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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

Sat, 19 Dec 2009 09:56:08 -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/2009/Dec/19/t1261241854vbk316w5emz93h7.htm/, Retrieved Sat, 04 May 2024 00:42:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69703, Retrieved Sat, 04 May 2024 00:42:17 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

108

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

-     [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-21 15:20:27] [005278dde49cfd8c32bf201feaeb19d6]
-    D  [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-23 16:19:40] [9d9b7f5939a0141f3b220bbc5743a411]
-  M D      [Standard Deviation-Mean Plot] [Standard Deviatio...] [2009-12-19 16:56:08] [986e3c28a4248c495afaef9fd432264f] [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	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=69703&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=69703&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69703&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	588.25	23.7185198066444	76
2	570.083333333333	21.6142138979016	70
3	541.083333333333	23.9714160591065	79
4	507.666666666667	23.41069426695	77
5	474.416666666667	24.5707081088376	82
6	469.75	28.1784088846891	82
7	491.5	28.1957443597434	70
8	538.083333333333	30.422654039184	79
9	576.666666666667	29.105867366418	76
10	596.25	21.9757097310148	62
11	588.333333333333	22.7129651934482	69
12	532.583333333333	21.8318296960834	66

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 588.25 & 23.7185198066444 & 76 \tabularnewline
2 & 570.083333333333 & 21.6142138979016 & 70 \tabularnewline
3 & 541.083333333333 & 23.9714160591065 & 79 \tabularnewline
4 & 507.666666666667 & 23.41069426695 & 77 \tabularnewline
5 & 474.416666666667 & 24.5707081088376 & 82 \tabularnewline
6 & 469.75 & 28.1784088846891 & 82 \tabularnewline
7 & 491.5 & 28.1957443597434 & 70 \tabularnewline
8 & 538.083333333333 & 30.422654039184 & 79 \tabularnewline
9 & 576.666666666667 & 29.105867366418 & 76 \tabularnewline
10 & 596.25 & 21.9757097310148 & 62 \tabularnewline
11 & 588.333333333333 & 22.7129651934482 & 69 \tabularnewline
12 & 532.583333333333 & 21.8318296960834 & 66 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69703&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]588.25[/C][C]23.7185198066444[/C][C]76[/C][/ROW]
[ROW][C]2[/C][C]570.083333333333[/C][C]21.6142138979016[/C][C]70[/C][/ROW]
[ROW][C]3[/C][C]541.083333333333[/C][C]23.9714160591065[/C][C]79[/C][/ROW]
[ROW][C]4[/C][C]507.666666666667[/C][C]23.41069426695[/C][C]77[/C][/ROW]
[ROW][C]5[/C][C]474.416666666667[/C][C]24.5707081088376[/C][C]82[/C][/ROW]
[ROW][C]6[/C][C]469.75[/C][C]28.1784088846891[/C][C]82[/C][/ROW]
[ROW][C]7[/C][C]491.5[/C][C]28.1957443597434[/C][C]70[/C][/ROW]
[ROW][C]8[/C][C]538.083333333333[/C][C]30.422654039184[/C][C]79[/C][/ROW]
[ROW][C]9[/C][C]576.666666666667[/C][C]29.105867366418[/C][C]76[/C][/ROW]
[ROW][C]10[/C][C]596.25[/C][C]21.9757097310148[/C][C]62[/C][/ROW]
[ROW][C]11[/C][C]588.333333333333[/C][C]22.7129651934482[/C][C]69[/C][/ROW]
[ROW][C]12[/C][C]532.583333333333[/C][C]21.8318296960834[/C][C]66[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69703&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69703&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	588.25	23.7185198066444	76
2	570.083333333333	21.6142138979016	70
3	541.083333333333	23.9714160591065	79
4	507.666666666667	23.41069426695	77
5	474.416666666667	24.5707081088376	82
6	469.75	28.1784088846891	82
7	491.5	28.1957443597434	70
8	538.083333333333	30.422654039184	79
9	576.666666666667	29.105867366418	76
10	596.25	21.9757097310148	62
11	588.333333333333	22.7129651934482	69
12	532.583333333333	21.8318296960834	66

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	38.7357619867392
beta	-0.0255025348688504
S.D.	0.020215625988774
T-STAT	-1.2615258554453
p-value	0.235751854466778

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 38.7357619867392 \tabularnewline
beta & -0.0255025348688504 \tabularnewline
S.D. & 0.020215625988774 \tabularnewline
T-STAT & -1.2615258554453 \tabularnewline
p-value & 0.235751854466778 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69703&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]38.7357619867392[/C][/ROW]
[ROW][C]beta[/C][C]-0.0255025348688504[/C][/ROW]
[ROW][C]S.D.[/C][C]0.020215625988774[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.2615258554453[/C][/ROW]
[ROW][C]p-value[/C][C]0.235751854466778[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69703&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69703&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	38.7357619867392
beta	-0.0255025348688504
S.D.	0.020215625988774
T-STAT	-1.2615258554453
p-value	0.235751854466778

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	6.67490323906841
beta	-0.55093500961385
S.D.	0.416383460686854
T-STAT	-1.32314335613870
p-value	0.215242862851659
Lambda	1.55093500961385

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 6.67490323906841 \tabularnewline
beta & -0.55093500961385 \tabularnewline
S.D. & 0.416383460686854 \tabularnewline
T-STAT & -1.32314335613870 \tabularnewline
p-value & 0.215242862851659 \tabularnewline
Lambda & 1.55093500961385 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69703&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.67490323906841[/C][/ROW]
[ROW][C]beta[/C][C]-0.55093500961385[/C][/ROW]
[ROW][C]S.D.[/C][C]0.416383460686854[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.32314335613870[/C][/ROW]
[ROW][C]p-value[/C][C]0.215242862851659[/C][/ROW]
[ROW][C]Lambda[/C][C]1.55093500961385[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69703&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69703&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	6.67490323906841
beta	-0.55093500961385
S.D.	0.416383460686854
T-STAT	-1.32314335613870
p-value	0.215242862851659
Lambda	1.55093500961385

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