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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, 24 Nov 2014 20:07:49 +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/24/t1416859688yd4q3zozhhxdm5k.htm/, Retrieved Sun, 19 May 2024 14:06:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=258440, Retrieved Sun, 19 May 2024 14:06:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58

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] [] [2014-11-24 20:07:49] [77e76d07a5b02a0482982fb19d5d5436] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21.94
21.95
21.96
22.1
22.13
22.18
22.18
22.27
22.3
22.04
22.05
22.06
22.06
22.06
21.97
22.03
22.08
22.13
22.13
22.4
22.4
22.12
22.22
22.14
22.14
22.19
22.29
22.24
22.26
22.29
22.29
22.29
22.29
22.35
22.39
22.43
22.43
22.11
22.12
22.05
22.05
22.08
22.08
22.09
22.09
22.24
22.25
22.24
22.24
22.25
22.28
22.23
22.29
22.31
22.31
22.31
22.39
22.42
22.42
22.42
22.15
21.95
21.96
21.97
21.66
21.66
21.68
21.75
21.55
21.59
21.54
21.54

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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258440&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258440&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258440&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'Sir Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
122.09666666666670.119797809460420.359999999999999
222.1450.1346037957049570.43
322.28750.07921489758877420.289999999999999
422.15250.1144254421804070.379999999999999
522.32250.07200063131036440.190000000000001
621.750.2061332314084970.609999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 22.0966666666667 & 0.11979780946042 & 0.359999999999999 \tabularnewline
2 & 22.145 & 0.134603795704957 & 0.43 \tabularnewline
3 & 22.2875 & 0.0792148975887742 & 0.289999999999999 \tabularnewline
4 & 22.1525 & 0.114425442180407 & 0.379999999999999 \tabularnewline
5 & 22.3225 & 0.0720006313103644 & 0.190000000000001 \tabularnewline
6 & 21.75 & 0.206133231408497 & 0.609999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258440&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]22.0966666666667[/C][C]0.11979780946042[/C][C]0.359999999999999[/C][/ROW]
[ROW][C]2[/C][C]22.145[/C][C]0.134603795704957[/C][C]0.43[/C][/ROW]
[ROW][C]3[/C][C]22.2875[/C][C]0.0792148975887742[/C][C]0.289999999999999[/C][/ROW]
[ROW][C]4[/C][C]22.1525[/C][C]0.114425442180407[/C][C]0.379999999999999[/C][/ROW]
[ROW][C]5[/C][C]22.3225[/C][C]0.0720006313103644[/C][C]0.190000000000001[/C][/ROW]
[ROW][C]6[/C][C]21.75[/C][C]0.206133231408497[/C][C]0.609999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258440&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258440&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
122.09666666666670.119797809460420.359999999999999
222.1450.1346037957049570.43
322.28750.07921489758877420.289999999999999
422.15250.1144254421804070.379999999999999
522.32250.07200063131036440.190000000000001
621.750.2061332314084970.609999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.25553900807353
beta-0.232060951564265
S.D.0.0225589138466267
T-STAT-10.286884960065
p-value0.000503661539373728

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.25553900807353 \tabularnewline
beta & -0.232060951564265 \tabularnewline
S.D. & 0.0225589138466267 \tabularnewline
T-STAT & -10.286884960065 \tabularnewline
p-value & 0.000503661539373728 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258440&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.25553900807353[/C][/ROW]
[ROW][C]beta[/C][C]-0.232060951564265[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0225589138466267[/C][/ROW]
[ROW][C]T-STAT[/C][C]-10.286884960065[/C][/ROW]
[ROW][C]p-value[/C][C]0.000503661539373728[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258440&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258440&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)
alpha5.25553900807353
beta-0.232060951564265
S.D.0.0225589138466267
T-STAT-10.286884960065
p-value0.000503661539373728






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha119.037119516933
beta-39.1418226422067
S.D.6.28318913968645
T-STAT-6.22961075530507
p-value0.00338186162845139
Lambda40.1418226422067

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 119.037119516933 \tabularnewline
beta & -39.1418226422067 \tabularnewline
S.D. & 6.28318913968645 \tabularnewline
T-STAT & -6.22961075530507 \tabularnewline
p-value & 0.00338186162845139 \tabularnewline
Lambda & 40.1418226422067 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258440&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]119.037119516933[/C][/ROW]
[ROW][C]beta[/C][C]-39.1418226422067[/C][/ROW]
[ROW][C]S.D.[/C][C]6.28318913968645[/C][/ROW]
[ROW][C]T-STAT[/C][C]-6.22961075530507[/C][/ROW]
[ROW][C]p-value[/C][C]0.00338186162845139[/C][/ROW]
[ROW][C]Lambda[/C][C]40.1418226422067[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258440&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258440&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)
alpha119.037119516933
beta-39.1418226422067
S.D.6.28318913968645
T-STAT-6.22961075530507
p-value0.00338186162845139
Lambda40.1418226422067


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')