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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

Mon, 19 Jul 2010 15:02:03 +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/Jul/19/t12795530924afb0nivxxpvqry.htm/, Retrieved Fri, 03 May 2024 08:24:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78021, Retrieved Fri, 03 May 2024 08:24:14 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Van Puyenbroeck Cassandra

Estimated Impact

221

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...] [2010-07-19 15:02:03] [0e5311d1fc10a1511b42f76588fb6510] [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	1 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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78021&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78021&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78021&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	347.25	1.70782512765993	4
2	354.25	12.5266382827424	26
3	341	1.4142135623731	3
4	340	3.46410161513775	8
5	343.5	15.2643375224737	32
6	334.75	4.57347424467075	10
7	320.5	7.85281265959316	17
8	309.25	14.3149106412393	30
9	309	5.16397779494322	12
10	309.75	1.70782512765993	4
11	293.75	15.6498136304132	34
12	292	5.16397779494322	12
13	288.5	5.8022983951764	13
14	268.5	9.1104335791443	21
15	275.5	4.12310562561766	8
16	282.25	4.5	9
17	255.25	10.0788557551606	24
18	260.75	4.5	10
19	261	7.61577310586391	18
20	231.25	4.99165971062398	10
21	228.75	5.56027577253743	13
22	223	6.78232998312527	15
23	199.5	8.06225774829855	18
24	181.5	14.5258390463339	32
25	173.25	5.1234753829798	11
26	146.5	9.03696114115064	19
27	132.25	12.8160056179763	30
28	128.25	6.18465843842649	12
29	105.25	6.8495741960115	16
30	110	9.8657657246325	24

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 347.25 & 1.70782512765993 & 4 \tabularnewline
2 & 354.25 & 12.5266382827424 & 26 \tabularnewline
3 & 341 & 1.4142135623731 & 3 \tabularnewline
4 & 340 & 3.46410161513775 & 8 \tabularnewline
5 & 343.5 & 15.2643375224737 & 32 \tabularnewline
6 & 334.75 & 4.57347424467075 & 10 \tabularnewline
7 & 320.5 & 7.85281265959316 & 17 \tabularnewline
8 & 309.25 & 14.3149106412393 & 30 \tabularnewline
9 & 309 & 5.16397779494322 & 12 \tabularnewline
10 & 309.75 & 1.70782512765993 & 4 \tabularnewline
11 & 293.75 & 15.6498136304132 & 34 \tabularnewline
12 & 292 & 5.16397779494322 & 12 \tabularnewline
13 & 288.5 & 5.8022983951764 & 13 \tabularnewline
14 & 268.5 & 9.1104335791443 & 21 \tabularnewline
15 & 275.5 & 4.12310562561766 & 8 \tabularnewline
16 & 282.25 & 4.5 & 9 \tabularnewline
17 & 255.25 & 10.0788557551606 & 24 \tabularnewline
18 & 260.75 & 4.5 & 10 \tabularnewline
19 & 261 & 7.61577310586391 & 18 \tabularnewline
20 & 231.25 & 4.99165971062398 & 10 \tabularnewline
21 & 228.75 & 5.56027577253743 & 13 \tabularnewline
22 & 223 & 6.78232998312527 & 15 \tabularnewline
23 & 199.5 & 8.06225774829855 & 18 \tabularnewline
24 & 181.5 & 14.5258390463339 & 32 \tabularnewline
25 & 173.25 & 5.1234753829798 & 11 \tabularnewline
26 & 146.5 & 9.03696114115064 & 19 \tabularnewline
27 & 132.25 & 12.8160056179763 & 30 \tabularnewline
28 & 128.25 & 6.18465843842649 & 12 \tabularnewline
29 & 105.25 & 6.8495741960115 & 16 \tabularnewline
30 & 110 & 9.8657657246325 & 24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78021&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]347.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]354.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]341[/C][C]1.4142135623731[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]340[/C][C]3.46410161513775[/C][C]8[/C][/ROW]
[ROW][C]5[/C][C]343.5[/C][C]15.2643375224737[/C][C]32[/C][/ROW]
[ROW][C]6[/C][C]334.75[/C][C]4.57347424467075[/C][C]10[/C][/ROW]
[ROW][C]7[/C][C]320.5[/C][C]7.85281265959316[/C][C]17[/C][/ROW]
[ROW][C]8[/C][C]309.25[/C][C]14.3149106412393[/C][C]30[/C][/ROW]
[ROW][C]9[/C][C]309[/C][C]5.16397779494322[/C][C]12[/C][/ROW]
[ROW][C]10[/C][C]309.75[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]11[/C][C]293.75[/C][C]15.6498136304132[/C][C]34[/C][/ROW]
[ROW][C]12[/C][C]292[/C][C]5.16397779494322[/C][C]12[/C][/ROW]
[ROW][C]13[/C][C]288.5[/C][C]5.8022983951764[/C][C]13[/C][/ROW]
[ROW][C]14[/C][C]268.5[/C][C]9.1104335791443[/C][C]21[/C][/ROW]
[ROW][C]15[/C][C]275.5[/C][C]4.12310562561766[/C][C]8[/C][/ROW]
[ROW][C]16[/C][C]282.25[/C][C]4.5[/C][C]9[/C][/ROW]
[ROW][C]17[/C][C]255.25[/C][C]10.0788557551606[/C][C]24[/C][/ROW]
[ROW][C]18[/C][C]260.75[/C][C]4.5[/C][C]10[/C][/ROW]
[ROW][C]19[/C][C]261[/C][C]7.61577310586391[/C][C]18[/C][/ROW]
[ROW][C]20[/C][C]231.25[/C][C]4.99165971062398[/C][C]10[/C][/ROW]
[ROW][C]21[/C][C]228.75[/C][C]5.56027577253743[/C][C]13[/C][/ROW]
[ROW][C]22[/C][C]223[/C][C]6.78232998312527[/C][C]15[/C][/ROW]
[ROW][C]23[/C][C]199.5[/C][C]8.06225774829855[/C][C]18[/C][/ROW]
[ROW][C]24[/C][C]181.5[/C][C]14.5258390463339[/C][C]32[/C][/ROW]
[ROW][C]25[/C][C]173.25[/C][C]5.1234753829798[/C][C]11[/C][/ROW]
[ROW][C]26[/C][C]146.5[/C][C]9.03696114115064[/C][C]19[/C][/ROW]
[ROW][C]27[/C][C]132.25[/C][C]12.8160056179763[/C][C]30[/C][/ROW]
[ROW][C]28[/C][C]128.25[/C][C]6.18465843842649[/C][C]12[/C][/ROW]
[ROW][C]29[/C][C]105.25[/C][C]6.8495741960115[/C][C]16[/C][/ROW]
[ROW][C]30[/C][C]110[/C][C]9.8657657246325[/C][C]24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78021&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78021&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	347.25	1.70782512765993	4
2	354.25	12.5266382827424	26
3	341	1.4142135623731	3
4	340	3.46410161513775	8
5	343.5	15.2643375224737	32
6	334.75	4.57347424467075	10
7	320.5	7.85281265959316	17
8	309.25	14.3149106412393	30
9	309	5.16397779494322	12
10	309.75	1.70782512765993	4
11	293.75	15.6498136304132	34
12	292	5.16397779494322	12
13	288.5	5.8022983951764	13
14	268.5	9.1104335791443	21
15	275.5	4.12310562561766	8
16	282.25	4.5	9
17	255.25	10.0788557551606	24
18	260.75	4.5	10
19	261	7.61577310586391	18
20	231.25	4.99165971062398	10
21	228.75	5.56027577253743	13
22	223	6.78232998312527	15
23	199.5	8.06225774829855	18
24	181.5	14.5258390463339	32
25	173.25	5.1234753829798	11
26	146.5	9.03696114115064	19
27	132.25	12.8160056179763	30
28	128.25	6.18465843842649	12
29	105.25	6.8495741960115	16
30	110	9.8657657246325	24

