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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 11:13:57 +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/t1281957207f7hqz58eygb87yd.htm/, Retrieved Thu, 16 May 2024 07:33:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78956, Retrieved Thu, 16 May 2024 07:33:14 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

134

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

-       [Standard Deviation-Mean Plot] [Aantal bezoekers] [2010-08-16 11:13:57] [5e78ed906b09bab42b8ec3dd93b6358a] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78956&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78956&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78956&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	554.25	1.70782512765993	4
2	561.25	12.5266382827424	26
3	548	1.41421356237310	3
4	552.25	3.20156211871642	6
5	554.25	18.1360598440418	38
6	538.5	3.51188458428425	7
7	547.5	1	2
8	544.5	20.2237484161567	36
9	531	8.28653526310404	19
10	530.75	8.42120339777319	20
11	521.25	21.7159695462425	40
12	506.25	13.0735101126923	30
13	504.5	8.06225774829855	18
14	495.25	26.2979720384165	47
15	457.25	19.4657819433658	44
16	443.75	15.5214904782584	37
17	425.5	25.4099717958652	45
18	381.5	22.5757982509294	52
19	368.5	13.4783777461038	33
20	354.5	30.4247706099268	60
21	298	24.3173463464526	55
22	284.5	12.1243556529821	29
23	268.25	34.9892840738418	64
24	214.5	24.2005509579155	55
25	197.5	19.6892525674965	48
26	171.25	33.8956732735414	62
27	123	21.6794833886788	51
28	120.5	13.8684293751431	31
29	104.75	36.2893464623802	69
30	55.5	18.6993761036743	43

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 554.25 & 1.70782512765993 & 4 \tabularnewline
2 & 561.25 & 12.5266382827424 & 26 \tabularnewline
3 & 548 & 1.41421356237310 & 3 \tabularnewline
4 & 552.25 & 3.20156211871642 & 6 \tabularnewline
5 & 554.25 & 18.1360598440418 & 38 \tabularnewline
6 & 538.5 & 3.51188458428425 & 7 \tabularnewline
7 & 547.5 & 1 & 2 \tabularnewline
8 & 544.5 & 20.2237484161567 & 36 \tabularnewline
9 & 531 & 8.28653526310404 & 19 \tabularnewline
10 & 530.75 & 8.42120339777319 & 20 \tabularnewline
11 & 521.25 & 21.7159695462425 & 40 \tabularnewline
12 & 506.25 & 13.0735101126923 & 30 \tabularnewline
13 & 504.5 & 8.06225774829855 & 18 \tabularnewline
14 & 495.25 & 26.2979720384165 & 47 \tabularnewline
15 & 457.25 & 19.4657819433658 & 44 \tabularnewline
16 & 443.75 & 15.5214904782584 & 37 \tabularnewline
17 & 425.5 & 25.4099717958652 & 45 \tabularnewline
18 & 381.5 & 22.5757982509294 & 52 \tabularnewline
19 & 368.5 & 13.4783777461038 & 33 \tabularnewline
20 & 354.5 & 30.4247706099268 & 60 \tabularnewline
21 & 298 & 24.3173463464526 & 55 \tabularnewline
22 & 284.5 & 12.1243556529821 & 29 \tabularnewline
23 & 268.25 & 34.9892840738418 & 64 \tabularnewline
24 & 214.5 & 24.2005509579155 & 55 \tabularnewline
25 & 197.5 & 19.6892525674965 & 48 \tabularnewline
26 & 171.25 & 33.8956732735414 & 62 \tabularnewline
27 & 123 & 21.6794833886788 & 51 \tabularnewline
28 & 120.5 & 13.8684293751431 & 31 \tabularnewline
29 & 104.75 & 36.2893464623802 & 69 \tabularnewline
30 & 55.5 & 18.6993761036743 & 43 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78956&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]554.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]561.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]548[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]552.25[/C][C]3.20156211871642[/C][C]6[/C][/ROW]
[ROW][C]5[/C][C]554.25[/C][C]18.1360598440418[/C][C]38[/C][/ROW]
[ROW][C]6[/C][C]538.5[/C][C]3.51188458428425[/C][C]7[/C][/ROW]
[ROW][C]7[/C][C]547.5[/C][C]1[/C][C]2[/C][/ROW]
[ROW][C]8[/C][C]544.5[/C][C]20.2237484161567[/C][C]36[/C][/ROW]
[ROW][C]9[/C][C]531[/C][C]8.28653526310404[/C][C]19[/C][/ROW]
[ROW][C]10[/C][C]530.75[/C][C]8.42120339777319[/C][C]20[/C][/ROW]
[ROW][C]11[/C][C]521.25[/C][C]21.7159695462425[/C][C]40[/C][/ROW]
[ROW][C]12[/C][C]506.25[/C][C]13.0735101126923[/C][C]30[/C][/ROW]
[ROW][C]13[/C][C]504.5[/C][C]8.06225774829855[/C][C]18[/C][/ROW]
[ROW][C]14[/C][C]495.25[/C][C]26.2979720384165[/C][C]47[/C][/ROW]
[ROW][C]15[/C][C]457.25[/C][C]19.4657819433658[/C][C]44[/C][/ROW]
[ROW][C]16[/C][C]443.75[/C][C]15.5214904782584[/C][C]37[/C][/ROW]
[ROW][C]17[/C][C]425.5[/C][C]25.4099717958652[/C][C]45[/C][/ROW]
[ROW][C]18[/C][C]381.5[/C][C]22.5757982509294[/C][C]52[/C][/ROW]
[ROW][C]19[/C][C]368.5[/C][C]13.4783777461038[/C][C]33[/C][/ROW]
[ROW][C]20[/C][C]354.5[/C][C]30.4247706099268[/C][C]60[/C][/ROW]
[ROW][C]21[/C][C]298[/C][C]24.3173463464526[/C][C]55[/C][/ROW]
[ROW][C]22[/C][C]284.5[/C][C]12.1243556529821[/C][C]29[/C][/ROW]
[ROW][C]23[/C][C]268.25[/C][C]34.9892840738418[/C][C]64[/C][/ROW]
[ROW][C]24[/C][C]214.5[/C][C]24.2005509579155[/C][C]55[/C][/ROW]
[ROW][C]25[/C][C]197.5[/C][C]19.6892525674965[/C][C]48[/C][/ROW]
[ROW][C]26[/C][C]171.25[/C][C]33.8956732735414[/C][C]62[/C][/ROW]
[ROW][C]27[/C][C]123[/C][C]21.6794833886788[/C][C]51[/C][/ROW]
[ROW][C]28[/C][C]120.5[/C][C]13.8684293751431[/C][C]31[/C][/ROW]
[ROW][C]29[/C][C]104.75[/C][C]36.2893464623802[/C][C]69[/C][/ROW]
[ROW][C]30[/C][C]55.5[/C][C]18.6993761036743[/C][C]43[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78956&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78956&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	554.25	1.70782512765993	4
2	561.25	12.5266382827424	26
3	548	1.41421356237310	3
4	552.25	3.20156211871642	6
5	554.25	18.1360598440418	38
6	538.5	3.51188458428425	7
7	547.5	1	2
8	544.5	20.2237484161567	36
9	531	8.28653526310404	19
10	530.75	8.42120339777319	20
11	521.25	21.7159695462425	40
12	506.25	13.0735101126923	30
13	504.5	8.06225774829855	18
14	495.25	26.2979720384165	47
15	457.25	19.4657819433658	44
16	443.75	15.5214904782584	37
17	425.5	25.4099717958652	45
18	381.5	22.5757982509294	52
19	368.5	13.4783777461038	33
20	354.5	30.4247706099268	60
21	298	24.3173463464526	55
22	284.5	12.1243556529821	29
23	268.25	34.9892840738418	64
24	214.5	24.2005509579155	55
25	197.5	19.6892525674965	48
26	171.25	33.8956732735414	62
27	123	21.6794833886788	51
28	120.5	13.8684293751431	31
29	104.75	36.2893464623802	69
30	55.5	18.6993761036743	43

