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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, 01 Dec 2008 13:43:13 -0700
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/Dec/01/t1228164224r19znxl429s2bk2.htm/, Retrieved Sun, 05 May 2024 20:23:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27375, Retrieved Sun, 05 May 2024 20:23:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact200

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- RMPD  [Variance Reduction Matrix] [Q6 reproduce vari...] [2008-12-01 20:00:25] [4242609301e759e844b9196c1994e4ef]
-    D    [Variance Reduction Matrix] [Q8 voeding varian...] [2008-12-01 20:29:24] [4242609301e759e844b9196c1994e4ef]
- RM D        [Standard Deviation-Mean Plot] [Q8 voeding transf...] [2008-12-01 20:43:13] [c040f376c7eef5bfe1cb52dcc7980437] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
113.5
121.2
130.4
115.2
117.9
110.7
107.6
124.3
115.1
112.5
127.9
117.4
119.3
130.4
126
125.4
130.5
115.9
108.7
124
119.4
118.6
131.3
111.1
124.8
132.3
126.7
131.7
130.9
122.1
113.2
133.6
119.2
129.4
131.4
117.1
130.5
132.3
140.8
137.5
128.6
126.7
120.8
139.3
128.6
131.3
136.3
128.8
133.2
136.3
151.1
145
134.4
135.7
128.7
129.2
138.6
132.7
132.5
135.2

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27375&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27375&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27375&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1117.8083333333336.9401936485077922.8
2121.7166666666677.4979795258254122.6
3126.0333333333336.7493209534984620.4
4131.7916666666675.789246823886420
5136.056.3933914744409822.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 117.808333333333 & 6.94019364850779 & 22.8 \tabularnewline
2 & 121.716666666667 & 7.49797952582541 & 22.6 \tabularnewline
3 & 126.033333333333 & 6.74932095349846 & 20.4 \tabularnewline
4 & 131.791666666667 & 5.7892468238864 & 20 \tabularnewline
5 & 136.05 & 6.39339147444098 & 22.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27375&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]117.808333333333[/C][C]6.94019364850779[/C][C]22.8[/C][/ROW]
[ROW][C]2[/C][C]121.716666666667[/C][C]7.49797952582541[/C][C]22.6[/C][/ROW]
[ROW][C]3[/C][C]126.033333333333[/C][C]6.74932095349846[/C][C]20.4[/C][/ROW]
[ROW][C]4[/C][C]131.791666666667[/C][C]5.7892468238864[/C][C]20[/C][/ROW]
[ROW][C]5[/C][C]136.05[/C][C]6.39339147444098[/C][C]22.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27375&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27375&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
1117.8083333333336.9401936485077922.8
2121.7166666666677.4979795258254122.6
3126.0333333333336.7493209534984620.4
4131.7916666666675.789246823886420
5136.056.3933914744409822.4






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha14.6185890898141
beta-0.0627136296541072
S.D.0.0341329300444848
T-STAT-1.83733507707583
p-value0.163470927515201

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 14.6185890898141 \tabularnewline
beta & -0.0627136296541072 \tabularnewline
S.D. & 0.0341329300444848 \tabularnewline
T-STAT & -1.83733507707583 \tabularnewline
p-value & 0.163470927515201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27375&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]14.6185890898141[/C][/ROW]
[ROW][C]beta[/C][C]-0.0627136296541072[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0341329300444848[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.83733507707583[/C][/ROW]
[ROW][C]p-value[/C][C]0.163470927515201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27375&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27375&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)
alpha14.6185890898141
beta-0.0627136296541072
S.D.0.0341329300444848
T-STAT-1.83733507707583
p-value0.163470927515201






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha7.70808372310485
beta-1.2010698034883
S.D.0.659561464086382
T-STAT-1.82101270145006
p-value0.166152556104741
Lambda2.2010698034883

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.70808372310485 \tabularnewline
beta & -1.2010698034883 \tabularnewline
S.D. & 0.659561464086382 \tabularnewline
T-STAT & -1.82101270145006 \tabularnewline
p-value & 0.166152556104741 \tabularnewline
Lambda & 2.2010698034883 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27375&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.70808372310485[/C][/ROW]
[ROW][C]beta[/C][C]-1.2010698034883[/C][/ROW]
[ROW][C]S.D.[/C][C]0.659561464086382[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.82101270145006[/C][/ROW]
[ROW][C]p-value[/C][C]0.166152556104741[/C][/ROW]
[ROW][C]Lambda[/C][C]2.2010698034883[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27375&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27375&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)
alpha7.70808372310485
beta-1.2010698034883
S.D.0.659561464086382
T-STAT-1.82101270145006
p-value0.166152556104741
Lambda2.2010698034883


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')