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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, 23 May 2012 08:12:24 -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/2012/May/23/t1337775180hf4yajzvk59gi5x.htm/, Retrieved Sun, 28 Apr 2024 21:55:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167171, Retrieved Sun, 28 Apr 2024 21:55:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107

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...] [2012-05-23 12:12:24] [6aa41422895d0082cb99bdd8f056be10] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
86.9
85.8
84.4
80.4
84.4
90.7
91.6
91.9
92.5
92.5
92
92
94.5
95.5
96.3
100
103.1
109.2
108.7
107.5
104.5
103.8
102.5
100.8
100.7
102.7
106.5
105.5
110.1
110.1
109
106.9
108
106.1
101.7
100.6
102.6
100.5
105.2
104.3
104.1
104.8
105.2
102.7
101
93.9
90.2
92.4
94.4
93.3
93.9
95.1
97.6
99.3
101.1
100.6
99.3
97
96.4
98.7

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167171&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167171&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167171&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'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
188.75833333333334.1646692181936512.1
2102.24.9898077937112814.7
3105.6583333333333.479409127824429.5
4100.5755.3492777762304215
597.2252.646137837404827.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 88.7583333333333 & 4.16466921819365 & 12.1 \tabularnewline
2 & 102.2 & 4.98980779371128 & 14.7 \tabularnewline
3 & 105.658333333333 & 3.47940912782442 & 9.5 \tabularnewline
4 & 100.575 & 5.34927777623042 & 15 \tabularnewline
5 & 97.225 & 2.64613783740482 & 7.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167171&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]88.7583333333333[/C][C]4.16466921819365[/C][C]12.1[/C][/ROW]
[ROW][C]2[/C][C]102.2[/C][C]4.98980779371128[/C][C]14.7[/C][/ROW]
[ROW][C]3[/C][C]105.658333333333[/C][C]3.47940912782442[/C][C]9.5[/C][/ROW]
[ROW][C]4[/C][C]100.575[/C][C]5.34927777623042[/C][C]15[/C][/ROW]
[ROW][C]5[/C][C]97.225[/C][C]2.64613783740482[/C][C]7.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167171&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167171&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
188.75833333333334.1646692181936512.1
2102.24.9898077937112814.7
3105.6583333333333.479409127824429.5
4100.5755.3492777762304215
597.2252.646137837404827.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.55821951871517
beta0.0158534383815042
S.D.0.0985740418836297
T-STAT0.16082771973802
p-value0.882449025075683

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.55821951871517 \tabularnewline
beta & 0.0158534383815042 \tabularnewline
S.D. & 0.0985740418836297 \tabularnewline
T-STAT & 0.16082771973802 \tabularnewline
p-value & 0.882449025075683 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167171&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.55821951871517[/C][/ROW]
[ROW][C]beta[/C][C]0.0158534383815042[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0985740418836297[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.16082771973802[/C][/ROW]
[ROW][C]p-value[/C][C]0.882449025075683[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167171&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167171&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)
alpha2.55821951871517
beta0.0158534383815042
S.D.0.0985740418836297
T-STAT0.16082771973802
p-value0.882449025075683






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.0697775095680866
beta0.31705281910784
S.D.2.46729831482744
T-STAT0.128502020693032
p-value0.905882419526722
Lambda0.68294718089216

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.0697775095680866 \tabularnewline
beta & 0.31705281910784 \tabularnewline
S.D. & 2.46729831482744 \tabularnewline
T-STAT & 0.128502020693032 \tabularnewline
p-value & 0.905882419526722 \tabularnewline
Lambda & 0.68294718089216 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167171&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0697775095680866[/C][/ROW]
[ROW][C]beta[/C][C]0.31705281910784[/C][/ROW]
[ROW][C]S.D.[/C][C]2.46729831482744[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.128502020693032[/C][/ROW]
[ROW][C]p-value[/C][C]0.905882419526722[/C][/ROW]
[ROW][C]Lambda[/C][C]0.68294718089216[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167171&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167171&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-0.0697775095680866
beta0.31705281910784
S.D.2.46729831482744
T-STAT0.128502020693032
p-value0.905882419526722
Lambda0.68294718089216


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')