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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, 17 Dec 2009 20:37:03 +0100

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/2009/Dec/17/t1261078659lcdv5zytvefthcn.htm/, Retrieved Tue, 30 Apr 2024 06:09:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69068, Retrieved Tue, 30 Apr 2024 06:09:22 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

207

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

-     [Univariate Data Series] [] [2009-12-17 19:09:08] [b98453cac15ba1066b407e146608df68]
- RMP     [Standard Deviation-Mean Plot] [] [2009-12-17 19:37:03] [d76b387543b13b5e3afd8ff9e5fdc89f] [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	4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69068&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]4 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=69068&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69068&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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	268.366666666667	22.7468812381084	67.4
2	280.525	25.9186182642376	86.2
3	288.475	27.9542524005334	103.5
4	303.833333333333	26.0240215372201	79.4
5	315.716666666667	27.9636723213703	83.3
6	331.233333333333	32.5301352129022	95.6
7	331.083333333333	32.9423417320002	99.3
8	346.908333333333	31.6539085144698	101.6
9	364.791666666667	47.3099155152554	162.7
10	394.983333333333	32.1104863453255	94.8
11	396.25	32.6875428037265	101.2
12	398.683333333333	37.1288134456084	113
13	412.508333333333	34.2209255050801	106.2
14	422.075	36.9104105787366	105.2
15	454.941666666667	41.4957929594475	129.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 268.366666666667 & 22.7468812381084 & 67.4 \tabularnewline
2 & 280.525 & 25.9186182642376 & 86.2 \tabularnewline
3 & 288.475 & 27.9542524005334 & 103.5 \tabularnewline
4 & 303.833333333333 & 26.0240215372201 & 79.4 \tabularnewline
5 & 315.716666666667 & 27.9636723213703 & 83.3 \tabularnewline
6 & 331.233333333333 & 32.5301352129022 & 95.6 \tabularnewline
7 & 331.083333333333 & 32.9423417320002 & 99.3 \tabularnewline
8 & 346.908333333333 & 31.6539085144698 & 101.6 \tabularnewline
9 & 364.791666666667 & 47.3099155152554 & 162.7 \tabularnewline
10 & 394.983333333333 & 32.1104863453255 & 94.8 \tabularnewline
11 & 396.25 & 32.6875428037265 & 101.2 \tabularnewline
12 & 398.683333333333 & 37.1288134456084 & 113 \tabularnewline
13 & 412.508333333333 & 34.2209255050801 & 106.2 \tabularnewline
14 & 422.075 & 36.9104105787366 & 105.2 \tabularnewline
15 & 454.941666666667 & 41.4957929594475 & 129.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69068&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]268.366666666667[/C][C]22.7468812381084[/C][C]67.4[/C][/ROW]
[ROW][C]2[/C][C]280.525[/C][C]25.9186182642376[/C][C]86.2[/C][/ROW]
[ROW][C]3[/C][C]288.475[/C][C]27.9542524005334[/C][C]103.5[/C][/ROW]
[ROW][C]4[/C][C]303.833333333333[/C][C]26.0240215372201[/C][C]79.4[/C][/ROW]
[ROW][C]5[/C][C]315.716666666667[/C][C]27.9636723213703[/C][C]83.3[/C][/ROW]
[ROW][C]6[/C][C]331.233333333333[/C][C]32.5301352129022[/C][C]95.6[/C][/ROW]
[ROW][C]7[/C][C]331.083333333333[/C][C]32.9423417320002[/C][C]99.3[/C][/ROW]
[ROW][C]8[/C][C]346.908333333333[/C][C]31.6539085144698[/C][C]101.6[/C][/ROW]
[ROW][C]9[/C][C]364.791666666667[/C][C]47.3099155152554[/C][C]162.7[/C][/ROW]
[ROW][C]10[/C][C]394.983333333333[/C][C]32.1104863453255[/C][C]94.8[/C][/ROW]
[ROW][C]11[/C][C]396.25[/C][C]32.6875428037265[/C][C]101.2[/C][/ROW]
[ROW][C]12[/C][C]398.683333333333[/C][C]37.1288134456084[/C][C]113[/C][/ROW]
[ROW][C]13[/C][C]412.508333333333[/C][C]34.2209255050801[/C][C]106.2[/C][/ROW]
[ROW][C]14[/C][C]422.075[/C][C]36.9104105787366[/C][C]105.2[/C][/ROW]
[ROW][C]15[/C][C]454.941666666667[/C][C]41.4957929594475[/C][C]129.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69068&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69068&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	268.366666666667	22.7468812381084	67.4
2	280.525	25.9186182642376	86.2
3	288.475	27.9542524005334	103.5
4	303.833333333333	26.0240215372201	79.4
5	315.716666666667	27.9636723213703	83.3
6	331.233333333333	32.5301352129022	95.6
7	331.083333333333	32.9423417320002	99.3
8	346.908333333333	31.6539085144698	101.6
9	364.791666666667	47.3099155152554	162.7
10	394.983333333333	32.1104863453255	94.8
11	396.25	32.6875428037265	101.2
12	398.683333333333	37.1288134456084	113
13	412.508333333333	34.2209255050801	106.2
14	422.075	36.9104105787366	105.2
15	454.941666666667	41.4957929594475	129.1

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	3.51748086120304
beta	0.0822607641561992
S.D.	0.0206970529120850
T-STAT	3.97451581660532
p-value	0.00158645261384556

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.51748086120304 \tabularnewline
beta & 0.0822607641561992 \tabularnewline
S.D. & 0.0206970529120850 \tabularnewline
T-STAT & 3.97451581660532 \tabularnewline
p-value & 0.00158645261384556 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69068&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.51748086120304[/C][/ROW]
[ROW][C]beta[/C][C]0.0822607641561992[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0206970529120850[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.97451581660532[/C][/ROW]
[ROW][C]p-value[/C][C]0.00158645261384556[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69068&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69068&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	3.51748086120304
beta	0.0822607641561992
S.D.	0.0206970529120850
T-STAT	3.97451581660532
p-value	0.00158645261384556

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-2.00328592611815
beta	0.934209687438927
S.D.	0.194384336907637
T-STAT	4.8059926139153
p-value	0.000343135243352155
Lambda	0.0657903125610733

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.00328592611815 \tabularnewline
beta & 0.934209687438927 \tabularnewline
S.D. & 0.194384336907637 \tabularnewline
T-STAT & 4.8059926139153 \tabularnewline
p-value & 0.000343135243352155 \tabularnewline
Lambda & 0.0657903125610733 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69068&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.00328592611815[/C][/ROW]
[ROW][C]beta[/C][C]0.934209687438927[/C][/ROW]
[ROW][C]S.D.[/C][C]0.194384336907637[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.8059926139153[/C][/ROW]
[ROW][C]p-value[/C][C]0.000343135243352155[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0657903125610733[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69068&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69068&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	-2.00328592611815
beta	0.934209687438927
S.D.	0.194384336907637
T-STAT	4.8059926139153
p-value	0.000343135243352155
Lambda	0.0657903125610733

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