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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, 01 Dec 2011 16:39:37 -0500

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/Dec/01/t13227756107l1gm5kcofwoo1i.htm/, Retrieved Sat, 27 Apr 2024 02:34:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150006, Retrieved Sat, 27 Apr 2024 02:34:08 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

130

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

-     [(Partial) Autocorrelation Function] [] [2011-12-01 19:58:02] [ee8c3a74bf3b349877806e9a50913c60]
- R P   [(Partial) Autocorrelation Function] [] [2011-12-01 20:01:46] [ee8c3a74bf3b349877806e9a50913c60]
- RMP     [Spectral Analysis] [] [2011-12-01 20:13:31] [ee8c3a74bf3b349877806e9a50913c60]
- RMP         [Standard Deviation-Mean Plot] [] [2011-12-01 21:39:37] [7dc03dd48c8acabd98b217fada4a6bc0] [Current]

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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	0 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150006&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150006&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150006&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	0 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	246.583333333333	25.4717609532715	83
2	205.833333333333	13.4626306583232	43
3	259.583333333333	20.6197536945581	65
4	340.083333333333	19.0809678301006	63
5	419.333333333333	15.8993043491808	56
6	441.25	30.3498539759854	94
7	365.5	43.8644606611196	127
8	305.666666666667	38.186940493347	123
9	267.333333333333	23.488230450525	73
10	326.666666666667	24.2499609496718	74
11	389.083333333333	23.7044619249523	73

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 246.583333333333 & 25.4717609532715 & 83 \tabularnewline
2 & 205.833333333333 & 13.4626306583232 & 43 \tabularnewline
3 & 259.583333333333 & 20.6197536945581 & 65 \tabularnewline
4 & 340.083333333333 & 19.0809678301006 & 63 \tabularnewline
5 & 419.333333333333 & 15.8993043491808 & 56 \tabularnewline
6 & 441.25 & 30.3498539759854 & 94 \tabularnewline
7 & 365.5 & 43.8644606611196 & 127 \tabularnewline
8 & 305.666666666667 & 38.186940493347 & 123 \tabularnewline
9 & 267.333333333333 & 23.488230450525 & 73 \tabularnewline
10 & 326.666666666667 & 24.2499609496718 & 74 \tabularnewline
11 & 389.083333333333 & 23.7044619249523 & 73 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150006&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]246.583333333333[/C][C]25.4717609532715[/C][C]83[/C][/ROW]
[ROW][C]2[/C][C]205.833333333333[/C][C]13.4626306583232[/C][C]43[/C][/ROW]
[ROW][C]3[/C][C]259.583333333333[/C][C]20.6197536945581[/C][C]65[/C][/ROW]
[ROW][C]4[/C][C]340.083333333333[/C][C]19.0809678301006[/C][C]63[/C][/ROW]
[ROW][C]5[/C][C]419.333333333333[/C][C]15.8993043491808[/C][C]56[/C][/ROW]
[ROW][C]6[/C][C]441.25[/C][C]30.3498539759854[/C][C]94[/C][/ROW]
[ROW][C]7[/C][C]365.5[/C][C]43.8644606611196[/C][C]127[/C][/ROW]
[ROW][C]8[/C][C]305.666666666667[/C][C]38.186940493347[/C][C]123[/C][/ROW]
[ROW][C]9[/C][C]267.333333333333[/C][C]23.488230450525[/C][C]73[/C][/ROW]
[ROW][C]10[/C][C]326.666666666667[/C][C]24.2499609496718[/C][C]74[/C][/ROW]
[ROW][C]11[/C][C]389.083333333333[/C][C]23.7044619249523[/C][C]73[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150006&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150006&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	246.583333333333	25.4717609532715	83
2	205.833333333333	13.4626306583232	43
3	259.583333333333	20.6197536945581	65
4	340.083333333333	19.0809678301006	63
5	419.333333333333	15.8993043491808	56
6	441.25	30.3498539759854	94
7	365.5	43.8644606611196	127
8	305.666666666667	38.186940493347	123
9	267.333333333333	23.488230450525	73
10	326.666666666667	24.2499609496718	74
11	389.083333333333	23.7044619249523	73

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	14.9408671471312
beta	0.0319684472553584
S.D.	0.0389485641069823
T-STAT	0.820786285408334
p-value	0.432969769195702

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 14.9408671471312 \tabularnewline
beta & 0.0319684472553584 \tabularnewline
S.D. & 0.0389485641069823 \tabularnewline
T-STAT & 0.820786285408334 \tabularnewline
p-value & 0.432969769195702 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150006&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]14.9408671471312[/C][/ROW]
[ROW][C]beta[/C][C]0.0319684472553584[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0389485641069823[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.820786285408334[/C][/ROW]
[ROW][C]p-value[/C][C]0.432969769195702[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150006&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150006&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	14.9408671471312
beta	0.0319684472553584
S.D.	0.0389485641069823
T-STAT	0.820786285408334
p-value	0.432969769195702

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.35817173062132
beta	0.489380785928451
S.D.	0.456684684159484
T-STAT	1.07159447842912
p-value	0.311795335295064
Lambda	0.510619214071549

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.35817173062132 \tabularnewline
beta & 0.489380785928451 \tabularnewline
S.D. & 0.456684684159484 \tabularnewline
T-STAT & 1.07159447842912 \tabularnewline
p-value & 0.311795335295064 \tabularnewline
Lambda & 0.510619214071549 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150006&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.35817173062132[/C][/ROW]
[ROW][C]beta[/C][C]0.489380785928451[/C][/ROW]
[ROW][C]S.D.[/C][C]0.456684684159484[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.07159447842912[/C][/ROW]
[ROW][C]p-value[/C][C]0.311795335295064[/C][/ROW]
[ROW][C]Lambda[/C][C]0.510619214071549[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150006&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150006&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	0.35817173062132
beta	0.489380785928451
S.D.	0.456684684159484
T-STAT	1.07159447842912
p-value	0.311795335295064
Lambda	0.510619214071549

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