Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Fri, 13 Aug 2010 14:37:49 +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/Aug/13/t1281710245qkaicjzw3ysuxch.htm/, Retrieved Mon, 06 May 2024 07:42:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78754, Retrieved Mon, 06 May 2024 07:42:21 +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

Reuben Vermoet

Estimated Impact

150

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

-       [Standard Deviation-Mean Plot] [Tijdreeks 1 - sta...] [2010-08-13 14:37:49] [2c3906e099e396db093769aeca236bf5] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78754&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78754&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78754&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	208.25	1.70782512765993	4
2	215.25	12.5266382827424	26
3	202	1.4142135623731	3
4	194	4.69041575982343	10
5	207.5	14.3874945699382	30
6	195.25	2.98607881119482	7
7	176.5	5.44671154612273	13
8	198.25	14.2682631505497	31
9	191.5	3.51188458428425	7
10	165.5	6.85565460040104	15
11	193.25	14.4769932421526	33
12	190.75	6.65206734782504	15
13	180	7.07106781186548	17
14	200.5	16.1967074843418	34
15	185.75	3.40342964277702	7
16	165.75	5.5	13
17	189.75	17.9513230710162	39
18	181.5	7.85281265959316	19
19	163.5	6.13731754650732	13
20	185.75	19.5682566077478	44
21	172.5	2.88675134594813	5
22	145.25	5.31507290636732	12
23	160.75	19.6192932254622	44
24	135.75	3.86221007541882	8
25	105.75	11.7011395456454	25
26	119.25	21.203380233664	49
27	96.5	4.79583152331272	11
28	61.75	16.9779268463496	38
29	64.5	19.192012227313	43
30	36	5.94418483337567	14

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 208.25 & 1.70782512765993 & 4 \tabularnewline
2 & 215.25 & 12.5266382827424 & 26 \tabularnewline
3 & 202 & 1.4142135623731 & 3 \tabularnewline
4 & 194 & 4.69041575982343 & 10 \tabularnewline
5 & 207.5 & 14.3874945699382 & 30 \tabularnewline
6 & 195.25 & 2.98607881119482 & 7 \tabularnewline
7 & 176.5 & 5.44671154612273 & 13 \tabularnewline
8 & 198.25 & 14.2682631505497 & 31 \tabularnewline
9 & 191.5 & 3.51188458428425 & 7 \tabularnewline
10 & 165.5 & 6.85565460040104 & 15 \tabularnewline
11 & 193.25 & 14.4769932421526 & 33 \tabularnewline
12 & 190.75 & 6.65206734782504 & 15 \tabularnewline
13 & 180 & 7.07106781186548 & 17 \tabularnewline
14 & 200.5 & 16.1967074843418 & 34 \tabularnewline
15 & 185.75 & 3.40342964277702 & 7 \tabularnewline
16 & 165.75 & 5.5 & 13 \tabularnewline
17 & 189.75 & 17.9513230710162 & 39 \tabularnewline
18 & 181.5 & 7.85281265959316 & 19 \tabularnewline
19 & 163.5 & 6.13731754650732 & 13 \tabularnewline
20 & 185.75 & 19.5682566077478 & 44 \tabularnewline
21 & 172.5 & 2.88675134594813 & 5 \tabularnewline
22 & 145.25 & 5.31507290636732 & 12 \tabularnewline
23 & 160.75 & 19.6192932254622 & 44 \tabularnewline
24 & 135.75 & 3.86221007541882 & 8 \tabularnewline
25 & 105.75 & 11.7011395456454 & 25 \tabularnewline
26 & 119.25 & 21.203380233664 & 49 \tabularnewline
27 & 96.5 & 4.79583152331272 & 11 \tabularnewline
28 & 61.75 & 16.9779268463496 & 38 \tabularnewline
29 & 64.5 & 19.192012227313 & 43 \tabularnewline
30 & 36 & 5.94418483337567 & 14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78754&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]208.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]215.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]202[/C][C]1.4142135623731[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]194[/C][C]4.69041575982343[/C][C]10[/C][/ROW]
[ROW][C]5[/C][C]207.5[/C][C]14.3874945699382[/C][C]30[/C][/ROW]
[ROW][C]6[/C][C]195.25[/C][C]2.98607881119482[/C][C]7[/C][/ROW]
[ROW][C]7[/C][C]176.5[/C][C]5.44671154612273[/C][C]13[/C][/ROW]
[ROW][C]8[/C][C]198.25[/C][C]14.2682631505497[/C][C]31[/C][/ROW]
[ROW][C]9[/C][C]191.5[/C][C]3.51188458428425[/C][C]7[/C][/ROW]
[ROW][C]10[/C][C]165.5[/C][C]6.85565460040104[/C][C]15[/C][/ROW]
[ROW][C]11[/C][C]193.25[/C][C]14.4769932421526[/C][C]33[/C][/ROW]
[ROW][C]12[/C][C]190.75[/C][C]6.65206734782504[/C][C]15[/C][/ROW]
[ROW][C]13[/C][C]180[/C][C]7.07106781186548[/C][C]17[/C][/ROW]
[ROW][C]14[/C][C]200.5[/C][C]16.1967074843418[/C][C]34[/C][/ROW]
[ROW][C]15[/C][C]185.75[/C][C]3.40342964277702[/C][C]7[/C][/ROW]
[ROW][C]16[/C][C]165.75[/C][C]5.5[/C][C]13[/C][/ROW]
[ROW][C]17[/C][C]189.75[/C][C]17.9513230710162[/C][C]39[/C][/ROW]
[ROW][C]18[/C][C]181.5[/C][C]7.85281265959316[/C][C]19[/C][/ROW]
[ROW][C]19[/C][C]163.5[/C][C]6.13731754650732[/C][C]13[/C][/ROW]
[ROW][C]20[/C][C]185.75[/C][C]19.5682566077478[/C][C]44[/C][/ROW]
[ROW][C]21[/C][C]172.5[/C][C]2.88675134594813[/C][C]5[/C][/ROW]
[ROW][C]22[/C][C]145.25[/C][C]5.31507290636732[/C][C]12[/C][/ROW]
[ROW][C]23[/C][C]160.75[/C][C]19.6192932254622[/C][C]44[/C][/ROW]
[ROW][C]24[/C][C]135.75[/C][C]3.86221007541882[/C][C]8[/C][/ROW]
[ROW][C]25[/C][C]105.75[/C][C]11.7011395456454[/C][C]25[/C][/ROW]
[ROW][C]26[/C][C]119.25[/C][C]21.203380233664[/C][C]49[/C][/ROW]
[ROW][C]27[/C][C]96.5[/C][C]4.79583152331272[/C][C]11[/C][/ROW]
[ROW][C]28[/C][C]61.75[/C][C]16.9779268463496[/C][C]38[/C][/ROW]
[ROW][C]29[/C][C]64.5[/C][C]19.192012227313[/C][C]43[/C][/ROW]
[ROW][C]30[/C][C]36[/C][C]5.94418483337567[/C][C]14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78754&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78754&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	208.25	1.70782512765993	4
2	215.25	12.5266382827424	26
3	202	1.4142135623731	3
4	194	4.69041575982343	10
5	207.5	14.3874945699382	30
6	195.25	2.98607881119482	7
7	176.5	5.44671154612273	13
8	198.25	14.2682631505497	31
9	191.5	3.51188458428425	7
10	165.5	6.85565460040104	15
11	193.25	14.4769932421526	33
12	190.75	6.65206734782504	15
13	180	7.07106781186548	17
14	200.5	16.1967074843418	34
15	185.75	3.40342964277702	7
16	165.75	5.5	13
17	189.75	17.9513230710162	39
18	181.5	7.85281265959316	19
19	163.5	6.13731754650732	13
20	185.75	19.5682566077478	44
21	172.5	2.88675134594813	5
22	145.25	5.31507290636732	12
23	160.75	19.6192932254622	44
24	135.75	3.86221007541882	8
25	105.75	11.7011395456454	25
26	119.25	21.203380233664	49
27	96.5	4.79583152331272	11
28	61.75	16.9779268463496	38
29	64.5	19.192012227313	43
30	36	5.94418483337567	14

