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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

Tue, 28 Dec 2010 19:27:52 +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/28/t1293564335nik3z8qyg1hlai7.htm/, Retrieved Sun, 05 May 2024 07:33:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116516, Retrieved Sun, 05 May 2024 07:33:07 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

131

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

-     [] [correlation betwe...] [1970-01-01 00:00:00] [1df589bc3feb749f1946d8c1ee38b85f]
-       [Spectral Analysis] [paper: spectral a...] [2010-12-20 18:13:32] [1df589bc3feb749f1946d8c1ee38b85f]
- RMPD    [Spectral Analysis] [paper: spectral a...] [2010-12-20 18:26:23] [1df589bc3feb749f1946d8c1ee38b85f]
- RMP       [Standard Deviation-Mean Plot] [paper: standard d...] [2010-12-21 13:34:54] [1df589bc3feb749f1946d8c1ee38b85f]
-               [Standard Deviation-Mean Plot] [paper] [2010-12-28 19:27:52] [fdda052f11cae2ac9ab9683c59d96811] [Current]

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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=116516&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=116516&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116516&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	557.4235	28.9928268427439	68.247
2	516.761	22.6630255261737	49.335
3	500.84475	19.3844696836583	43.1770000000001
4	459.42475	20.8225332012382	43.7
5	419.304	20.3720509358614	45.48
6	402.79	25.6678876809137	55.684
7	429.496	30.4463356196877	62.977
8	472.9065	34.8406707216341	70.944
9	549.7385	42.6800917563837	79.515
10	588.67625	24.185793204207	56.237
11	596.87225	29.0274963597736	63.3090000000001
12	588.251	23.0717899175595	50.933
13	570.04575	22.5363921894492	55.16
14	541.0475	24.1779538905452	54.5899999999999
15	507.63225	23.2730539089738	54.471
16	474.42675	23.7489296653554	57.501
17	469.7395	28.3565516180417	65.444
18	491.48075	30.9907850752984	64.471
19	538.1405	33.1517496018938	70.024
20	576.612	31.4403791643803	64.641
21	596.39725	23.6003649883499	56.089
22	588.26125	23.6080377184692	51.55
23	532.45875	21.0700082482977	41.997
24	504.865	19.5863059984946	47.578
25	554.52875	27.26852318914	55.781

