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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, 16 Aug 2010 12:59:21 +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/16/t128196357015isgukox3qn5wl.htm/, Retrieved Thu, 16 May 2024 05:07:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78979, Retrieved Thu, 16 May 2024 05:07:17 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

112

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

-       [Standard Deviation-Mean Plot] [Standard Deviatio...] [2010-08-16 12:59:21] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78979&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78979&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78979&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	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	242.25	1.70782512765993	4
2	249.25	12.5266382827424	26
3	236	1.41421356237310	3
4	234.75	3.5	7
5	239.25	11.7295922066086	25
6	229.5	4.12310562561766	8
7	210.75	9.14239210126832	21
8	215.25	8.34166250416147	18
9	198	4.96655480858378	11
10	178.5	13.4039795085887	32
11	182.25	11.1766124861993	25
12	165.25	1.5	3
13	136.75	20.6296711882020	50
14	143.25	2.98607881119482	7
15	137.5	5.56776436283002	13
16	104	23.079572497485	55
17	101.25	2.75378527364305	6
18	94	3.55902608401044	8
19	66.25	25.7471681290713	61
20	67	3.36650164612069	7
21	66.5	5.8022983951764	14
22	49.25	20.2875166871979	48
23	66.5	5.56776436283002	13
24	59	7.7028133388609	17
25	48.5	19.5362910161235	47
26	71	6.48074069840786	15
27	66.5	9.67815409397198	21
28	55.25	18.4639287982452	45
29	81.5	4.12310562561766	8
30	67.5	5.25991127935317	10

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 242.25 & 1.70782512765993 & 4 \tabularnewline
2 & 249.25 & 12.5266382827424 & 26 \tabularnewline
3 & 236 & 1.41421356237310 & 3 \tabularnewline
4 & 234.75 & 3.5 & 7 \tabularnewline
5 & 239.25 & 11.7295922066086 & 25 \tabularnewline
6 & 229.5 & 4.12310562561766 & 8 \tabularnewline
7 & 210.75 & 9.14239210126832 & 21 \tabularnewline
8 & 215.25 & 8.34166250416147 & 18 \tabularnewline
9 & 198 & 4.96655480858378 & 11 \tabularnewline
10 & 178.5 & 13.4039795085887 & 32 \tabularnewline
11 & 182.25 & 11.1766124861993 & 25 \tabularnewline
12 & 165.25 & 1.5 & 3 \tabularnewline
13 & 136.75 & 20.6296711882020 & 50 \tabularnewline
14 & 143.25 & 2.98607881119482 & 7 \tabularnewline
15 & 137.5 & 5.56776436283002 & 13 \tabularnewline
16 & 104 & 23.079572497485 & 55 \tabularnewline
17 & 101.25 & 2.75378527364305 & 6 \tabularnewline
18 & 94 & 3.55902608401044 & 8 \tabularnewline
19 & 66.25 & 25.7471681290713 & 61 \tabularnewline
20 & 67 & 3.36650164612069 & 7 \tabularnewline
21 & 66.5 & 5.8022983951764 & 14 \tabularnewline
22 & 49.25 & 20.2875166871979 & 48 \tabularnewline
23 & 66.5 & 5.56776436283002 & 13 \tabularnewline
24 & 59 & 7.7028133388609 & 17 \tabularnewline
25 & 48.5 & 19.5362910161235 & 47 \tabularnewline
26 & 71 & 6.48074069840786 & 15 \tabularnewline
27 & 66.5 & 9.67815409397198 & 21 \tabularnewline
28 & 55.25 & 18.4639287982452 & 45 \tabularnewline
29 & 81.5 & 4.12310562561766 & 8 \tabularnewline
30 & 67.5 & 5.25991127935317 & 10 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78979&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]242.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]249.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]236[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]234.75[/C][C]3.5[/C][C]7[/C][/ROW]
[ROW][C]5[/C][C]239.25[/C][C]11.7295922066086[/C][C]25[/C][/ROW]
[ROW][C]6[/C][C]229.5[/C][C]4.12310562561766[/C][C]8[/C][/ROW]
[ROW][C]7[/C][C]210.75[/C][C]9.14239210126832[/C][C]21[/C][/ROW]
[ROW][C]8[/C][C]215.25[/C][C]8.34166250416147[/C][C]18[/C][/ROW]
[ROW][C]9[/C][C]198[/C][C]4.96655480858378[/C][C]11[/C][/ROW]
[ROW][C]10[/C][C]178.5[/C][C]13.4039795085887[/C][C]32[/C][/ROW]
[ROW][C]11[/C][C]182.25[/C][C]11.1766124861993[/C][C]25[/C][/ROW]
[ROW][C]12[/C][C]165.25[/C][C]1.5[/C][C]3[/C][/ROW]
[ROW][C]13[/C][C]136.75[/C][C]20.6296711882020[/C][C]50[/C][/ROW]
[ROW][C]14[/C][C]143.25[/C][C]2.98607881119482[/C][C]7[/C][/ROW]
[ROW][C]15[/C][C]137.5[/C][C]5.56776436283002[/C][C]13[/C][/ROW]
[ROW][C]16[/C][C]104[/C][C]23.079572497485[/C][C]55[/C][/ROW]
[ROW][C]17[/C][C]101.25[/C][C]2.75378527364305[/C][C]6[/C][/ROW]
[ROW][C]18[/C][C]94[/C][C]3.55902608401044[/C][C]8[/C][/ROW]
[ROW][C]19[/C][C]66.25[/C][C]25.7471681290713[/C][C]61[/C][/ROW]
[ROW][C]20[/C][C]67[/C][C]3.36650164612069[/C][C]7[/C][/ROW]
[ROW][C]21[/C][C]66.5[/C][C]5.8022983951764[/C][C]14[/C][/ROW]
[ROW][C]22[/C][C]49.25[/C][C]20.2875166871979[/C][C]48[/C][/ROW]
[ROW][C]23[/C][C]66.5[/C][C]5.56776436283002[/C][C]13[/C][/ROW]
[ROW][C]24[/C][C]59[/C][C]7.7028133388609[/C][C]17[/C][/ROW]
[ROW][C]25[/C][C]48.5[/C][C]19.5362910161235[/C][C]47[/C][/ROW]
[ROW][C]26[/C][C]71[/C][C]6.48074069840786[/C][C]15[/C][/ROW]
[ROW][C]27[/C][C]66.5[/C][C]9.67815409397198[/C][C]21[/C][/ROW]
[ROW][C]28[/C][C]55.25[/C][C]18.4639287982452[/C][C]45[/C][/ROW]
[ROW][C]29[/C][C]81.5[/C][C]4.12310562561766[/C][C]8[/C][/ROW]
[ROW][C]30[/C][C]67.5[/C][C]5.25991127935317[/C][C]10[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78979&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78979&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	242.25	1.70782512765993	4
2	249.25	12.5266382827424	26
3	236	1.41421356237310	3
4	234.75	3.5	7
5	239.25	11.7295922066086	25
6	229.5	4.12310562561766	8
7	210.75	9.14239210126832	21
8	215.25	8.34166250416147	18
9	198	4.96655480858378	11
10	178.5	13.4039795085887	32
11	182.25	11.1766124861993	25
12	165.25	1.5	3
13	136.75	20.6296711882020	50
14	143.25	2.98607881119482	7
15	137.5	5.56776436283002	13
16	104	23.079572497485	55
17	101.25	2.75378527364305	6
18	94	3.55902608401044	8
19	66.25	25.7471681290713	61
20	67	3.36650164612069	7
21	66.5	5.8022983951764	14
22	49.25	20.2875166871979	48
23	66.5	5.56776436283002	13
24	59	7.7028133388609	17
25	48.5	19.5362910161235	47
26	71	6.48074069840786	15
27	66.5	9.67815409397198	21
28	55.25	18.4639287982452	45
29	81.5	4.12310562561766	8
30	67.5	5.25991127935317	10

