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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, 08 Dec 2010 19:31:11 +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/2010/Dec/08/t12918365701tp6i1xnt63fa5x.htm/, Retrieved Fri, 03 May 2024 12:00:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107102, Retrieved Fri, 03 May 2024 12:00:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
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] [Opdracht 8 oefeni...] [2010-12-08 19:31:11] [8926b0113c2f0aa20b2cf07d29df363f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
110.04
111.73
110.99
115.83
125.33
123.03
123.46
130.34
131.21
132.97
133.91
133.14
135.31
133.09
135.39
131.85
130.25
127.65
118.3
119.73
122.51
123.28
133.52
153.2
163.63
168.45
166.26
162.31
161.56
156.59
157.97
158.68
163.55
162.89
164.95
159.82
159.05
166.76
164.55
163.22
160.68
155.24
157.6
156.56
154.82
151.11
149.65
148.99
148.53
146.7
145.11
142.7
143.59
140.96
140.77
139.81
140.58
139.59
138.05
136.06
135.98
134.75
132.22
135.37
138.84
138.83
136.55
135.63
139.14
136.09
135.97
134.51
134.54
134.08
132.86
134.48
129.08
133.13
134.78
134.13
132.43
127.84
128.12
128.94

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107102&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107102&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107102&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1123.4983333333339.2235526909333723.87
2130.349.3840696734606434.9
3162.2216666666673.5069796207856711.86
4157.35255.7877662907518617.77
5141.8708333333333.6096095440651312.47
6136.1566666666672.012602717122716.91999999999999
7132.0341666666672.724152773493686.94

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 123.498333333333 & 9.22355269093337 & 23.87 \tabularnewline
2 & 130.34 & 9.38406967346064 & 34.9 \tabularnewline
3 & 162.221666666667 & 3.50697962078567 & 11.86 \tabularnewline
4 & 157.3525 & 5.78776629075186 & 17.77 \tabularnewline
5 & 141.870833333333 & 3.60960954406513 & 12.47 \tabularnewline
6 & 136.156666666667 & 2.01260271712271 & 6.91999999999999 \tabularnewline
7 & 132.034166666667 & 2.72415277349368 & 6.94 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107102&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]123.498333333333[/C][C]9.22355269093337[/C][C]23.87[/C][/ROW]
[ROW][C]2[/C][C]130.34[/C][C]9.38406967346064[/C][C]34.9[/C][/ROW]
[ROW][C]3[/C][C]162.221666666667[/C][C]3.50697962078567[/C][C]11.86[/C][/ROW]
[ROW][C]4[/C][C]157.3525[/C][C]5.78776629075186[/C][C]17.77[/C][/ROW]
[ROW][C]5[/C][C]141.870833333333[/C][C]3.60960954406513[/C][C]12.47[/C][/ROW]
[ROW][C]6[/C][C]136.156666666667[/C][C]2.01260271712271[/C][C]6.91999999999999[/C][/ROW]
[ROW][C]7[/C][C]132.034166666667[/C][C]2.72415277349368[/C][C]6.94[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107102&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107102&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
1123.4983333333339.2235526909333723.87
2130.349.3840696734606434.9
3162.2216666666673.5069796207856711.86
4157.35255.7877662907518617.77
5141.8708333333333.6096095440651312.47
6136.1566666666672.012602717122716.91999999999999
7132.0341666666672.724152773493686.94






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha17.0886898584522
beta-0.084773040842678
S.D.0.0868697564125662
T-STAT-0.975863687703574
p-value0.373950297063732

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 17.0886898584522 \tabularnewline
beta & -0.084773040842678 \tabularnewline
S.D. & 0.0868697564125662 \tabularnewline
T-STAT & -0.975863687703574 \tabularnewline
p-value & 0.373950297063732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107102&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]17.0886898584522[/C][/ROW]
[ROW][C]beta[/C][C]-0.084773040842678[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0868697564125662[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.975863687703574[/C][/ROW]
[ROW][C]p-value[/C][C]0.373950297063732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107102&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107102&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)
alpha17.0886898584522
beta-0.084773040842678
S.D.0.0868697564125662
T-STAT-0.975863687703574
p-value0.373950297063732






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha9.73694853911974
beta-1.66838688459942
S.D.2.54344790890072
T-STAT-0.655954807944347
p-value0.540833061079143
Lambda2.66838688459942

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 9.73694853911974 \tabularnewline
beta & -1.66838688459942 \tabularnewline
S.D. & 2.54344790890072 \tabularnewline
T-STAT & -0.655954807944347 \tabularnewline
p-value & 0.540833061079143 \tabularnewline
Lambda & 2.66838688459942 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107102&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.73694853911974[/C][/ROW]
[ROW][C]beta[/C][C]-1.66838688459942[/C][/ROW]
[ROW][C]S.D.[/C][C]2.54344790890072[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.655954807944347[/C][/ROW]
[ROW][C]p-value[/C][C]0.540833061079143[/C][/ROW]
[ROW][C]Lambda[/C][C]2.66838688459942[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107102&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107102&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)
alpha9.73694853911974
beta-1.66838688459942
S.D.2.54344790890072
T-STAT-0.655954807944347
p-value0.540833061079143
Lambda2.66838688459942


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')