Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

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

Sun, 21 Dec 2008 12:08:57 -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/2008/Dec/21/t1229886610hegxzko1xtcsum6.htm/, Retrieved Sun, 19 May 2024 10:21:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35767, Retrieved Sun, 19 May 2024 10:21:39 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

142

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

-       [Standard Deviation-Mean Plot] [paper-SDMP] [2008-12-21 19:08:57] [a16dfd7e948381d8b6391003c5d09447] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

7.5
7.2
6.9
6.7
6.4
6.3
6.8
7.3
7.1
7.1
6.8
6.5
6.3
6.1
6.1
6.3
6.3
6
6.2
6.4
6.8
7.5
7.5
7.6
7.6
7.4
7.3
7.1
6.9
6.8
7.5
7.6
7.8
8
8.1
8.2
8.3
8.2
8
7.9
7.6
7.6
8.2
8.3
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.5
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.6
8.2
8.1
8
8.6
8.7
8.8
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.1
8.2
8.1
8.1
7.9
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.6
6.2
6.2
6.8
6.9
6.8
6.7

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=35767&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=35767&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35767&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	7.075	0.35	0.8
2	6.7	0.454606056566195	1
3	6.875	0.287228132326901	0.6
4	6.2	0.115470053837925	0.2
5	6.225	0.170782512765993	0.4
6	7.35	0.369684550213647	0.8
7	7.35	0.208166599946613	0.5
8	7.2	0.408248290463863	0.8
9	8.025	0.170782512765993	0.399999999999999
10	8.1	0.182574185835055	0.4
11	7.925	0.377491721763538	0.700000000000001
12	8.45	0.0999999999999996	0.199999999999999
13	8.375	0.639661368746516	1.4
14	8.2	1.00995049383621	2.1
15	8.625	0.499165971062398	1.10000000000000
16	8.475	0.189296944860009	0.4
17	8.35	0.351188458428424	0.700
18	8.55	0.173205080756888	0.4
19	8.625	0.0957427107756335	0.199999999999999
20	8.175	0.0957427107756342	0.200000000000001
21	7.95	0.0999999999999996	0.199999999999999
22	7.975	0.0499999999999998	0.0999999999999996
23	7.425	0.221735578260835	0.5
24	7.05	0.1	0.2
25	6.95	0.310912635102961	0.7
26	6.525	0.377491721763537	0.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7.075 & 0.35 & 0.8 \tabularnewline
2 & 6.7 & 0.454606056566195 & 1 \tabularnewline
3 & 6.875 & 0.287228132326901 & 0.6 \tabularnewline
4 & 6.2 & 0.115470053837925 & 0.2 \tabularnewline
5 & 6.225 & 0.170782512765993 & 0.4 \tabularnewline
6 & 7.35 & 0.369684550213647 & 0.8 \tabularnewline
7 & 7.35 & 0.208166599946613 & 0.5 \tabularnewline
8 & 7.2 & 0.408248290463863 & 0.8 \tabularnewline
9 & 8.025 & 0.170782512765993 & 0.399999999999999 \tabularnewline
10 & 8.1 & 0.182574185835055 & 0.4 \tabularnewline
11 & 7.925 & 0.377491721763538 & 0.700000000000001 \tabularnewline
12 & 8.45 & 0.0999999999999996 & 0.199999999999999 \tabularnewline
13 & 8.375 & 0.639661368746516 & 1.4 \tabularnewline
14 & 8.2 & 1.00995049383621 & 2.1 \tabularnewline
15 & 8.625 & 0.499165971062398 & 1.10000000000000 \tabularnewline
16 & 8.475 & 0.189296944860009 & 0.4 \tabularnewline
17 & 8.35 & 0.351188458428424 & 0.700 \tabularnewline
18 & 8.55 & 0.173205080756888 & 0.4 \tabularnewline
19 & 8.625 & 0.0957427107756335 & 0.199999999999999 \tabularnewline
20 & 8.175 & 0.0957427107756342 & 0.200000000000001 \tabularnewline
21 & 7.95 & 0.0999999999999996 & 0.199999999999999 \tabularnewline
22 & 7.975 & 0.0499999999999998 & 0.0999999999999996 \tabularnewline
23 & 7.425 & 0.221735578260835 & 0.5 \tabularnewline
24 & 7.05 & 0.1 & 0.2 \tabularnewline
25 & 6.95 & 0.310912635102961 & 0.7 \tabularnewline
26 & 6.525 & 0.377491721763537 & 0.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35767&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]7.075[/C][C]0.35[/C][C]0.8[/C][/ROW]
[ROW][C]2[/C][C]6.7[/C][C]0.454606056566195[/C][C]1[/C][/ROW]
[ROW][C]3[/C][C]6.875[/C][C]0.287228132326901[/C][C]0.6[/C][/ROW]
[ROW][C]4[/C][C]6.2[/C][C]0.115470053837925[/C][C]0.2[/C][/ROW]
[ROW][C]5[/C][C]6.225[/C][C]0.170782512765993[/C][C]0.4[/C][/ROW]
[ROW][C]6[/C][C]7.35[/C][C]0.369684550213647[/C][C]0.8[/C][/ROW]
[ROW][C]7[/C][C]7.35[/C][C]0.208166599946613[/C][C]0.5[/C][/ROW]
[ROW][C]8[/C][C]7.2[/C][C]0.408248290463863[/C][C]0.8[/C][/ROW]
[ROW][C]9[/C][C]8.025[/C][C]0.170782512765993[/C][C]0.399999999999999[/C][/ROW]
[ROW][C]10[/C][C]8.1[/C][C]0.182574185835055[/C][C]0.4[/C][/ROW]
[ROW][C]11[/C][C]7.925[/C][C]0.377491721763538[/C][C]0.700000000000001[/C][/ROW]
[ROW][C]12[/C][C]8.45[/C][C]0.0999999999999996[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]13[/C][C]8.375[/C][C]0.639661368746516[/C][C]1.4[/C][/ROW]
[ROW][C]14[/C][C]8.2[/C][C]1.00995049383621[/C][C]2.1[/C][/ROW]
[ROW][C]15[/C][C]8.625[/C][C]0.499165971062398[/C][C]1.10000000000000[/C][/ROW]
[ROW][C]16[/C][C]8.475[/C][C]0.189296944860009[/C][C]0.4[/C][/ROW]
[ROW][C]17[/C][C]8.35[/C][C]0.351188458428424[/C][C]0.700[/C][/ROW]
[ROW][C]18[/C][C]8.55[/C][C]0.173205080756888[/C][C]0.4[/C][/ROW]
[ROW][C]19[/C][C]8.625[/C][C]0.0957427107756335[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]20[/C][C]8.175[/C][C]0.0957427107756342[/C][C]0.200000000000001[/C][/ROW]
[ROW][C]21[/C][C]7.95[/C][C]0.0999999999999996[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]22[/C][C]7.975[/C][C]0.0499999999999998[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]23[/C][C]7.425[/C][C]0.221735578260835[/C][C]0.5[/C][/ROW]
[ROW][C]24[/C][C]7.05[/C][C]0.1[/C][C]0.2[/C][/ROW]
[ROW][C]25[/C][C]6.95[/C][C]0.310912635102961[/C][C]0.7[/C][/ROW]
[ROW][C]26[/C][C]6.525[/C][C]0.377491721763537[/C][C]0.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35767&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35767&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	7.075	0.35	0.8
2	6.7	0.454606056566195	1
3	6.875	0.287228132326901	0.6
4	6.2	0.115470053837925	0.2
5	6.225	0.170782512765993	0.4
6	7.35	0.369684550213647	0.8
7	7.35	0.208166599946613	0.5
8	7.2	0.408248290463863	0.8
9	8.025	0.170782512765993	0.399999999999999
10	8.1	0.182574185835055	0.4
11	7.925	0.377491721763538	0.700000000000001
12	8.45	0.0999999999999996	0.199999999999999
13	8.375	0.639661368746516	1.4
14	8.2	1.00995049383621	2.1
15	8.625	0.499165971062398	1.10000000000000
16	8.475	0.189296944860009	0.4
17	8.35	0.351188458428424	0.700
18	8.55	0.173205080756888	0.4
19	8.625	0.0957427107756335	0.199999999999999
20	8.175	0.0957427107756342	0.200000000000001
21	7.95	0.0999999999999996	0.199999999999999
22	7.975	0.0499999999999998	0.0999999999999996
23	7.425	0.221735578260835	0.5
24	7.05	0.1	0.2
25	6.95	0.310912635102961	0.7
26	6.525	0.377491721763537	0.7

