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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, 28 Apr 2014 05:10:25 -0400
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/Apr/28/t139867623024uiwux05x7lwkn.htm/, Retrieved Fri, 17 May 2024 02:29:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234650, Retrieved Fri, 17 May 2024 02:29:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104

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] [] [2014-04-28 09:10:25] [b3e3d38149b35cb70244b37a39776b3a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
83.5
83.6
83.9
83.9
84.2
84.4
84.6
84.8
84.8
84.9
85
85.1
85.3
85.5
86.1
86.2
86.3
86.5
86.5
86.6
86.8
87.3
87.7
87.8
88.1
88.8
89.3
89.2
89.3
89.6
89.6
89.9
90.2
90.2
90.4
90.5
91.5
91.5
91.8
92.2
92.4
92.7
93.1
93.1
93.5
93.9
94.3
94.7
95.3
95.9
96.2
96.7
96.7
96.9
97.3
97.4
97.9
98.4
98.4
98.8
98.9
98.9
99.3
99.4
99.7
99.8
99.7
99.9
100.4
101.1
101.3
101.4
101.8
102.2
102.4
102.5
102.8
103
103.2
103.2
103.6
103.7
103.7
103.8
104.2
104.5
104.5
104.8
105.2
105.3
105.5
105.4
105.7
106.8
106.8
107

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=234650&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=234650&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234650&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
184.39166666666670.5599648257351571.59999999999999
286.550.7728342171984412.5
389.59166666666670.7064100448855152.40000000000001
492.89166666666671.068097998000813.2
597.15833333333331.080789554263953.5
699.98333333333330.8799104637645932.5
7102.9916666666670.6598323937779862
8105.4750.9526279441628822.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 84.3916666666667 & 0.559964825735157 & 1.59999999999999 \tabularnewline
2 & 86.55 & 0.772834217198441 & 2.5 \tabularnewline
3 & 89.5916666666667 & 0.706410044885515 & 2.40000000000001 \tabularnewline
4 & 92.8916666666667 & 1.06809799800081 & 3.2 \tabularnewline
5 & 97.1583333333333 & 1.08078955426395 & 3.5 \tabularnewline
6 & 99.9833333333333 & 0.879910463764593 & 2.5 \tabularnewline
7 & 102.991666666667 & 0.659832393777986 & 2 \tabularnewline
8 & 105.475 & 0.952627944162882 & 2.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234650&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]84.3916666666667[/C][C]0.559964825735157[/C][C]1.59999999999999[/C][/ROW]
[ROW][C]2[/C][C]86.55[/C][C]0.772834217198441[/C][C]2.5[/C][/ROW]
[ROW][C]3[/C][C]89.5916666666667[/C][C]0.706410044885515[/C][C]2.40000000000001[/C][/ROW]
[ROW][C]4[/C][C]92.8916666666667[/C][C]1.06809799800081[/C][C]3.2[/C][/ROW]
[ROW][C]5[/C][C]97.1583333333333[/C][C]1.08078955426395[/C][C]3.5[/C][/ROW]
[ROW][C]6[/C][C]99.9833333333333[/C][C]0.879910463764593[/C][C]2.5[/C][/ROW]
[ROW][C]7[/C][C]102.991666666667[/C][C]0.659832393777986[/C][C]2[/C][/ROW]
[ROW][C]8[/C][C]105.475[/C][C]0.952627944162882[/C][C]2.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234650&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234650&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
184.39166666666670.5599648257351571.59999999999999
286.550.7728342171984412.5
389.59166666666670.7064100448855152.40000000000001
492.89166666666671.068097998000813.2
597.15833333333331.080789554263953.5
699.98333333333330.8799104637645932.5
7102.9916666666670.6598323937779862
8105.4750.9526279441628822.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.119955387411314
beta0.0100655797388079
S.D.0.00922400861739099
T-STAT1.09123702679876
p-value0.317039084862612

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.119955387411314 \tabularnewline
beta & 0.0100655797388079 \tabularnewline
S.D. & 0.00922400861739099 \tabularnewline
T-STAT & 1.09123702679876 \tabularnewline
p-value & 0.317039084862612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234650&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.119955387411314[/C][/ROW]
[ROW][C]beta[/C][C]0.0100655797388079[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00922400861739099[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.09123702679876[/C][/ROW]
[ROW][C]p-value[/C][C]0.317039084862612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234650&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234650&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-0.119955387411314
beta0.0100655797388079
S.D.0.00922400861739099
T-STAT1.09123702679876
p-value0.317039084862612






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.12171429707411
beta1.30064174396485
S.D.1.05117166706674
T-STAT1.237325723965
p-value0.262191204634849
Lambda-0.30064174396485

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.12171429707411 \tabularnewline
beta & 1.30064174396485 \tabularnewline
S.D. & 1.05117166706674 \tabularnewline
T-STAT & 1.237325723965 \tabularnewline
p-value & 0.262191204634849 \tabularnewline
Lambda & -0.30064174396485 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234650&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.12171429707411[/C][/ROW]
[ROW][C]beta[/C][C]1.30064174396485[/C][/ROW]
[ROW][C]S.D.[/C][C]1.05117166706674[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.237325723965[/C][/ROW]
[ROW][C]p-value[/C][C]0.262191204634849[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.30064174396485[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234650&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234650&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-6.12171429707411
beta1.30064174396485
S.D.1.05117166706674
T-STAT1.237325723965
p-value0.262191204634849
Lambda-0.30064174396485


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')