18681	1513.98745041034	2774
28	18939	763.925389026965	1741
29	20607	480.555928066651	921
30	20938.5	1134.44509195759	2359

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5563.25 & 172.490337893653 & 404 \tabularnewline
2 & 6279.25 & 1283.15272538645 & 2662 \tabularnewline
3 & 4922.75 & 148.032372585639 & 314 \tabularnewline
4 & 3799.5 & 533.912289925352 & 1124 \tabularnewline
5 & 4282.75 & 1512.73645534618 & 3280 \tabularnewline
6 & 3642.25 & 561.104491160069 & 1134 \tabularnewline
7 & 3645 & 433.724182709088 & 1033 \tabularnewline
8 & 3796.5 & 1515.25850379839 & 3280 \tabularnewline
9 & 3566.5 & 436.071477321475 & 1022 \tabularnewline
10 & 2926.25 & 291.966179548248 & 708 \tabularnewline
11 & 4819 & 950.438846007464 & 1741 \tabularnewline
12 & 4953.5 & 807.979166398078 & 1842 \tabularnewline
13 & 4872.25 & 981.992320065013 & 2258 \tabularnewline
14 & 6796 & 244.198007089875 & 517 \tabularnewline
15 & 6975.5 & 796.862807096261 & 1944 \tabularnewline
16 & 7231.25 & 861.604462616113 & 2055 \tabularnewline
17 & 10253 & 441.93061295487 & 1022 \tabularnewline
18 & 10766.75 & 944.238802775371 & 2156 \tabularnewline
19 & 10764 & 1087.13415302191 & 2561 \tabularnewline
20 & 13611.25 & 757.852393279852 & 1741 \tabularnewline
21 & 14431.75 & 906.820958072761 & 1843 \tabularnewline
22 & 13763.25 & 762.750887686581 & 1742 \tabularnewline
23 & 15815.75 & 754.891327719869 & 1741 \tabularnewline
24 & 16403 & 1151.5424438552 & 2359 \tabularnewline
25 & 16273.75 & 644.984948144787 & 1539 \tabularnewline
26 & 17865.5 & 403.677676700938 & 820 \tabularnewline
27 & 18681 & 1513.98745041034 & 2774 \tabularnewline
28 & 18939 & 763.925389026965 & 1741 \tabularnewline
29 & 20607 & 480.555928066651 & 921 \tabularnewline
30 & 20938.5 & 1134.44509195759 & 2359 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123369&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]5563.25[/C][C]172.490337893653[/C][C]404[/C][/ROW]
[ROW][C]2[/C][C]6279.25[/C][C]1283.15272538645[/C][C]2662[/C][/ROW]
[ROW][C]3[/C][C]4922.75[/C][C]148.032372585639[/C][C]314[/C][/ROW]
[ROW][C]4[/C][C]3799.5[/C][C]533.912289925352[/C][C]1124[/C][/ROW]
[ROW][C]5[/C][C]4282.75[/C][C]1512.73645534618[/C][C]3280[/C][/ROW]
[ROW][C]6[/C][C]3642.25[/C][C]561.104491160069[/C][C]1134[/C][/ROW]
[ROW][C]7[/C][C]3645[/C][C]433.724182709088[/C][C]1033[/C][/ROW]
[ROW][C]8[/C][C]3796.5[/C][C]1515.25850379839[/C][C]3280[/C][/ROW]
[ROW][C]9[/C][C]3566.5[/C][C]436.071477321475[/C][C]1022[/C][/ROW]
[ROW][C]10[/C][C]2926.25[/C][C]291.966179548248[/C][C]708[/C][/ROW]
[ROW][C]11[/C][C]4819[/C][C]950.438846007464[/C][C]1741[/C][/ROW]
[ROW][C]12[/C][C]4953.5[/C][C]807.979166398078[/C][C]1842[/C][/ROW]
[ROW][C]13[/C][C]4872.25[/C][C]981.992320065013[/C][C]2258[/C][/ROW]
[ROW][C]14[/C][C]6796[/C][C]244.198007089875[/C][C]517[/C][/ROW]
[ROW][C]15[/C][C]6975.5[/C][C]796.862807096261[/C][C]1944[/C][/ROW]
[ROW][C]16[/C][C]7231.25[/C][C]861.604462616113[/C][C]2055[/C][/ROW]
[ROW][C]17[/C][C]10253[/C][C]441.93061295487[/C][C]1022[/C][/ROW]
[ROW][C]18[/C][C]10766.75[/C][C]944.238802775371[/C][C]2156[/C][/ROW]
[ROW][C]19[/C][C]10764[/C][C]1087.13415302191[/C][C]2561[/C][/ROW]
[ROW][C]20[/C][C]13611.25[/C][C]757.852393279852[/C][C]1741[/C][/ROW]
[ROW][C]21[/C][C]14431.75[/C][C]906.820958072761[/C][C]1843[/C][/ROW]
[ROW][C]22[/C][C]13763.25[/C][C]762.750887686581[/C][C]1742[/C][/ROW]
[ROW][C]23[/C][C]15815.75[/C][C]754.891327719869[/C][C]1741[/C][/ROW]
[ROW][C]24[/C][C]16403[/C][C]1151.5424438552[/C][C]2359[/C][/ROW]
[ROW][C]25[/C][C]16273.75[/C][C]644.984948144787[/C][C]1539[/C][/ROW]
[ROW][C]26[/C][C]17865.5[/C][C]403.677676700938[/C][C]820[/C][/ROW]
[ROW][C]27[/C][C]18681[/C][C]1513.98745041034[/C][C]2774[/C][/ROW]
[ROW][C]28[/C][C]18939[/C][C]763.925389026965[/C][C]1741[/C][/ROW]
[ROW][C]29[/C][C]20607[/C][C]480.555928066651[/C][C]921[/C][/ROW]
[ROW][C]30[/C][C]20938.5[/C][C]1134.44509195759[/C][C]2359[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123369&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123369&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	5563.25	172.490337893653	404
2	6279.25	1283.15272538645	2662
3	4922.75	148.032372585639	314
4	3799.5	533.912289925352	1124
5	4282.75	1512.73645534618	3280
6	3642.25	561.104491160069	1134
7	3645	433.724182709088	1033
8	3796.5	1515.25850379839	3280
9	3566.5	436.071477321475	1022
10	2926.25	291.966179548248	708
11	4819	950.438846007464	1741
12	4953.5	807.979166398078	1842
13	4872.25	981.992320065013	2258
14	6796	244.198007089875	517
15	6975.5	796.862807096261	1944
16	7231.25	861.604462616113	2055
17	10253	441.93061295487	1022
18	10766.75	944.238802775371	2156
19	10764	1087.13415302191	2561
20	13611.25	757.852393279852	1741
21	14431.75	906.820958072761	1843
22	13763.25	762.750887686581	1742
23	15815.75	754.891327719869	1741
24	16403	1151.5424438552	2359
25	16273.75	644.984948144787	1539
26	17865.5	403.677676700938	820
27	18681	1513.98745041034	2774
28	18939	763.925389026965	1741
29	20607	480.555928066651	921
30	20938.5	1134.44509195759	2359