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.151445403216419
beta	0.017469104577823
S.D.	0.0556500795218583
T-STAT	0.313909786435461
p-value	0.756301840383595

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.151445403216419 \tabularnewline
beta & 0.017469104577823 \tabularnewline
S.D. & 0.0556500795218583 \tabularnewline
T-STAT & 0.313909786435461 \tabularnewline
p-value & 0.756301840383595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35767&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.151445403216419[/C][/ROW]
[ROW][C]beta[/C][C]0.017469104577823[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0556500795218583[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.313909786435461[/C][/ROW]
[ROW][C]p-value[/C][C]0.756301840383595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35767&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35767&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	0.151445403216419
beta	0.017469104577823
S.D.	0.0556500795218583
T-STAT	0.313909786435461
p-value	0.756301840383595

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.652288275975541
beta	-0.413187498846451
S.D.	1.40181969158158
T-STAT	-0.294750816619133
p-value	0.770718819550992
Lambda	1.41318749884645

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.652288275975541 \tabularnewline
beta & -0.413187498846451 \tabularnewline
S.D. & 1.40181969158158 \tabularnewline
T-STAT & -0.294750816619133 \tabularnewline
p-value & 0.770718819550992 \tabularnewline
Lambda & 1.41318749884645 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35767&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.652288275975541[/C][/ROW]
[ROW][C]beta[/C][C]-0.413187498846451[/C][/ROW]
[ROW][C]S.D.[/C][C]1.40181969158158[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.294750816619133[/C][/ROW]
[ROW][C]p-value[/C][C]0.770718819550992[/C][/ROW]
[ROW][C]Lambda[/C][C]1.41318749884645[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35767&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35767&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	-0.652288275975541
beta	-0.413187498846451
S.D.	1.40181969158158
T-STAT	-0.294750816619133
p-value	0.770718819550992
Lambda	1.41318749884645

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

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