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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 computationTue, 13 Dec 2016 19:15:38 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/13/t1481653070frbxe9d5qdpnq0b.htm/, Retrieved Fri, 17 May 2024 14:54:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299190, Retrieved Fri, 17 May 2024 14:54:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [Univariate analys...] [2016-12-13 18:15:38] [bd7223969ac5b08f41438741a34686d6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5350
6100
4820
5130
4060
6710
4510
5630
5200
4510
4810
4930
4720
4400
4090
4160
5020
5930
4390
4490
5760
5040
4800
4820
4620
4380
4250
4230
3800
6360
4280
4680
5070
4560
4690
4820
4370
3850
5050
4010
4570
4240
3850
4830
5400
4680
4390
4140
4300
4180
4120
3910
4300
4240
3610
3600
3970
3790
3750
3680
3970
4290
3670
3760
4160
3620
4280
4410
4500
4690
3650
3720
3770
3970
3390
3400
3130
3930
3740
3400
3620
3980
3440
3420
3740
3630
3650
3940
3540
3590
3740
3910
3670
3510
3430
3420
3630
3690
3350
3470
3380
3990
3790
3440
3580
3600
3990
3640

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299190&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299190&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299190&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
15146.66666666667731.7144665824652650
24801.66666666667575.9708536396821840
34645633.123569728262560
44448.33333333333480.3376337788271550
53954.16666666667267.868975207634700
64060375.5964952881311070
73599.16666666667276.683551876124850
83647.5166.576490756431520
93629.16666666667212.023083363081640

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5146.66666666667 & 731.714466582465 & 2650 \tabularnewline
2 & 4801.66666666667 & 575.970853639682 & 1840 \tabularnewline
3 & 4645 & 633.12356972826 & 2560 \tabularnewline
4 & 4448.33333333333 & 480.337633778827 & 1550 \tabularnewline
5 & 3954.16666666667 & 267.868975207634 & 700 \tabularnewline
6 & 4060 & 375.596495288131 & 1070 \tabularnewline
7 & 3599.16666666667 & 276.683551876124 & 850 \tabularnewline
8 & 3647.5 & 166.576490756431 & 520 \tabularnewline
9 & 3629.16666666667 & 212.023083363081 & 640 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299190&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]5146.66666666667[/C][C]731.714466582465[/C][C]2650[/C][/ROW]
[ROW][C]2[/C][C]4801.66666666667[/C][C]575.970853639682[/C][C]1840[/C][/ROW]
[ROW][C]3[/C][C]4645[/C][C]633.12356972826[/C][C]2560[/C][/ROW]
[ROW][C]4[/C][C]4448.33333333333[/C][C]480.337633778827[/C][C]1550[/C][/ROW]
[ROW][C]5[/C][C]3954.16666666667[/C][C]267.868975207634[/C][C]700[/C][/ROW]
[ROW][C]6[/C][C]4060[/C][C]375.596495288131[/C][C]1070[/C][/ROW]
[ROW][C]7[/C][C]3599.16666666667[/C][C]276.683551876124[/C][C]850[/C][/ROW]
[ROW][C]8[/C][C]3647.5[/C][C]166.576490756431[/C][C]520[/C][/ROW]
[ROW][C]9[/C][C]3629.16666666667[/C][C]212.023083363081[/C][C]640[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299190&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299190&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
15146.66666666667731.7144665824652650
24801.66666666667575.9708536396821840
34645633.123569728262560
44448.33333333333480.3376337788271550
53954.16666666667267.868975207634700
64060375.5964952881311070
73599.16666666667276.683551876124850
83647.5166.576490756431520
93629.16666666667212.023083363081640






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1032.9177058907
beta0.343147444261265
S.D.0.0319889435880909
T-STAT10.7270639718473
p-value1.34453163421527e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1032.9177058907 \tabularnewline
beta & 0.343147444261265 \tabularnewline
S.D. & 0.0319889435880909 \tabularnewline
T-STAT & 10.7270639718473 \tabularnewline
p-value & 1.34453163421527e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299190&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1032.9177058907[/C][/ROW]
[ROW][C]beta[/C][C]0.343147444261265[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0319889435880909[/C][/ROW]
[ROW][C]T-STAT[/C][C]10.7270639718473[/C][/ROW]
[ROW][C]p-value[/C][C]1.34453163421527e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299190&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299190&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-1032.9177058907
beta0.343147444261265
S.D.0.0319889435880909
T-STAT10.7270639718473
p-value1.34453163421527e-05






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-24.8147500652895
beta3.68476124901959
S.D.0.47041158848358
T-STAT7.83305798417467
p-value0.000104261633919383
Lambda-2.68476124901959

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -24.8147500652895 \tabularnewline
beta & 3.68476124901959 \tabularnewline
S.D. & 0.47041158848358 \tabularnewline
T-STAT & 7.83305798417467 \tabularnewline
p-value & 0.000104261633919383 \tabularnewline
Lambda & -2.68476124901959 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299190&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-24.8147500652895[/C][/ROW]
[ROW][C]beta[/C][C]3.68476124901959[/C][/ROW]
[ROW][C]S.D.[/C][C]0.47041158848358[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.83305798417467[/C][/ROW]
[ROW][C]p-value[/C][C]0.000104261633919383[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.68476124901959[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299190&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299190&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-24.8147500652895
beta3.68476124901959
S.D.0.47041158848358
T-STAT7.83305798417467
p-value0.000104261633919383
Lambda-2.68476124901959


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
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')