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	13.5000268303909
beta	-0.0247310722593749
S.D.	0.0247517686798331
T-STAT	-0.99916384074504
p-value	0.326272405667898

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 13.5000268303909 \tabularnewline
beta & -0.0247310722593749 \tabularnewline
S.D. & 0.0247517686798331 \tabularnewline
T-STAT & -0.99916384074504 \tabularnewline
p-value & 0.326272405667898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78754&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]13.5000268303909[/C][/ROW]
[ROW][C]beta[/C][C]-0.0247310722593749[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0247517686798331[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.99916384074504[/C][/ROW]
[ROW][C]p-value[/C][C]0.326272405667898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78754&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78754&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	13.5000268303909
beta	-0.0247310722593749
S.D.	0.0247517686798331
T-STAT	-0.99916384074504
p-value	0.326272405667898

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	3.79441896821747
beta	-0.35732938400383
S.D.	0.335665931915483
T-STAT	-1.06453872743273
p-value	0.296179254582703
Lambda	1.35732938400383

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.79441896821747 \tabularnewline
beta & -0.35732938400383 \tabularnewline
S.D. & 0.335665931915483 \tabularnewline
T-STAT & -1.06453872743273 \tabularnewline
p-value & 0.296179254582703 \tabularnewline
Lambda & 1.35732938400383 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78754&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.79441896821747[/C][/ROW]
[ROW][C]beta[/C][C]-0.35732938400383[/C][/ROW]
[ROW][C]S.D.[/C][C]0.335665931915483[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.06453872743273[/C][/ROW]
[ROW][C]p-value[/C][C]0.296179254582703[/C][/ROW]
[ROW][C]Lambda[/C][C]1.35732938400383[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78754&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78754&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	3.79441896821747
beta	-0.35732938400383
S.D.	0.335665931915483
T-STAT	-1.06453872743273
p-value	0.296179254582703
Lambda	1.35732938400383

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;

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