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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, 18 Dec 2012 07:26:14 -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/18/t1355833600dmk0pti9v4yeyai.htm/, Retrieved Thu, 25 Apr 2024 21:41:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201408, Retrieved Thu, 25 Apr 2024 21:41:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63

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] [standar deviation...] [2012-12-18 12:26:14] [239167cccea8953a8e1721fd6db07280] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4143
4429
5219
4929
5761
5592
4163
4962
5208
4755
4491
5732
5731
5040
6102
4904
5369
5578
4619
4731
5011
5299
4146
4625
4736
4219
5116
4205
4121
5103
4300
4578
3809
5657
4248
3830
4736
4839
4411
4570
4104
4801
3953
3828
4440
4026
4109
4785
3224
3552
3940
3913
3681
4309
3830
4143
4087
3818
3380
3430
3458
3970
5260
5024
5634
6549
4676

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201408&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201408&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201408&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14948.66666666667573.0034639484911618
25096.25547.3607959190091956
34493.5562.6640366878071848
44383.5366.9484729743151011
53775.58333333333331.1521096067031085

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4948.66666666667 & 573.003463948491 & 1618 \tabularnewline
2 & 5096.25 & 547.360795919009 & 1956 \tabularnewline
3 & 4493.5 & 562.664036687807 & 1848 \tabularnewline
4 & 4383.5 & 366.948472974315 & 1011 \tabularnewline
5 & 3775.58333333333 & 331.152109606703 & 1085 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201408&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]4948.66666666667[/C][C]573.003463948491[/C][C]1618[/C][/ROW]
[ROW][C]2[/C][C]5096.25[/C][C]547.360795919009[/C][C]1956[/C][/ROW]
[ROW][C]3[/C][C]4493.5[/C][C]562.664036687807[/C][C]1848[/C][/ROW]
[ROW][C]4[/C][C]4383.5[/C][C]366.948472974315[/C][C]1011[/C][/ROW]
[ROW][C]5[/C][C]3775.58333333333[/C][C]331.152109606703[/C][C]1085[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201408&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201408&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
14948.66666666667573.0034639484911618
25096.25547.3607959190091956
34493.5562.6640366878071848
44383.5366.9484729743151011
53775.58333333333331.1521096067031085






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-371.62754972902
beta0.18677240347093
S.D.0.0720874762295068
T-STAT2.59091333529693
p-value0.0810099875984098

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -371.62754972902 \tabularnewline
beta & 0.18677240347093 \tabularnewline
S.D. & 0.0720874762295068 \tabularnewline
T-STAT & 2.59091333529693 \tabularnewline
p-value & 0.0810099875984098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201408&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-371.62754972902[/C][/ROW]
[ROW][C]beta[/C][C]0.18677240347093[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0720874762295068[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.59091333529693[/C][/ROW]
[ROW][C]p-value[/C][C]0.0810099875984098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201408&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201408&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-371.62754972902
beta0.18677240347093
S.D.0.0720874762295068
T-STAT2.59091333529693
p-value0.0810099875984098






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-9.7560064403401
beta1.88890539773239
S.D.0.682372349484237
T-STAT2.7681446927914
p-value0.0696763512558865
Lambda-0.888905397732391

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -9.7560064403401 \tabularnewline
beta & 1.88890539773239 \tabularnewline
S.D. & 0.682372349484237 \tabularnewline
T-STAT & 2.7681446927914 \tabularnewline
p-value & 0.0696763512558865 \tabularnewline
Lambda & -0.888905397732391 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201408&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-9.7560064403401[/C][/ROW]
[ROW][C]beta[/C][C]1.88890539773239[/C][/ROW]
[ROW][C]S.D.[/C][C]0.682372349484237[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.7681446927914[/C][/ROW]
[ROW][C]p-value[/C][C]0.0696763512558865[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.888905397732391[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201408&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201408&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-9.7560064403401
beta1.88890539773239
S.D.0.682372349484237
T-STAT2.7681446927914
p-value0.0696763512558865
Lambda-0.888905397732391


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')