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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

Sun, 15 Aug 2010 16:06:10 +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/Aug/15/t128188834153swxt7oh7gobmt.htm/, Retrieved Sat, 27 Apr 2024 16:53:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78898, Retrieved Sat, 27 Apr 2024 16:53:22 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

128

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

-     [Mean Plot] [Mean vs Median pl...] [2010-08-15 15:07:22] [f5ecd041e4b32af12787a4e421b18aaf]
-   P   [Mean Plot] [Mean&Median Plot ...] [2010-08-15 15:22:42] [f5ecd041e4b32af12787a4e421b18aaf]
- RM        [Standard Deviation-Mean Plot] [SD Mean Plot omze...] [2010-08-15 16:06:10] [05b8da000f2ebbd12b039a4b088dd3f2] [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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78898&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78898&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78898&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	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	116.25	1.70782512765993	4
2	112.25	1.25830573921179	3
3	116	1.41421356237310	3
4	125.75	3.86221007541882	9
5	112	4.96655480858378	11
6	122.5	4.20317340430616	10
7	132.5	6.1913918736689	14
8	101.5	8.9628864398325	21
9	124.75	9.77667291737498	23
10	147	7.74596669241483	18
11	122.5	10.7857931249090	25
12	140.5	9.74679434480896	23
13	165	7.52772652709081	18
14	144.25	11.6726175299288	28
15	165.5	11.0302614051829	26
16	196.5	10.3762549441823	22
17	171.75	16.6408132814075	35
18	166.75	12.8160056179763	30
19	198.25	12.5266382827424	26
20	160.25	18.5539753152795	39
21	149.5	11.9023807142381	28

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 116.25 & 1.70782512765993 & 4 \tabularnewline
2 & 112.25 & 1.25830573921179 & 3 \tabularnewline
3 & 116 & 1.41421356237310 & 3 \tabularnewline
4 & 125.75 & 3.86221007541882 & 9 \tabularnewline
5 & 112 & 4.96655480858378 & 11 \tabularnewline
6 & 122.5 & 4.20317340430616 & 10 \tabularnewline
7 & 132.5 & 6.1913918736689 & 14 \tabularnewline
8 & 101.5 & 8.9628864398325 & 21 \tabularnewline
9 & 124.75 & 9.77667291737498 & 23 \tabularnewline
10 & 147 & 7.74596669241483 & 18 \tabularnewline
11 & 122.5 & 10.7857931249090 & 25 \tabularnewline
12 & 140.5 & 9.74679434480896 & 23 \tabularnewline
13 & 165 & 7.52772652709081 & 18 \tabularnewline
14 & 144.25 & 11.6726175299288 & 28 \tabularnewline
15 & 165.5 & 11.0302614051829 & 26 \tabularnewline
16 & 196.5 & 10.3762549441823 & 22 \tabularnewline
17 & 171.75 & 16.6408132814075 & 35 \tabularnewline
18 & 166.75 & 12.8160056179763 & 30 \tabularnewline
19 & 198.25 & 12.5266382827424 & 26 \tabularnewline
20 & 160.25 & 18.5539753152795 & 39 \tabularnewline
21 & 149.5 & 11.9023807142381 & 28 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78898&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]116.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]112.25[/C][C]1.25830573921179[/C][C]3[/C][/ROW]
[ROW][C]3[/C][C]116[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]125.75[/C][C]3.86221007541882[/C][C]9[/C][/ROW]
[ROW][C]5[/C][C]112[/C][C]4.96655480858378[/C][C]11[/C][/ROW]
[ROW][C]6[/C][C]122.5[/C][C]4.20317340430616[/C][C]10[/C][/ROW]
[ROW][C]7[/C][C]132.5[/C][C]6.1913918736689[/C][C]14[/C][/ROW]
[ROW][C]8[/C][C]101.5[/C][C]8.9628864398325[/C][C]21[/C][/ROW]
[ROW][C]9[/C][C]124.75[/C][C]9.77667291737498[/C][C]23[/C][/ROW]
[ROW][C]10[/C][C]147[/C][C]7.74596669241483[/C][C]18[/C][/ROW]
[ROW][C]11[/C][C]122.5[/C][C]10.7857931249090[/C][C]25[/C][/ROW]
[ROW][C]12[/C][C]140.5[/C][C]9.74679434480896[/C][C]23[/C][/ROW]
[ROW][C]13[/C][C]165[/C][C]7.52772652709081[/C][C]18[/C][/ROW]
[ROW][C]14[/C][C]144.25[/C][C]11.6726175299288[/C][C]28[/C][/ROW]
[ROW][C]15[/C][C]165.5[/C][C]11.0302614051829[/C][C]26[/C][/ROW]
[ROW][C]16[/C][C]196.5[/C][C]10.3762549441823[/C][C]22[/C][/ROW]
[ROW][C]17[/C][C]171.75[/C][C]16.6408132814075[/C][C]35[/C][/ROW]
[ROW][C]18[/C][C]166.75[/C][C]12.8160056179763[/C][C]30[/C][/ROW]
[ROW][C]19[/C][C]198.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]20[/C][C]160.25[/C][C]18.5539753152795[/C][C]39[/C][/ROW]
[ROW][C]21[/C][C]149.5[/C][C]11.9023807142381[/C][C]28[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78898&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78898&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	116.25	1.70782512765993	4
2	112.25	1.25830573921179	3
3	116	1.41421356237310	3
4	125.75	3.86221007541882	9
5	112	4.96655480858378	11
6	122.5	4.20317340430616	10
7	132.5	6.1913918736689	14
8	101.5	8.9628864398325	21
9	124.75	9.77667291737498	23
10	147	7.74596669241483	18
11	122.5	10.7857931249090	25
12	140.5	9.74679434480896	23
13	165	7.52772652709081	18
14	144.25	11.6726175299288	28
15	165.5	11.0302614051829	26
16	196.5	10.3762549441823	22
17	171.75	16.6408132814075	35
18	166.75	12.8160056179763	30
19	198.25	12.5266382827424	26
20	160.25	18.5539753152795	39
21	149.5	11.9023807142381	28