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	9.86733054859569
beta	-0.00937541137563665
S.D.	0.00994364654297592
T-STAT	-0.94285444832704
p-value	0.353820112149839

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.86733054859569 \tabularnewline
beta & -0.00937541137563665 \tabularnewline
S.D. & 0.00994364654297592 \tabularnewline
T-STAT & -0.94285444832704 \tabularnewline
p-value & 0.353820112149839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78021&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.86733054859569[/C][/ROW]
[ROW][C]beta[/C][C]-0.00937541137563665[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00994364654297592[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.94285444832704[/C][/ROW]
[ROW][C]p-value[/C][C]0.353820112149839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78021&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78021&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	9.86733054859569
beta	-0.00937541137563665
S.D.	0.00994364654297592
T-STAT	-0.94285444832704
p-value	0.353820112149839

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.75316246797811
beta	-0.530163514954486
S.D.	0.315834173139326
T-STAT	-1.67861352584102
p-value	0.104355443476231
Lambda	1.53016351495449

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.75316246797811 \tabularnewline
beta & -0.530163514954486 \tabularnewline
S.D. & 0.315834173139326 \tabularnewline
T-STAT & -1.67861352584102 \tabularnewline
p-value & 0.104355443476231 \tabularnewline
Lambda & 1.53016351495449 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78021&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.75316246797811[/C][/ROW]
[ROW][C]beta[/C][C]-0.530163514954486[/C][/ROW]
[ROW][C]S.D.[/C][C]0.315834173139326[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.67861352584102[/C][/ROW]
[ROW][C]p-value[/C][C]0.104355443476231[/C][/ROW]
[ROW][C]Lambda[/C][C]1.53016351495449[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78021&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78021&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	4.75316246797811
beta	-0.530163514954486
S.D.	0.315834173139326
T-STAT	-1.67861352584102
p-value	0.104355443476231
Lambda	1.53016351495449

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