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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSat, 22 Nov 2014 15:59:05 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/22/t1416671980cm9grqw5wsdv30t.htm/, Retrieved Tue, 28 May 2024 23:18:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=257885, Retrieved Tue, 28 May 2024 23:18:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83

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] [] [2014-11-22 15:59:05] [072d4f39c76834f6beee313555a90f83] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
164,88
164,88
164,57
164,53
165,03
165,92
165,92
165,92
165,92
166,12
166,34
165,48
165,61
165,61
165,94
165,88
166,23
166,32
166,43
166,43
166,2
166,21
168,02
168,68
168,65
168,65
168,75
168,8
168,58
168,98
169
169
168,94
169,96
171,59
172,41
172,65
172,65
172,65
172,38
171,95
171,95
171,87
171,87
171,91
171,99
172,15
172,73
173,2
164,97
164,97
164,43
163,16
162,98
161,69
162,19
162
162,22
164,08
164,58
164,68

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257885&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257885&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257885&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1165.4591666666670.6446628200192331.81
2166.4633333333330.9350773748571293.06999999999999
3169.44251.259004837885143.82999999999998
4172.2291666666670.3547203337158950.859999999999985
5164.2058333333333.0758249694064611.51

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 165.459166666667 & 0.644662820019233 & 1.81 \tabularnewline
2 & 166.463333333333 & 0.935077374857129 & 3.06999999999999 \tabularnewline
3 & 169.4425 & 1.25900483788514 & 3.82999999999998 \tabularnewline
4 & 172.229166666667 & 0.354720333715895 & 0.859999999999985 \tabularnewline
5 & 164.205833333333 & 3.07582496940646 & 11.51 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257885&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]165.459166666667[/C][C]0.644662820019233[/C][C]1.81[/C][/ROW]
[ROW][C]2[/C][C]166.463333333333[/C][C]0.935077374857129[/C][C]3.06999999999999[/C][/ROW]
[ROW][C]3[/C][C]169.4425[/C][C]1.25900483788514[/C][C]3.82999999999998[/C][/ROW]
[ROW][C]4[/C][C]172.229166666667[/C][C]0.354720333715895[/C][C]0.859999999999985[/C][/ROW]
[ROW][C]5[/C][C]164.205833333333[/C][C]3.07582496940646[/C][C]11.51[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257885&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257885&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
1165.4591666666670.6446628200192331.81
2166.4633333333330.9350773748571293.06999999999999
3169.44251.259004837885143.82999999999998
4172.2291666666670.3547203337158950.859999999999985
5164.2058333333333.0758249694064611.51






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha35.6708901935963
beta-0.205401242100857
S.D.0.149224352654998
T-STAT-1.37645926047833
p-value0.262422761314584

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 35.6708901935963 \tabularnewline
beta & -0.205401242100857 \tabularnewline
S.D. & 0.149224352654998 \tabularnewline
T-STAT & -1.37645926047833 \tabularnewline
p-value & 0.262422761314584 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257885&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]35.6708901935963[/C][/ROW]
[ROW][C]beta[/C][C]-0.205401242100857[/C][/ROW]
[ROW][C]S.D.[/C][C]0.149224352654998[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.37645926047833[/C][/ROW]
[ROW][C]p-value[/C][C]0.262422761314584[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257885&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257885&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)
alpha35.6708901935963
beta-0.205401242100857
S.D.0.149224352654998
T-STAT-1.37645926047833
p-value0.262422761314584






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha146.528907989535
beta-28.6196350360378
S.D.17.4242411081857
T-STAT-1.6425183087367
p-value0.199024467762114
Lambda29.6196350360378

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 146.528907989535 \tabularnewline
beta & -28.6196350360378 \tabularnewline
S.D. & 17.4242411081857 \tabularnewline
T-STAT & -1.6425183087367 \tabularnewline
p-value & 0.199024467762114 \tabularnewline
Lambda & 29.6196350360378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257885&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]146.528907989535[/C][/ROW]
[ROW][C]beta[/C][C]-28.6196350360378[/C][/ROW]
[ROW][C]S.D.[/C][C]17.4242411081857[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.6425183087367[/C][/ROW]
[ROW][C]p-value[/C][C]0.199024467762114[/C][/ROW]
[ROW][C]Lambda[/C][C]29.6196350360378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257885&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257885&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)
alpha146.528907989535
beta-28.6196350360378
S.D.17.4242411081857
T-STAT-1.6425183087367
p-value0.199024467762114
Lambda29.6196350360378


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')