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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, 26 May 2013 20:32:38 -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/2013/May/26/t1369614766olz2f8rhmacvc4l.htm/, Retrieved Mon, 29 Apr 2024 10:58:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210708, Retrieved Mon, 29 Apr 2024 10:58:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

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] [] [2013-05-27 00:32:38] [72493e16725cf12b5fc5a9dfdf9b34f2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
106.1
106.17
105.75
106.49
106.61
106.61
106.61
106.61
106.92
106.94
107.28
107.36
107.36
107.39
107.46
107.51
108.21
108.33
108.33
108.36
108.89
109.3
109.55
109.45
109.45
109.4
109.45
109.5
109.91
109.9
109.9
109.92
109.74
110.28
110.97
111.02
111.02
111
111.43
111.52
112.29
112.27
112.27
112.39
112.31
112.91
112.9
113.08
113.08
113.54
114
115.28
116.4
116.56
116.56
116.59
116.96
117.17
117.83
117.84
117.84
117.84
117.69
117.9
118.05
118.08
118.08
118.08
118.16
118.53
118.5
118.62

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' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210708&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210708&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210708&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' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1106.6208333333330.4693023513362121.61
2108.3450.8126108316016742.19
3109.9533333333330.5519112796510491.61999999999999
4112.1158333333330.7158778251950962.08
5115.9841666666671.630774820492244.76000000000001
6118.1141666666670.2959563337979970.930000000000007

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 106.620833333333 & 0.469302351336212 & 1.61 \tabularnewline
2 & 108.345 & 0.812610831601674 & 2.19 \tabularnewline
3 & 109.953333333333 & 0.551911279651049 & 1.61999999999999 \tabularnewline
4 & 112.115833333333 & 0.715877825195096 & 2.08 \tabularnewline
5 & 115.984166666667 & 1.63077482049224 & 4.76000000000001 \tabularnewline
6 & 118.114166666667 & 0.295956333797997 & 0.930000000000007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210708&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]106.620833333333[/C][C]0.469302351336212[/C][C]1.61[/C][/ROW]
[ROW][C]2[/C][C]108.345[/C][C]0.812610831601674[/C][C]2.19[/C][/ROW]
[ROW][C]3[/C][C]109.953333333333[/C][C]0.551911279651049[/C][C]1.61999999999999[/C][/ROW]
[ROW][C]4[/C][C]112.115833333333[/C][C]0.715877825195096[/C][C]2.08[/C][/ROW]
[ROW][C]5[/C][C]115.984166666667[/C][C]1.63077482049224[/C][C]4.76000000000001[/C][/ROW]
[ROW][C]6[/C][C]118.114166666667[/C][C]0.295956333797997[/C][C]0.930000000000007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210708&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210708&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
1106.6208333333330.4693023513362121.61
2108.3450.8126108316016742.19
3109.9533333333330.5519112796510491.61999999999999
4112.1158333333330.7158778251950962.08
5115.9841666666671.630774820492244.76000000000001
6118.1141666666670.2959563337979970.930000000000007






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.96217453479746
beta0.0242120005724531
S.D.0.0512455862929216
T-STAT0.47246996910244
p-value0.661215806005388

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.96217453479746 \tabularnewline
beta & 0.0242120005724531 \tabularnewline
S.D. & 0.0512455862929216 \tabularnewline
T-STAT & 0.47246996910244 \tabularnewline
p-value & 0.661215806005388 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210708&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.96217453479746[/C][/ROW]
[ROW][C]beta[/C][C]0.0242120005724531[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0512455862929216[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.47246996910244[/C][/ROW]
[ROW][C]p-value[/C][C]0.661215806005388[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210708&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210708&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-1.96217453479746
beta0.0242120005724531
S.D.0.0512455862929216
T-STAT0.47246996910244
p-value0.661215806005388






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.63507350709979
beta0.254046208010429
S.D.7.24510898122146
T-STAT0.0350645116131296
p-value0.973708350447573
Lambda0.745953791989571

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.63507350709979 \tabularnewline
beta & 0.254046208010429 \tabularnewline
S.D. & 7.24510898122146 \tabularnewline
T-STAT & 0.0350645116131296 \tabularnewline
p-value & 0.973708350447573 \tabularnewline
Lambda & 0.745953791989571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210708&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.63507350709979[/C][/ROW]
[ROW][C]beta[/C][C]0.254046208010429[/C][/ROW]
[ROW][C]S.D.[/C][C]7.24510898122146[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0350645116131296[/C][/ROW]
[ROW][C]p-value[/C][C]0.973708350447573[/C][/ROW]
[ROW][C]Lambda[/C][C]0.745953791989571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210708&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210708&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-1.63507350709979
beta0.254046208010429
S.D.7.24510898122146
T-STAT0.0350645116131296
p-value0.973708350447573
Lambda0.745953791989571


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')