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	13.0378963627019
beta	-0.0288030085855783
S.D.	0.0176026505504006
T-STAT	-1.63628815462242
p-value	0.112972132068010

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 13.0378963627019 \tabularnewline
beta & -0.0288030085855783 \tabularnewline
S.D. & 0.0176026505504006 \tabularnewline
T-STAT & -1.63628815462242 \tabularnewline
p-value & 0.112972132068010 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78979&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]13.0378963627019[/C][/ROW]
[ROW][C]beta[/C][C]-0.0288030085855783[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0176026505504006[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.63628815462242[/C][/ROW]
[ROW][C]p-value[/C][C]0.112972132068010[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78979&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78979&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	13.0378963627019
beta	-0.0288030085855783
S.D.	0.0176026505504006
T-STAT	-1.63628815462242
p-value	0.112972132068010

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.18304937583329
beta	-0.478264612426929
S.D.	0.256356069732124
T-STAT	-1.8656262476121
p-value	0.0726032769100583
Lambda	1.47826461242693

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.18304937583329 \tabularnewline
beta & -0.478264612426929 \tabularnewline
S.D. & 0.256356069732124 \tabularnewline
T-STAT & -1.8656262476121 \tabularnewline
p-value & 0.0726032769100583 \tabularnewline
Lambda & 1.47826461242693 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78979&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.18304937583329[/C][/ROW]
[ROW][C]beta[/C][C]-0.478264612426929[/C][/ROW]
[ROW][C]S.D.[/C][C]0.256356069732124[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.8656262476121[/C][/ROW]
[ROW][C]p-value[/C][C]0.0726032769100583[/C][/ROW]
[ROW][C]Lambda[/C][C]1.47826461242693[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78979&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78979&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	4.18304937583329
beta	-0.478264612426929
S.D.	0.256356069732124
T-STAT	-1.8656262476121
p-value	0.0726032769100583
Lambda	1.47826461242693

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