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	31.1504599322046
beta	-0.0357455513275429
S.D.	0.00928544538990654
T-STAT	-3.84963238989042
p-value	0.0006279520876671

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 31.1504599322046 \tabularnewline
beta & -0.0357455513275429 \tabularnewline
S.D. & 0.00928544538990654 \tabularnewline
T-STAT & -3.84963238989042 \tabularnewline
p-value & 0.0006279520876671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78956&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]31.1504599322046[/C][/ROW]
[ROW][C]beta[/C][C]-0.0357455513275429[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00928544538990654[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.84963238989042[/C][/ROW]
[ROW][C]p-value[/C][C]0.0006279520876671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78956&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78956&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	31.1504599322046
beta	-0.0357455513275429
S.D.	0.00928544538990654
T-STAT	-3.84963238989042
p-value	0.0006279520876671

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	6.68560755644032
beta	-0.710767435643548
S.D.	0.26378315358349
T-STAT	-2.6945141340066
p-value	0.0117808602285926
Lambda	1.71076743564355

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 6.68560755644032 \tabularnewline
beta & -0.710767435643548 \tabularnewline
S.D. & 0.26378315358349 \tabularnewline
T-STAT & -2.6945141340066 \tabularnewline
p-value & 0.0117808602285926 \tabularnewline
Lambda & 1.71076743564355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78956&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.68560755644032[/C][/ROW]
[ROW][C]beta[/C][C]-0.710767435643548[/C][/ROW]
[ROW][C]S.D.[/C][C]0.26378315358349[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.6945141340066[/C][/ROW]
[ROW][C]p-value[/C][C]0.0117808602285926[/C][/ROW]
[ROW][C]Lambda[/C][C]1.71076743564355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78956&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78956&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	6.68560755644032
beta	-0.710767435643548
S.D.	0.26378315358349
T-STAT	-2.6945141340066
p-value	0.0117808602285926
Lambda	1.71076743564355

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