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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 computationSun, 18 May 2008 09:56:58 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/18/t1211126274zgv62htlcz9vyho.htm/, Retrieved Tue, 14 May 2024 00:46:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12770, Retrieved Tue, 14 May 2024 00:46:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

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...] [2008-05-18 15:56:58] [18a9c7462de321e50920adc850709d38] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
161,79
161,79
161,85
161,77
161,86
161,89
161,89
161,89
162,18
162,43
162,58
162,57
162,57
162,57
162,44
162,79
163,15
163,23
163,23
163,23
163,38
163,71
163,73
163,73
163,73
163,73
163,93
164,27
164,57
164,73
164,73
164,76
165,75
165,86
165,99
166,13
166,13
166,13
166,15
166,45
166,48
166,51
166,51
166,51
166,58
166,82
167,35
167,5
167,5
167,6
167,72
167,29
166,98
166,98
166,98
166,98
167,63
167,83
167,85
167,87
167,87
167,96
167,7
169,25
168,79
168,77
168,77
169
168,92
169,23
169,28
169,29

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12770&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12770&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12770&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1162.0408333333330.3130628264954750.810000000000002
2163.1466666666670.4636678539513811.28999999999999
3164.8483333333330.8829169973686262.40000000000001
4166.5933333333330.4396555125288091.37000000000000
5167.4341666666670.3713968309781470.890000000000015
6168.7358333333330.5756649646410231.59000000000000

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 162.040833333333 & 0.313062826495475 & 0.810000000000002 \tabularnewline
2 & 163.146666666667 & 0.463667853951381 & 1.28999999999999 \tabularnewline
3 & 164.848333333333 & 0.882916997368626 & 2.40000000000001 \tabularnewline
4 & 166.593333333333 & 0.439655512528809 & 1.37000000000000 \tabularnewline
5 & 167.434166666667 & 0.371396830978147 & 0.890000000000015 \tabularnewline
6 & 168.735833333333 & 0.575664964641023 & 1.59000000000000 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12770&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]162.040833333333[/C][C]0.313062826495475[/C][C]0.810000000000002[/C][/ROW]
[ROW][C]2[/C][C]163.146666666667[/C][C]0.463667853951381[/C][C]1.28999999999999[/C][/ROW]
[ROW][C]3[/C][C]164.848333333333[/C][C]0.882916997368626[/C][C]2.40000000000001[/C][/ROW]
[ROW][C]4[/C][C]166.593333333333[/C][C]0.439655512528809[/C][C]1.37000000000000[/C][/ROW]
[ROW][C]5[/C][C]167.434166666667[/C][C]0.371396830978147[/C][C]0.890000000000015[/C][/ROW]
[ROW][C]6[/C][C]168.735833333333[/C][C]0.575664964641023[/C][C]1.59000000000000[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12770&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12770&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
1162.0408333333330.3130628264954750.810000000000002
2163.1466666666670.4636678539513811.28999999999999
3164.8483333333330.8829169973686262.40000000000001
4166.5933333333330.4396555125288091.37000000000000
5167.4341666666670.3713968309781470.890000000000015
6168.7358333333330.5756649646410231.59000000000000






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.54907054509455
beta0.0124302967517238
S.D.0.0390494942323703
T-STAT0.318321581266976
p-value0.766168160239076

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.54907054509455 \tabularnewline
beta & 0.0124302967517238 \tabularnewline
S.D. & 0.0390494942323703 \tabularnewline
T-STAT & 0.318321581266976 \tabularnewline
p-value & 0.766168160239076 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12770&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.54907054509455[/C][/ROW]
[ROW][C]beta[/C][C]0.0124302967517238[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0390494942323703[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.318321581266976[/C][/ROW]
[ROW][C]p-value[/C][C]0.766168160239076[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12770&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12770&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-1.54907054509455
beta0.0124302967517238
S.D.0.0390494942323703
T-STAT0.318321581266976
p-value0.766168160239076






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-30.3716384703018
beta5.80095481958112
S.D.11.2802157977613
T-STAT0.514259205992531
p-value0.634178322776772
Lambda-4.80095481958112

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -30.3716384703018 \tabularnewline
beta & 5.80095481958112 \tabularnewline
S.D. & 11.2802157977613 \tabularnewline
T-STAT & 0.514259205992531 \tabularnewline
p-value & 0.634178322776772 \tabularnewline
Lambda & -4.80095481958112 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12770&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-30.3716384703018[/C][/ROW]
[ROW][C]beta[/C][C]5.80095481958112[/C][/ROW]
[ROW][C]S.D.[/C][C]11.2802157977613[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.514259205992531[/C][/ROW]
[ROW][C]p-value[/C][C]0.634178322776772[/C][/ROW]
[ROW][C]Lambda[/C][C]-4.80095481958112[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12770&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12770&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-30.3716384703018
beta5.80095481958112
S.D.11.2802157977613
T-STAT0.514259205992531
p-value0.634178322776772
Lambda-4.80095481958112


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')