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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 computationFri, 21 Dec 2012 11:27:44 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356107530sai0x83mxelp0ld.htm/, Retrieved Sat, 20 Apr 2024 14:20:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203917, Retrieved Sat, 20 Apr 2024 14:20:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
- RMPD  [Multiple Regression] [forecast] [2012-11-24 21:49:17] [0883bf8f4217d775edf6393676d58a73]
- R  D    [Multiple Regression] [] [2012-12-21 11:22:02] [0604709baf8ca89a71bc0fcadc3cdffd]
- RMP       [(Partial) Autocorrelation Function] [] [2012-12-21 15:18:29] [0604709baf8ca89a71bc0fcadc3cdffd]
- RM            [Standard Deviation-Mean Plot] [] [2012-12-21 16:27:44] [b650a28572edc4a1d205c228043a3295] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.4761
1.4721
1.487
1.5167
1.5812
1.554
1.5508
1.5764
1.5611
1.4735
1.4303
1.2757
1.2727
1.3917
1.2816
1.2644
1.3308
1.3275
1.4098
1.4134
1.4138
1.4272
1.4643
1.48
1.5023
1.4406
1.3966
1.357
1.3479
1.3315
1.2307
1.2271
1.3028
1.268
1.3648
1.3857
1.2998
1.3362
1.3692
1.3834
1.4207
1.486
1.4385
1.4453
1.426
1.445
1.3503
1.4001
1.3418
1.2939
1.3176
1.3443
1.3356
1.3214
1.2403
1.259
1.2284
1.2611
1.293
1.2993
1.2986

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203917&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203917&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203917&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11.496241666666670.08483089551179650.3055
21.37310.07494363942930110.2156
31.346250.08178930247899170.2752
41.400041666666670.05382175055991150.1862
51.294641666666670.03973986911112940.1159

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.49624166666667 & 0.0848308955117965 & 0.3055 \tabularnewline
2 & 1.3731 & 0.0749436394293011 & 0.2156 \tabularnewline
3 & 1.34625 & 0.0817893024789917 & 0.2752 \tabularnewline
4 & 1.40004166666667 & 0.0538217505599115 & 0.1862 \tabularnewline
5 & 1.29464166666667 & 0.0397398691111294 & 0.1159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203917&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]1.49624166666667[/C][C]0.0848308955117965[/C][C]0.3055[/C][/ROW]
[ROW][C]2[/C][C]1.3731[/C][C]0.0749436394293011[/C][C]0.2156[/C][/ROW]
[ROW][C]3[/C][C]1.34625[/C][C]0.0817893024789917[/C][C]0.2752[/C][/ROW]
[ROW][C]4[/C][C]1.40004166666667[/C][C]0.0538217505599115[/C][C]0.1862[/C][/ROW]
[ROW][C]5[/C][C]1.29464166666667[/C][C]0.0397398691111294[/C][C]0.1159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203917&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203917&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
11.496241666666670.08483089551179650.3055
21.37310.07494363942930110.2156
31.346250.08178930247899170.2752
41.400041666666670.05382175055991150.1862
51.294641666666670.03973986911112940.1159






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.15427593172899
beta0.160124613815815
S.D.0.11855757568772
T-STAT1.35060634368556
p-value0.269666804323774

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.15427593172899 \tabularnewline
beta & 0.160124613815815 \tabularnewline
S.D. & 0.11855757568772 \tabularnewline
T-STAT & 1.35060634368556 \tabularnewline
p-value & 0.269666804323774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203917&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.15427593172899[/C][/ROW]
[ROW][C]beta[/C][C]0.160124613815815[/C][/ROW]
[ROW][C]S.D.[/C][C]0.11855757568772[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.35060634368556[/C][/ROW]
[ROW][C]p-value[/C][C]0.269666804323774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203917&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203917&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-0.15427593172899
beta0.160124613815815
S.D.0.11855757568772
T-STAT1.35060634368556
p-value0.269666804323774






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.97497470667181
beta3.8246541222681
S.D.2.71575961637895
T-STAT1.40831835748692
p-value0.25378080359514
Lambda-2.8246541222681

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.97497470667181 \tabularnewline
beta & 3.8246541222681 \tabularnewline
S.D. & 2.71575961637895 \tabularnewline
T-STAT & 1.40831835748692 \tabularnewline
p-value & 0.25378080359514 \tabularnewline
Lambda & -2.8246541222681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203917&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.97497470667181[/C][/ROW]
[ROW][C]beta[/C][C]3.8246541222681[/C][/ROW]
[ROW][C]S.D.[/C][C]2.71575961637895[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.40831835748692[/C][/ROW]
[ROW][C]p-value[/C][C]0.25378080359514[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.8246541222681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203917&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203917&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-3.97497470667181
beta3.8246541222681
S.D.2.71575961637895
T-STAT1.40831835748692
p-value0.25378080359514
Lambda-2.8246541222681


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')