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 557.4235 & 28.9928268427439 & 68.247 \tabularnewline
2 & 516.761 & 22.6630255261737 & 49.335 \tabularnewline
3 & 500.84475 & 19.3844696836583 & 43.1770000000001 \tabularnewline
4 & 459.42475 & 20.8225332012382 & 43.7 \tabularnewline
5 & 419.304 & 20.3720509358614 & 45.48 \tabularnewline
6 & 402.79 & 25.6678876809137 & 55.684 \tabularnewline
7 & 429.496 & 30.4463356196877 & 62.977 \tabularnewline
8 & 472.9065 & 34.8406707216341 & 70.944 \tabularnewline
9 & 549.7385 & 42.6800917563837 & 79.515 \tabularnewline
10 & 588.67625 & 24.185793204207 & 56.237 \tabularnewline
11 & 596.87225 & 29.0274963597736 & 63.3090000000001 \tabularnewline
12 & 588.251 & 23.0717899175595 & 50.933 \tabularnewline
13 & 570.04575 & 22.5363921894492 & 55.16 \tabularnewline
14 & 541.0475 & 24.1779538905452 & 54.5899999999999 \tabularnewline
15 & 507.63225 & 23.2730539089738 & 54.471 \tabularnewline
16 & 474.42675 & 23.7489296653554 & 57.501 \tabularnewline
17 & 469.7395 & 28.3565516180417 & 65.444 \tabularnewline
18 & 491.48075 & 30.9907850752984 & 64.471 \tabularnewline
19 & 538.1405 & 33.1517496018938 & 70.024 \tabularnewline
20 & 576.612 & 31.4403791643803 & 64.641 \tabularnewline
21 & 596.39725 & 23.6003649883499 & 56.089 \tabularnewline
22 & 588.26125 & 23.6080377184692 & 51.55 \tabularnewline
23 & 532.45875 & 21.0700082482977 & 41.997 \tabularnewline
24 & 504.865 & 19.5863059984946 & 47.578 \tabularnewline
25 & 554.52875 & 27.26852318914 & 55.781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116516&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]557.4235[/C][C]28.9928268427439[/C][C]68.247[/C][/ROW]
[ROW][C]2[/C][C]516.761[/C][C]22.6630255261737[/C][C]49.335[/C][/ROW]
[ROW][C]3[/C][C]500.84475[/C][C]19.3844696836583[/C][C]43.1770000000001[/C][/ROW]
[ROW][C]4[/C][C]459.42475[/C][C]20.8225332012382[/C][C]43.7[/C][/ROW]
[ROW][C]5[/C][C]419.304[/C][C]20.3720509358614[/C][C]45.48[/C][/ROW]
[ROW][C]6[/C][C]402.79[/C][C]25.6678876809137[/C][C]55.684[/C][/ROW]
[ROW][C]7[/C][C]429.496[/C][C]30.4463356196877[/C][C]62.977[/C][/ROW]
[ROW][C]8[/C][C]472.9065[/C][C]34.8406707216341[/C][C]70.944[/C][/ROW]
[ROW][C]9[/C][C]549.7385[/C][C]42.6800917563837[/C][C]79.515[/C][/ROW]
[ROW][C]10[/C][C]588.67625[/C][C]24.185793204207[/C][C]56.237[/C][/ROW]
[ROW][C]11[/C][C]596.87225[/C][C]29.0274963597736[/C][C]63.3090000000001[/C][/ROW]
[ROW][C]12[/C][C]588.251[/C][C]23.0717899175595[/C][C]50.933[/C][/ROW]
[ROW][C]13[/C][C]570.04575[/C][C]22.5363921894492[/C][C]55.16[/C][/ROW]
[ROW][C]14[/C][C]541.0475[/C][C]24.1779538905452[/C][C]54.5899999999999[/C][/ROW]
[ROW][C]15[/C][C]507.63225[/C][C]23.2730539089738[/C][C]54.471[/C][/ROW]
[ROW][C]16[/C][C]474.42675[/C][C]23.7489296653554[/C][C]57.501[/C][/ROW]
[ROW][C]17[/C][C]469.7395[/C][C]28.3565516180417[/C][C]65.444[/C][/ROW]
[ROW][C]18[/C][C]491.48075[/C][C]30.9907850752984[/C][C]64.471[/C][/ROW]
[ROW][C]19[/C][C]538.1405[/C][C]33.1517496018938[/C][C]70.024[/C][/ROW]
[ROW][C]20[/C][C]576.612[/C][C]31.4403791643803[/C][C]64.641[/C][/ROW]
[ROW][C]21[/C][C]596.39725[/C][C]23.6003649883499[/C][C]56.089[/C][/ROW]
[ROW][C]22[/C][C]588.26125[/C][C]23.6080377184692[/C][C]51.55[/C][/ROW]
[ROW][C]23[/C][C]532.45875[/C][C]21.0700082482977[/C][C]41.997[/C][/ROW]
[ROW][C]24[/C][C]504.865[/C][C]19.5863059984946[/C][C]47.578[/C][/ROW]
[ROW][C]25[/C][C]554.52875[/C][C]27.26852318914[/C][C]55.781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116516&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116516&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	557.4235	28.9928268427439	68.247
2	516.761	22.6630255261737	49.335
3	500.84475	19.3844696836583	43.1770000000001
4	459.42475	20.8225332012382	43.7
5	419.304	20.3720509358614	45.48
6	402.79	25.6678876809137	55.684
7	429.496	30.4463356196877	62.977
8	472.9065	34.8406707216341	70.944
9	549.7385	42.6800917563837	79.515
10	588.67625	24.185793204207	56.237
11	596.87225	29.0274963597736	63.3090000000001
12	588.251	23.0717899175595	50.933
13	570.04575	22.5363921894492	55.16
14	541.0475	24.1779538905452	54.5899999999999
15	507.63225	23.2730539089738	54.471
16	474.42675	23.7489296653554	57.501
17	469.7395	28.3565516180417	65.444
18	491.48075	30.9907850752984	64.471
19	538.1405	33.1517496018938	70.024
20	576.612	31.4403791643803	64.641
21	596.39725	23.6003649883499	56.089
22	588.26125	23.6080377184692	51.55
23	532.45875	21.0700082482977	41.997
24	504.865	19.5863059984946	47.578
25	554.52875	27.26852318914	55.781

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	22.3991917175778
beta	0.00729070510241742
S.D.	0.0199456201572606
T-STAT	0.365529125940135
p-value	0.718056692404912

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 22.3991917175778 \tabularnewline
beta & 0.00729070510241742 \tabularnewline
S.D. & 0.0199456201572606 \tabularnewline
T-STAT & 0.365529125940135 \tabularnewline
p-value & 0.718056692404912 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116516&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]22.3991917175778[/C][/ROW]
[ROW][C]beta[/C][C]0.00729070510241742[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0199456201572606[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.365529125940135[/C][/ROW]
[ROW][C]p-value[/C][C]0.718056692404912[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116516&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116516&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	22.3991917175778
beta	0.00729070510241742
S.D.	0.0199456201572606
T-STAT	0.365529125940135
p-value	0.718056692404912

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.2920135420893
beta	0.152675207330269
S.D.	0.357901713689886
T-STAT	0.426584175181007
p-value	0.67364853645006
Lambda	0.847324792669731

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.2920135420893 \tabularnewline
beta & 0.152675207330269 \tabularnewline
S.D. & 0.357901713689886 \tabularnewline
T-STAT & 0.426584175181007 \tabularnewline
p-value & 0.67364853645006 \tabularnewline
Lambda & 0.847324792669731 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116516&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.2920135420893[/C][/ROW]
[ROW][C]beta[/C][C]0.152675207330269[/C][/ROW]
[ROW][C]S.D.[/C][C]0.357901713689886[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.426584175181007[/C][/ROW]
[ROW][C]p-value[/C][C]0.67364853645006[/C][/ROW]
[ROW][C]Lambda[/C][C]0.847324792669731[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116516&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116516&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	2.2920135420893
beta	0.152675207330269
S.D.	0.357901713689886
T-STAT	0.426584175181007
p-value	0.67364853645006
Lambda	0.847324792669731

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