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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 computationWed, 20 May 2015 21:10:29 +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/2015/May/20/t1432152688bk2sszbdfpo5oj0.htm/, Retrieved Mon, 29 Apr 2024 03:00:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279183, Retrieved Mon, 29 Apr 2024 03:00:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135

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] [S.D. Mean plot - ...] [2015-05-20 20:10:29] [bc7b6c6baf6d03f57c49dbed118965bb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6.81
6.80
6.80
6.85
6.85
6.85
6.85
6.85
6.85
6.86
6.86
6.88
6.88
6.88
6.91
6.91
6.91
6.91
6.99
6.99
6.99
7.02
7.02
7.05
7.05
7.05
7.05
7.10
7.10
7.10
7.10
7.12
7.13
7.18
7.24
7.24
7.24
7.27
7.27
7.27
7.27
7.30
7.30
7.57
7.76
7.94
7.94
7.96
7.96
7.98
7.99
8.00
8.00
8.04
8.04
8.04
8.04
8.04
8.07
8.07
8.07
8.07
8.11
8.11
8.11
8.12
8.11
8.13
8.15
8.16
8.20
8.20
8.20
8.20
8.23
8.25
8.26
8.31
8.33
8.33
8.36
8.39
8.41
8.50
8.58
8.58
8.66
8.67
8.70
8.71
8.73
8.75
8.76
8.76
8.77
8.78

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=279183&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=279183&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279183&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
16.84250.02527125567985030.0800000000000001
26.9550.06067798762169170.17
37.121666666666670.06658328118479410.19
47.50750.3059745978761220.72
58.02250.03545163158189150.11
68.128333333333330.04260459500043980.129999999999999
78.314166666666670.0915977702520730.300000000000001
88.704166666666670.06947312539043520.199999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.8425 & 0.0252712556798503 & 0.0800000000000001 \tabularnewline
2 & 6.955 & 0.0606779876216917 & 0.17 \tabularnewline
3 & 7.12166666666667 & 0.0665832811847941 & 0.19 \tabularnewline
4 & 7.5075 & 0.305974597876122 & 0.72 \tabularnewline
5 & 8.0225 & 0.0354516315818915 & 0.11 \tabularnewline
6 & 8.12833333333333 & 0.0426045950004398 & 0.129999999999999 \tabularnewline
7 & 8.31416666666667 & 0.091597770252073 & 0.300000000000001 \tabularnewline
8 & 8.70416666666667 & 0.0694731253904352 & 0.199999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279183&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]6.8425[/C][C]0.0252712556798503[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]2[/C][C]6.955[/C][C]0.0606779876216917[/C][C]0.17[/C][/ROW]
[ROW][C]3[/C][C]7.12166666666667[/C][C]0.0665832811847941[/C][C]0.19[/C][/ROW]
[ROW][C]4[/C][C]7.5075[/C][C]0.305974597876122[/C][C]0.72[/C][/ROW]
[ROW][C]5[/C][C]8.0225[/C][C]0.0354516315818915[/C][C]0.11[/C][/ROW]
[ROW][C]6[/C][C]8.12833333333333[/C][C]0.0426045950004398[/C][C]0.129999999999999[/C][/ROW]
[ROW][C]7[/C][C]8.31416666666667[/C][C]0.091597770252073[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]8[/C][C]8.70416666666667[/C][C]0.0694731253904352[/C][C]0.199999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279183&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279183&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
16.84250.02527125567985030.0800000000000001
26.9550.06067798762169170.17
37.121666666666670.06658328118479410.19
47.50750.3059745978761220.72
58.02250.03545163158189150.11
68.128333333333330.04260459500043980.129999999999999
78.314166666666670.0915977702520730.300000000000001
88.704166666666670.06947312539043520.199999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.106178406491658
beta-0.00246433888676403
S.D.0.053748996298588
T-STAT-0.0458490214975189
p-value0.964918492365483

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.106178406491658 \tabularnewline
beta & -0.00246433888676403 \tabularnewline
S.D. & 0.053748996298588 \tabularnewline
T-STAT & -0.0458490214975189 \tabularnewline
p-value & 0.964918492365483 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279183&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.106178406491658[/C][/ROW]
[ROW][C]beta[/C][C]-0.00246433888676403[/C][/ROW]
[ROW][C]S.D.[/C][C]0.053748996298588[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0458490214975189[/C][/ROW]
[ROW][C]p-value[/C][C]0.964918492365483[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279183&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279183&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)
alpha0.106178406491658
beta-0.00246433888676403
S.D.0.053748996298588
T-STAT-0.0458490214975189
p-value0.964918492365483






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.0495202354299
beta1.13304530755513
S.D.3.38988241109358
T-STAT0.334243248039276
p-value0.749569810951153
Lambda-0.133045307555129

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.0495202354299 \tabularnewline
beta & 1.13304530755513 \tabularnewline
S.D. & 3.38988241109358 \tabularnewline
T-STAT & 0.334243248039276 \tabularnewline
p-value & 0.749569810951153 \tabularnewline
Lambda & -0.133045307555129 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279183&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.0495202354299[/C][/ROW]
[ROW][C]beta[/C][C]1.13304530755513[/C][/ROW]
[ROW][C]S.D.[/C][C]3.38988241109358[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.334243248039276[/C][/ROW]
[ROW][C]p-value[/C][C]0.749569810951153[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.133045307555129[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279183&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279183&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-5.0495202354299
beta1.13304530755513
S.D.3.38988241109358
T-STAT0.334243248039276
p-value0.749569810951153
Lambda-0.133045307555129


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')