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-7.06729621273609
beta	0.111017695677743
S.D.	0.0299297588886578
T-STAT	3.70927464169497
p-value	0.00148794886760987

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -7.06729621273609 \tabularnewline
beta & 0.111017695677743 \tabularnewline
S.D. & 0.0299297588886578 \tabularnewline
T-STAT & 3.70927464169497 \tabularnewline
p-value & 0.00148794886760987 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78898&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.06729621273609[/C][/ROW]
[ROW][C]beta[/C][C]0.111017695677743[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0299297588886578[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.70927464169497[/C][/ROW]
[ROW][C]p-value[/C][C]0.00148794886760987[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78898&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78898&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	-7.06729621273609
beta	0.111017695677743
S.D.	0.0299297588886578
T-STAT	3.70927464169497
p-value	0.00148794886760987

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-10.8429663653601
beta	2.58941668643878
S.D.	0.721881586152709
T-STAT	3.58703800749256
p-value	0.00196555831927006
Lambda	-1.58941668643878

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -10.8429663653601 \tabularnewline
beta & 2.58941668643878 \tabularnewline
S.D. & 0.721881586152709 \tabularnewline
T-STAT & 3.58703800749256 \tabularnewline
p-value & 0.00196555831927006 \tabularnewline
Lambda & -1.58941668643878 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78898&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.8429663653601[/C][/ROW]
[ROW][C]beta[/C][C]2.58941668643878[/C][/ROW]
[ROW][C]S.D.[/C][C]0.721881586152709[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.58703800749256[/C][/ROW]
[ROW][C]p-value[/C][C]0.00196555831927006[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.58941668643878[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78898&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78898&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	-10.8429663653601
beta	2.58941668643878
S.D.	0.721881586152709
T-STAT	3.58703800749256
p-value	0.00196555831927006
Lambda	-1.58941668643878

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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