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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 computationSun, 26 Dec 2010 14:57:13 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/26/t12933752934zq2cief76mp0m8.htm/, Retrieved Tue, 07 May 2024 04:06:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115634, Retrieved Tue, 07 May 2024 04:06:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114

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] [SMP soc] [2010-12-26 14:57:13] [346ac46ef4f6bb745e48fc42fac6253b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104.71
105.35
106.31
106.26
106.97
107.04
106.98
107.05
107.33
107.3
107.28
107.58
109.03
110.43
111.01
111.01
110.76
111.13
111.07
111.09
110.96
110.64
110.62
110.59
111.33
113.94
114.61
114.64
114.62
114.71
114.72
114.66
114.76
114.68
114.75
114.74
116.36
117.53
118.82
119.83
119.97
121.29
120.94
121.02
120.98
121.02
120.89
120.76
123.28
123.98
125.91
125.84
125.98
127.24
127.23
127.82
127.59
127.74
127.44
127.35

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=115634&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=115634&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115634&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
1106.680.8728532106103122.87000000000000
2110.6950.5737357643312172.09999999999999
3114.3466666666670.9753631802222873.43000000000001
4119.9508333333331.586943651020784.93000000000001
5126.451.504466078653214.53999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 106.68 & 0.872853210610312 & 2.87000000000000 \tabularnewline
2 & 110.695 & 0.573735764331217 & 2.09999999999999 \tabularnewline
3 & 114.346666666667 & 0.975363180222287 & 3.43000000000001 \tabularnewline
4 & 119.950833333333 & 1.58694365102078 & 4.93000000000001 \tabularnewline
5 & 126.45 & 1.50446607865321 & 4.53999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115634&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]106.68[/C][C]0.872853210610312[/C][C]2.87000000000000[/C][/ROW]
[ROW][C]2[/C][C]110.695[/C][C]0.573735764331217[/C][C]2.09999999999999[/C][/ROW]
[ROW][C]3[/C][C]114.346666666667[/C][C]0.975363180222287[/C][C]3.43000000000001[/C][/ROW]
[ROW][C]4[/C][C]119.950833333333[/C][C]1.58694365102078[/C][C]4.93000000000001[/C][/ROW]
[ROW][C]5[/C][C]126.45[/C][C]1.50446607865321[/C][C]4.53999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115634&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115634&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
1106.680.8728532106103122.87000000000000
2110.6950.5737357643312172.09999999999999
3114.3466666666670.9753631802222873.43000000000001
4119.9508333333331.586943651020784.93000000000001
5126.451.504466078653214.53999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.2856329872325
beta0.0466017614277257
S.D.0.0173948528431332
T-STAT2.6790546518548
p-value0.0751092710598015

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.2856329872325 \tabularnewline
beta & 0.0466017614277257 \tabularnewline
S.D. & 0.0173948528431332 \tabularnewline
T-STAT & 2.6790546518548 \tabularnewline
p-value & 0.0751092710598015 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115634&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.2856329872325[/C][/ROW]
[ROW][C]beta[/C][C]0.0466017614277257[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0173948528431332[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.6790546518548[/C][/ROW]
[ROW][C]p-value[/C][C]0.0751092710598015[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115634&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115634&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-4.2856329872325
beta0.0466017614277257
S.D.0.0173948528431332
T-STAT2.6790546518548
p-value0.0751092710598015






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-23.7089973472235
beta4.99936127492175
S.D.2.19118230212083
T-STAT2.28158162380324
p-value0.106779723822195
Lambda-3.99936127492175

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -23.7089973472235 \tabularnewline
beta & 4.99936127492175 \tabularnewline
S.D. & 2.19118230212083 \tabularnewline
T-STAT & 2.28158162380324 \tabularnewline
p-value & 0.106779723822195 \tabularnewline
Lambda & -3.99936127492175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115634&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-23.7089973472235[/C][/ROW]
[ROW][C]beta[/C][C]4.99936127492175[/C][/ROW]
[ROW][C]S.D.[/C][C]2.19118230212083[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.28158162380324[/C][/ROW]
[ROW][C]p-value[/C][C]0.106779723822195[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.99936127492175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115634&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115634&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-23.7089973472235
beta4.99936127492175
S.D.2.19118230212083
T-STAT2.28158162380324
p-value0.106779723822195
Lambda-3.99936127492175


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')