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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 30 Dec 2009 02:24:25 -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/2009/Dec/30/t1262165139c7zgbyjap55r4xp.htm/, Retrieved Sun, 28 Apr 2024 23:26:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71227, Retrieved Sun, 28 Apr 2024 23:26:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133

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] [] [2009-12-30 09:24:25] [abbb6febea381ea822009ab8520873eb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100.44
100.51
101.00
100.88
100.55
100.83
101.51
102.16
102.39
102.54
102.85
103.47
103.57
103.69
103.50
103.47
103.45
103.48
103.93
103.89
104.40
104.79
104.77
105.13
105.26
104.96
104.75
105.01
105.15
105.20
105.77
105.78
106.26
106.13
106.12
106.57
106.44
106.54
107.10
108.10
108.40
108.84
109.62
110.42
110.67
111.66
112.28
112.87
112.18
112.36
112.16
111.49
111.25
111.36
111.74
111.10
111.33
111.25
111.04
110.97
111.31
111.02
111.07
111.36

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71227&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71227&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71227&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1101.5941666666671.044287128169553.03
2104.0058333333330.6071761513662071.67999999999999
3105.580.5986803669890811.81999999999999
4109.4116666666672.20284457972516.43000000000001
5111.5191666666670.4783391404990121.39

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 101.594166666667 & 1.04428712816955 & 3.03 \tabularnewline
2 & 104.005833333333 & 0.607176151366207 & 1.67999999999999 \tabularnewline
3 & 105.58 & 0.598680366989081 & 1.81999999999999 \tabularnewline
4 & 109.411666666667 & 2.2028445797251 & 6.43000000000001 \tabularnewline
5 & 111.519166666667 & 0.478339140499012 & 1.39 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71227&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]101.594166666667[/C][C]1.04428712816955[/C][C]3.03[/C][/ROW]
[ROW][C]2[/C][C]104.005833333333[/C][C]0.607176151366207[/C][C]1.67999999999999[/C][/ROW]
[ROW][C]3[/C][C]105.58[/C][C]0.598680366989081[/C][C]1.81999999999999[/C][/ROW]
[ROW][C]4[/C][C]109.411666666667[/C][C]2.2028445797251[/C][C]6.43000000000001[/C][/ROW]
[ROW][C]5[/C][C]111.519166666667[/C][C]0.478339140499012[/C][C]1.39[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71227&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71227&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
1101.5941666666671.044287128169553.03
2104.0058333333330.6071761513662071.67999999999999
3105.580.5986803669890811.81999999999999
4109.4116666666672.20284457972516.43000000000001
5111.5191666666670.4783391404990121.39






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.31669441207497
beta0.0310363901514073
S.D.0.100762237823693
T-STAT0.308016086400469
p-value0.778217597316293

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.31669441207497 \tabularnewline
beta & 0.0310363901514073 \tabularnewline
S.D. & 0.100762237823693 \tabularnewline
T-STAT & 0.308016086400469 \tabularnewline
p-value & 0.778217597316293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71227&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.31669441207497[/C][/ROW]
[ROW][C]beta[/C][C]0.0310363901514073[/C][/ROW]
[ROW][C]S.D.[/C][C]0.100762237823693[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.308016086400469[/C][/ROW]
[ROW][C]p-value[/C][C]0.778217597316293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71227&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71227&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-2.31669441207497
beta0.0310363901514073
S.D.0.100762237823693
T-STAT0.308016086400469
p-value0.778217597316293






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.494312396749309
beta0.0666509177071824
S.D.9.40764022308394
T-STAT0.00708476473660611
p-value0.994792010735309
Lambda0.933349082292818

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.494312396749309 \tabularnewline
beta & 0.0666509177071824 \tabularnewline
S.D. & 9.40764022308394 \tabularnewline
T-STAT & 0.00708476473660611 \tabularnewline
p-value & 0.994792010735309 \tabularnewline
Lambda & 0.933349082292818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71227&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.494312396749309[/C][/ROW]
[ROW][C]beta[/C][C]0.0666509177071824[/C][/ROW]
[ROW][C]S.D.[/C][C]9.40764022308394[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.00708476473660611[/C][/ROW]
[ROW][C]p-value[/C][C]0.994792010735309[/C][/ROW]
[ROW][C]Lambda[/C][C]0.933349082292818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71227&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71227&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-0.494312396749309
beta0.0666509177071824
S.D.9.40764022308394
T-STAT0.00708476473660611
p-value0.994792010735309
Lambda0.933349082292818


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')