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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

Wed, 29 Dec 2010 16:36:49 +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/2010/Dec/29/t1293640453gkqb7hwtnzxdd5q.htm/, Retrieved Fri, 03 May 2024 11:20:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116965, Retrieved Fri, 03 May 2024 11:20:59 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

135

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

-     [Standard Deviation-Mean Plot] [standaard deviatie] [2010-12-27 13:58:51] [8e0d27d3447b6ae48398467ddbde7cca]
-         [Standard Deviation-Mean Plot] [] [2010-12-29 16:36:49] [bdfe30dae669994be8da33a8aaee8615] [Current]

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Dataseries X:

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Histogram

Boxplots

8.3
8.2
8.1
8
8.1
8.1
8
7.8
7.7
7.7
7.7
7.6
7.5
7.3
7.2
7.1
7.2
7.2
7.2
6.9
6.8
6.8
6.8
6.9
7
7.2
7.2
7.2
7
7
7.2
7.4
7.8
8
7.8
7.8
7.9
7.9
8
8
8
8
8.2
8.4
8.6
8.6
8.5
8.5
8.4
8.4
8.4
8.5
8.6
8.6
8.6
8.6
8.6
8.5
8.4
8.4
8.3
8.3
8.3
8.6
8.8
8.8
8.5
8.1
7.9
8
8.4
8.5
8.5
8.4
8.3
8.3
8.2
8.1
8.1
8.2
8.2
8.2
8.1
8.1
8
7.8
7.7
7.7
7.7
7.7
7.7
7.5
7.4
7.3
7.4
7.4
7.3
7.3
7.1
7
6.5
6.3
6.3
6.5
6.6
6.5
6.3
6.3
6.3
6.5
6.7
6.7
6.7
6.8
6.7
6.8
6.8
7
7
7.2
7.4
7.6
7.8
7.9
8.1
8.3
8.5
8.7
8.8
8.9
9
9
9.1
9.1
9.1
9.2
9.4
9.4
9.3
9.4
9.4
9.5
9.5
9.4
9.4
9.4
9.3
9.3
9.3
9.3
9.3
9.2
9.1
9.1
9.1
9.1
9.2
9.2
9.2
9.3
9.4
9.4
9.5
9.6
9.7
9.7
9.8
9.9
9.9
9.9
9.8
9.8
9.7
9.7
9.6
9.6
9.6
9.6
9.6
9.7
9.7
9.7
9.7
9.8
9.8
9.8
9.8
9.9
9.9
9.8
9.7
9.6
9.6
9.5
9.3
9.2
9
8.9
8.7
8.5
8.4
8.2
8.1
7.9
7.8
7.6
7.5
7.4
7.2
7.2
7.1
7
7
6.9
6.8
6.7
6.7
6.6
6.6
6.5
6.5
6.4
6.4
6.4
6.4
6.3
6.4
6.4
6.4
6.4
6.4
6.4
6.4
6.5
6.5
6.6
6.6
6.6
6.7
6.7
6.8

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' @ www.wessa.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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116965&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' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116965&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116965&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' @ www.wessa.org

