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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSun, 21 Dec 2008 10:50:16 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/21/t1229881911jva1a1zk343v87r.htm/, Retrieved Sat, 18 May 2024 09:22:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35713, Retrieved Sat, 18 May 2024 09:22:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean Plot] [Paper - Mean plot...] [2008-12-18 11:43:00] [85841a4a203c2f9589565c024425a91b]
- RMP     [Standard Deviation-Mean Plot] [Paper - Standard ...] [2008-12-21 17:50:16] [07b7cf1321bc38017c2c7efcf91ca696] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20.72
21.45
22.09
21.53
23.35
23.57
26.42
25.21
26.44
29.34
29.40
33.05
28.38
26.01
29.31
30.36
35.75
36.15
34.21
37.91
38.70
42.12
42.16
39.80
37.36
38.35
42.60
41.25
42.16
46.94
47.43
47.06
50.18
50.13
43.23
40.04
40.37
42.21
37.00
39.74
42.68
46.29
46.97
48.73
52.37
50.05
54.04
57.78
64.72
63.41
64.36
66.03
72.14
76.60
86.97
93.48
95.59
81.89
70.55
50.38
36.25

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 0 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35713&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35713&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35713&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
125.21416666666673.8468297651994212.33
235.07166666666675.4618991591059616.15
343.89416666666674.3755694867449412.82
446.51916666666676.3453912528318720.78
573.843333333333313.519415219556945.21

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 25.2141666666667 & 3.84682976519942 & 12.33 \tabularnewline
2 & 35.0716666666667 & 5.46189915910596 & 16.15 \tabularnewline
3 & 43.8941666666667 & 4.37556948674494 & 12.82 \tabularnewline
4 & 46.5191666666667 & 6.34539125283187 & 20.78 \tabularnewline
5 & 73.8433333333333 & 13.5194152195569 & 45.21 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35713&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]25.2141666666667[/C][C]3.84682976519942[/C][C]12.33[/C][/ROW]
[ROW][C]2[/C][C]35.0716666666667[/C][C]5.46189915910596[/C][C]16.15[/C][/ROW]
[ROW][C]3[/C][C]43.8941666666667[/C][C]4.37556948674494[/C][C]12.82[/C][/ROW]
[ROW][C]4[/C][C]46.5191666666667[/C][C]6.34539125283187[/C][C]20.78[/C][/ROW]
[ROW][C]5[/C][C]73.8433333333333[/C][C]13.5194152195569[/C][C]45.21[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35713&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35713&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
125.21416666666673.8468297651994212.33
235.07166666666675.4618991591059616.15
343.89416666666674.3755694867449412.82
446.51916666666676.3453912528318720.78
573.843333333333313.519415219556945.21






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.35251442716603
beta0.201795548812672
S.D.0.0440924880739955
T-STAT4.57664236307147
p-value0.0195795615501518

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.35251442716603 \tabularnewline
beta & 0.201795548812672 \tabularnewline
S.D. & 0.0440924880739955 \tabularnewline
T-STAT & 4.57664236307147 \tabularnewline
p-value & 0.0195795615501518 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35713&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.35251442716603[/C][/ROW]
[ROW][C]beta[/C][C]0.201795548812672[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0440924880739955[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.57664236307147[/C][/ROW]
[ROW][C]p-value[/C][C]0.0195795615501518[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35713&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35713&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.35251442716603
beta0.201795548812672
S.D.0.0440924880739955
T-STAT4.57664236307147
p-value0.0195795615501518






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.36895046043237
beta1.11274616301469
S.D.0.324512888375723
T-STAT3.4289737106723
p-value0.0415692109985349
Lambda-0.112746163014690

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.36895046043237 \tabularnewline
beta & 1.11274616301469 \tabularnewline
S.D. & 0.324512888375723 \tabularnewline
T-STAT & 3.4289737106723 \tabularnewline
p-value & 0.0415692109985349 \tabularnewline
Lambda & -0.112746163014690 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35713&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.36895046043237[/C][/ROW]
[ROW][C]beta[/C][C]1.11274616301469[/C][/ROW]
[ROW][C]S.D.[/C][C]0.324512888375723[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.4289737106723[/C][/ROW]
[ROW][C]p-value[/C][C]0.0415692109985349[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.112746163014690[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35713&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35713&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.36895046043237
beta1.11274616301469
S.D.0.324512888375723
T-STAT3.4289737106723
p-value0.0415692109985349
Lambda-0.112746163014690


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 12 ;
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')