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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 computationMon, 02 Dec 2013 10:31:10 -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/2013/Dec/02/t13859983385hwbgu6vfjtc1ot.htm/, Retrieved Tue, 23 Apr 2024 15:23:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230013, Retrieved Tue, 23 Apr 2024 15:23:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80

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] [Standard Deviatio...] [2013-12-02 15:31:10] [45baafc513cf820e9f0a314ccf5f72d1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
31.5
31.29
31.3
31.06
31.09
31.11
31.13
31.1
31.03
30.74
30.83
30.82
30.8
30.74
30.71
30.58
30.71
30.7
30.7
30.72
30.68
30.78
30.84
30.8
30.8
30.88
30.87
30.92
30.82
30.75
30.75
30.75
30.63
30.52
30.58
30.6
30.6
30.63
30.56
30.61
30.53
30.6
30.6
30.63
30.66
30.34
30.32
30.3
30.3
30.08
29.96
29.91
29.83
29.89
29.85
30.06
29.83
29.95
30.02
30.03
30.03
29.96
29.85
30.12
29.91
29.9
29.92
29.89
29.96
29.72
29.6
29.54
29.54
29.54
29.48
29.55
29.58
29.6
29.6
29.56
29.7
29.76
29.24
29.28

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230013&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230013&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230013&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
131.08333333333330.2176875715053090.760000000000002
230.730.06888725967444650.260000000000002
330.73916666666670.1296469565139630.400000000000002
430.53166666666670.1321041829448070.359999999999999
529.97583333333330.1344658343448650.470000000000002
629.86666666666670.1690257287210950.580000000000002
729.53583333333330.1490246064693120.520000000000003

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 31.0833333333333 & 0.217687571505309 & 0.760000000000002 \tabularnewline
2 & 30.73 & 0.0688872596744465 & 0.260000000000002 \tabularnewline
3 & 30.7391666666667 & 0.129646956513963 & 0.400000000000002 \tabularnewline
4 & 30.5316666666667 & 0.132104182944807 & 0.359999999999999 \tabularnewline
5 & 29.9758333333333 & 0.134465834344865 & 0.470000000000002 \tabularnewline
6 & 29.8666666666667 & 0.169025728721095 & 0.580000000000002 \tabularnewline
7 & 29.5358333333333 & 0.149024606469312 & 0.520000000000003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230013&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]31.0833333333333[/C][C]0.217687571505309[/C][C]0.760000000000002[/C][/ROW]
[ROW][C]2[/C][C]30.73[/C][C]0.0688872596744465[/C][C]0.260000000000002[/C][/ROW]
[ROW][C]3[/C][C]30.7391666666667[/C][C]0.129646956513963[/C][C]0.400000000000002[/C][/ROW]
[ROW][C]4[/C][C]30.5316666666667[/C][C]0.132104182944807[/C][C]0.359999999999999[/C][/ROW]
[ROW][C]5[/C][C]29.9758333333333[/C][C]0.134465834344865[/C][C]0.470000000000002[/C][/ROW]
[ROW][C]6[/C][C]29.8666666666667[/C][C]0.169025728721095[/C][C]0.580000000000002[/C][/ROW]
[ROW][C]7[/C][C]29.5358333333333[/C][C]0.149024606469312[/C][C]0.520000000000003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230013&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230013&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
131.08333333333330.2176875715053090.760000000000002
230.730.06888725967444650.260000000000002
330.73916666666670.1296469565139630.400000000000002
430.53166666666670.1321041829448070.359999999999999
529.97583333333330.1344658343448650.470000000000002
629.86666666666670.1690257287210950.580000000000002
729.53583333333330.1490246064693120.520000000000003






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0609783994629201
beta0.0027016219047284
S.D.0.0357194134917866
T-STAT0.0756345538918105
p-value0.942642843015059

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0609783994629201 \tabularnewline
beta & 0.0027016219047284 \tabularnewline
S.D. & 0.0357194134917866 \tabularnewline
T-STAT & 0.0756345538918105 \tabularnewline
p-value & 0.942642843015059 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230013&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0609783994629201[/C][/ROW]
[ROW][C]beta[/C][C]0.0027016219047284[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0357194134917866[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0756345538918105[/C][/ROW]
[ROW][C]p-value[/C][C]0.942642843015059[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230013&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230013&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)
alpha0.0609783994629201
beta0.0027016219047284
S.D.0.0357194134917866
T-STAT0.0756345538918105
p-value0.942642843015059






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha4.34309488155556
beta-1.85678051953421
S.D.8.42308665052141
T-STAT-0.220439441807151
p-value0.834247202874232
Lambda2.85678051953421

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.34309488155556 \tabularnewline
beta & -1.85678051953421 \tabularnewline
S.D. & 8.42308665052141 \tabularnewline
T-STAT & -0.220439441807151 \tabularnewline
p-value & 0.834247202874232 \tabularnewline
Lambda & 2.85678051953421 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230013&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.34309488155556[/C][/ROW]
[ROW][C]beta[/C][C]-1.85678051953421[/C][/ROW]
[ROW][C]S.D.[/C][C]8.42308665052141[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.220439441807151[/C][/ROW]
[ROW][C]p-value[/C][C]0.834247202874232[/C][/ROW]
[ROW][C]Lambda[/C][C]2.85678051953421[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230013&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230013&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)
alpha4.34309488155556
beta-1.85678051953421
S.D.8.42308665052141
T-STAT-0.220439441807151
p-value0.834247202874232
Lambda2.85678051953421


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')