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	7.94166666666667	0.231431644466797	0.700000000000001
2	7.075	0.230118546524493	0.7
3	7.38333333333333	0.366391081008291	1
4	8.21666666666667	0.282306517276824	0.7
5	8.5	0.095346258924559	0.199999999999999
6	8.375	0.286435777348876	0.9
7	8.225	0.128805702866407	0.4
8	7.60833333333333	0.206522432562458	0.7
9	6.66666666666667	0.396194014303216	1
10	6.76666666666667	0.234843597212092	0.9
11	8.33333333333333	0.56622085850493	1.6
12	9.31666666666667	0.152752523165195	0.4
13	9.24166666666667	0.116450015288132	0.300000000000001
14	9.49166666666667	0.246644143115813	0.700000000000001
15	9.70833333333333	0.116450015288132	0.300000000000001
16	9.76666666666667	0.08876253645986	0.300000000000001
17	8.775	0.564277494597375	1.7
18	7.18333333333333	0.335297244880184	1.1
19	6.46666666666667	0.115470053837925	0.4
20	6.51666666666667	0.119341628287971	0.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7.94166666666667 & 0.231431644466797 & 0.700000000000001 \tabularnewline
2 & 7.075 & 0.230118546524493 & 0.7 \tabularnewline
3 & 7.38333333333333 & 0.366391081008291 & 1 \tabularnewline
4 & 8.21666666666667 & 0.282306517276824 & 0.7 \tabularnewline
5 & 8.5 & 0.095346258924559 & 0.199999999999999 \tabularnewline
6 & 8.375 & 0.286435777348876 & 0.9 \tabularnewline
7 & 8.225 & 0.128805702866407 & 0.4 \tabularnewline
8 & 7.60833333333333 & 0.206522432562458 & 0.7 \tabularnewline
9 & 6.66666666666667 & 0.396194014303216 & 1 \tabularnewline
10 & 6.76666666666667 & 0.234843597212092 & 0.9 \tabularnewline
11 & 8.33333333333333 & 0.56622085850493 & 1.6 \tabularnewline
12 & 9.31666666666667 & 0.152752523165195 & 0.4 \tabularnewline
13 & 9.24166666666667 & 0.116450015288132 & 0.300000000000001 \tabularnewline
14 & 9.49166666666667 & 0.246644143115813 & 0.700000000000001 \tabularnewline
15 & 9.70833333333333 & 0.116450015288132 & 0.300000000000001 \tabularnewline
16 & 9.76666666666667 & 0.08876253645986 & 0.300000000000001 \tabularnewline
17 & 8.775 & 0.564277494597375 & 1.7 \tabularnewline
18 & 7.18333333333333 & 0.335297244880184 & 1.1 \tabularnewline
19 & 6.46666666666667 & 0.115470053837925 & 0.4 \tabularnewline
20 & 6.51666666666667 & 0.119341628287971 & 0.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116965&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]7.94166666666667[/C][C]0.231431644466797[/C][C]0.700000000000001[/C][/ROW]
[ROW][C]2[/C][C]7.075[/C][C]0.230118546524493[/C][C]0.7[/C][/ROW]
[ROW][C]3[/C][C]7.38333333333333[/C][C]0.366391081008291[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]8.21666666666667[/C][C]0.282306517276824[/C][C]0.7[/C][/ROW]
[ROW][C]5[/C][C]8.5[/C][C]0.095346258924559[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]6[/C][C]8.375[/C][C]0.286435777348876[/C][C]0.9[/C][/ROW]
[ROW][C]7[/C][C]8.225[/C][C]0.128805702866407[/C][C]0.4[/C][/ROW]
[ROW][C]8[/C][C]7.60833333333333[/C][C]0.206522432562458[/C][C]0.7[/C][/ROW]
[ROW][C]9[/C][C]6.66666666666667[/C][C]0.396194014303216[/C][C]1[/C][/ROW]
[ROW][C]10[/C][C]6.76666666666667[/C][C]0.234843597212092[/C][C]0.9[/C][/ROW]
[ROW][C]11[/C][C]8.33333333333333[/C][C]0.56622085850493[/C][C]1.6[/C][/ROW]
[ROW][C]12[/C][C]9.31666666666667[/C][C]0.152752523165195[/C][C]0.4[/C][/ROW]
[ROW][C]13[/C][C]9.24166666666667[/C][C]0.116450015288132[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]14[/C][C]9.49166666666667[/C][C]0.246644143115813[/C][C]0.700000000000001[/C][/ROW]
[ROW][C]15[/C][C]9.70833333333333[/C][C]0.116450015288132[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]16[/C][C]9.76666666666667[/C][C]0.08876253645986[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]17[/C][C]8.775[/C][C]0.564277494597375[/C][C]1.7[/C][/ROW]
[ROW][C]18[/C][C]7.18333333333333[/C][C]0.335297244880184[/C][C]1.1[/C][/ROW]
[ROW][C]19[/C][C]6.46666666666667[/C][C]0.115470053837925[/C][C]0.4[/C][/ROW]
[ROW][C]20[/C][C]6.51666666666667[/C][C]0.119341628287971[/C][C]0.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116965&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116965&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	7.94166666666667	0.231431644466797	0.700000000000001
2	7.075	0.230118546524493	0.7
3	7.38333333333333	0.366391081008291	1
4	8.21666666666667	0.282306517276824	0.7
5	8.5	0.095346258924559	0.199999999999999
6	8.375	0.286435777348876	0.9
7	8.225	0.128805702866407	0.4
8	7.60833333333333	0.206522432562458	0.7
9	6.66666666666667	0.396194014303216	1
10	6.76666666666667	0.234843597212092	0.9
11	8.33333333333333	0.56622085850493	1.6
12	9.31666666666667	0.152752523165195	0.4
13	9.24166666666667	0.116450015288132	0.300000000000001
14	9.49166666666667	0.246644143115813	0.700000000000001
15	9.70833333333333	0.116450015288132	0.300000000000001
16	9.76666666666667	0.08876253645986	0.300000000000001
17	8.775	0.564277494597375	1.7
18	7.18333333333333	0.335297244880184	1.1
19	6.46666666666667	0.115470053837925	0.4
20	6.51666666666667	0.119341628287971	0.3

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.394086040659209
beta	-0.0185794113205631
S.D.	0.0307168489847576
T-STAT	-0.60486058741841
p-value	0.552821130350247

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.394086040659209 \tabularnewline
beta & -0.0185794113205631 \tabularnewline
S.D. & 0.0307168489847576 \tabularnewline
T-STAT & -0.60486058741841 \tabularnewline
p-value & 0.552821130350247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116965&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.394086040659209[/C][/ROW]
[ROW][C]beta[/C][C]-0.0185794113205631[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0307168489847576[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.60486058741841[/C][/ROW]
[ROW][C]p-value[/C][C]0.552821130350247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116965&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116965&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	0.394086040659209
beta	-0.0185794113205631
S.D.	0.0307168489847576
T-STAT	-0.60486058741841
p-value	0.552821130350247

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.186375271111365
beta	-0.84239636824139
S.D.	0.969461017256858
T-STAT	-0.868932688624238
p-value	0.396322660203089
Lambda	1.84239636824139

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.186375271111365 \tabularnewline
beta & -0.84239636824139 \tabularnewline
S.D. & 0.969461017256858 \tabularnewline
T-STAT & -0.868932688624238 \tabularnewline
p-value & 0.396322660203089 \tabularnewline
Lambda & 1.84239636824139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116965&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.186375271111365[/C][/ROW]
[ROW][C]beta[/C][C]-0.84239636824139[/C][/ROW]
[ROW][C]S.D.[/C][C]0.969461017256858[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.868932688624238[/C][/ROW]
[ROW][C]p-value[/C][C]0.396322660203089[/C][/ROW]
[ROW][C]Lambda[/C][C]1.84239636824139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116965&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116965&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	0.186375271111365
beta	-0.84239636824139
S.D.	0.969461017256858
T-STAT	-0.868932688624238
p-value	0.396322660203089
Lambda	1.84239636824139

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 ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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