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	668.532000307139
beta	0.0108494798842702
S.D.	0.011947152476193
T-STAT	0.908122659846346
p-value	0.371563672700609

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 668.532000307139 \tabularnewline
beta & 0.0108494798842702 \tabularnewline
S.D. & 0.011947152476193 \tabularnewline
T-STAT & 0.908122659846346 \tabularnewline
p-value & 0.371563672700609 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123369&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]668.532000307139[/C][/ROW]
[ROW][C]beta[/C][C]0.0108494798842702[/C][/ROW]
[ROW][C]S.D.[/C][C]0.011947152476193[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.908122659846346[/C][/ROW]
[ROW][C]p-value[/C][C]0.371563672700609[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123369&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123369&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	668.532000307139
beta	0.0108494798842702
S.D.	0.011947152476193
T-STAT	0.908122659846346
p-value	0.371563672700609

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.33302469369681
beta	0.240952308795269
S.D.	0.171320277073607
T-STAT	1.40644360907579
p-value	0.170594572956905
Lambda	0.759047691204731

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.33302469369681 \tabularnewline
beta & 0.240952308795269 \tabularnewline
S.D. & 0.171320277073607 \tabularnewline
T-STAT & 1.40644360907579 \tabularnewline
p-value & 0.170594572956905 \tabularnewline
Lambda & 0.759047691204731 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123369&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.33302469369681[/C][/ROW]
[ROW][C]beta[/C][C]0.240952308795269[/C][/ROW]
[ROW][C]S.D.[/C][C]0.171320277073607[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.40644360907579[/C][/ROW]
[ROW][C]p-value[/C][C]0.170594572956905[/C][/ROW]
[ROW][C]Lambda[/C][C]0.759047691204731[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123369&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123369&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	4.33302469369681
beta	0.240952308795269
S.D.	0.171320277073607
T-STAT	1.40644360907579
p-value	0.170594572956905
Lambda	0.759047691204731

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