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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 computationTue, 23 Jan 2018 21:51:02 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Jan/23/t1516740869ewu07bp1wp0sps1.htm/, Retrieved Wed, 08 May 2024 23:24:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=311274, Retrieved Wed, 08 May 2024 23:24:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact34

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] [] [2018-01-23 20:51:02] [ee454057ec51d06973705bb1a258656a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10
8
8
9
5
10
8
9
8
7
10
10
9
4
4
8
9
10
8
5
10
8
7
8
8
9
8
6
8
8
5
9
8
8
8
6
6
9
8
9
10
8
8
7
7
10
8
7
10
7
7
9
9
8
6
8
9
2
6
8
8
7
8
6
10
10
10
8
8
7
10
5
3
2
3
4
2
6
8
8
5
10
9
8
9
8
5
7
9
8
4
7
8
7
7
9
6
7
4
6
10
9
10
8
4
8
5
8
9
8
4
8
10
6
7
10
9
8
3
8
7
7
8
8
7
7
9
9
9
4
6
6
6
8
3
8
8
6
10
2
9
6
6
5
4
7
5
8
6
9
6
4
7
2
8
9
6
5
7
8
4
9
9
9
7
5
7
9
8
6
9
8
7
7
7
8
10
6
6

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=311274&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=311274&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=311274&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
18.51.507556722888825
27.52.110579412044356
37.583333333333331.240112409372154
48.083333333333331.240112409372154
57.416666666666672.108783937953278
68.083333333333331.676486224400925
75.666666666666672.870962250261098
87.333333333333331.556997888323055
97.083333333333332.108783937953276
107.52.195035721390847
117.251.484771179187375
126.416666666666672.353269807709868
136.252.179449471770347
147.083333333333331.781640374554425

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.5 & 1.50755672288882 & 5 \tabularnewline
2 & 7.5 & 2.11057941204435 & 6 \tabularnewline
3 & 7.58333333333333 & 1.24011240937215 & 4 \tabularnewline
4 & 8.08333333333333 & 1.24011240937215 & 4 \tabularnewline
5 & 7.41666666666667 & 2.10878393795327 & 8 \tabularnewline
6 & 8.08333333333333 & 1.67648622440092 & 5 \tabularnewline
7 & 5.66666666666667 & 2.87096225026109 & 8 \tabularnewline
8 & 7.33333333333333 & 1.55699788832305 & 5 \tabularnewline
9 & 7.08333333333333 & 2.10878393795327 & 6 \tabularnewline
10 & 7.5 & 2.19503572139084 & 7 \tabularnewline
11 & 7.25 & 1.48477117918737 & 5 \tabularnewline
12 & 6.41666666666667 & 2.35326980770986 & 8 \tabularnewline
13 & 6.25 & 2.17944947177034 & 7 \tabularnewline
14 & 7.08333333333333 & 1.78164037455442 & 5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=311274&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]8.5[/C][C]1.50755672288882[/C][C]5[/C][/ROW]
[ROW][C]2[/C][C]7.5[/C][C]2.11057941204435[/C][C]6[/C][/ROW]
[ROW][C]3[/C][C]7.58333333333333[/C][C]1.24011240937215[/C][C]4[/C][/ROW]
[ROW][C]4[/C][C]8.08333333333333[/C][C]1.24011240937215[/C][C]4[/C][/ROW]
[ROW][C]5[/C][C]7.41666666666667[/C][C]2.10878393795327[/C][C]8[/C][/ROW]
[ROW][C]6[/C][C]8.08333333333333[/C][C]1.67648622440092[/C][C]5[/C][/ROW]
[ROW][C]7[/C][C]5.66666666666667[/C][C]2.87096225026109[/C][C]8[/C][/ROW]
[ROW][C]8[/C][C]7.33333333333333[/C][C]1.55699788832305[/C][C]5[/C][/ROW]
[ROW][C]9[/C][C]7.08333333333333[/C][C]2.10878393795327[/C][C]6[/C][/ROW]
[ROW][C]10[/C][C]7.5[/C][C]2.19503572139084[/C][C]7[/C][/ROW]
[ROW][C]11[/C][C]7.25[/C][C]1.48477117918737[/C][C]5[/C][/ROW]
[ROW][C]12[/C][C]6.41666666666667[/C][C]2.35326980770986[/C][C]8[/C][/ROW]
[ROW][C]13[/C][C]6.25[/C][C]2.17944947177034[/C][C]7[/C][/ROW]
[ROW][C]14[/C][C]7.08333333333333[/C][C]1.78164037455442[/C][C]5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=311274&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=311274&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
18.51.507556722888825
27.52.110579412044356
37.583333333333331.240112409372154
48.083333333333331.240112409372154
57.416666666666672.108783937953278
68.083333333333331.676486224400925
75.666666666666672.870962250261098
87.333333333333331.556997888323055
97.083333333333332.108783937953276
107.52.195035721390847
117.251.484771179187375
126.416666666666672.353269807709868
136.252.179449471770347
147.083333333333331.781640374554425






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.30969218580182
beta-0.470969521907062
S.D.0.11388747244429
T-STAT-4.13539357577231
p-value0.00138213590894078

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.30969218580182 \tabularnewline
beta & -0.470969521907062 \tabularnewline
S.D. & 0.11388747244429 \tabularnewline
T-STAT & -4.13539357577231 \tabularnewline
p-value & 0.00138213590894078 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=311274&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.30969218580182[/C][/ROW]
[ROW][C]beta[/C][C]-0.470969521907062[/C][/ROW]
[ROW][C]S.D.[/C][C]0.11388747244429[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.13539357577231[/C][/ROW]
[ROW][C]p-value[/C][C]0.00138213590894078[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=311274&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=311274&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)
alpha5.30969218580182
beta-0.470969521907062
S.D.0.11388747244429
T-STAT-4.13539357577231
p-value0.00138213590894078






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.95176145634511
beta-1.69120828314924
S.D.0.451012608054555
T-STAT-3.74980267279949
p-value0.00277196665411895
Lambda2.69120828314924

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.95176145634511 \tabularnewline
beta & -1.69120828314924 \tabularnewline
S.D. & 0.451012608054555 \tabularnewline
T-STAT & -3.74980267279949 \tabularnewline
p-value & 0.00277196665411895 \tabularnewline
Lambda & 2.69120828314924 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=311274&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.95176145634511[/C][/ROW]
[ROW][C]beta[/C][C]-1.69120828314924[/C][/ROW]
[ROW][C]S.D.[/C][C]0.451012608054555[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.74980267279949[/C][/ROW]
[ROW][C]p-value[/C][C]0.00277196665411895[/C][/ROW]
[ROW][C]Lambda[/C][C]2.69120828314924[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=311274&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=311274&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)
alpha3.95176145634511
beta-1.69120828314924
S.D.0.451012608054555
T-STAT-3.74980267279949
p-value0.00277196665411895
Lambda2.69120828314924


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = Exact Pearson Chi-Squared by Simulation ;
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')