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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 Jan 2019 14:49:47 +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/2019/Jan/30/t1548856223zfssvn9umujrton.htm/, Retrieved Sat, 27 Apr 2024 16:07:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=317046, Retrieved Sat, 27 Apr 2024 16:07:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82

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] [] [2019-01-30 13:49:47] [8461d222e3d4721e1dda75c02aa40f8f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.894
1.757
3.582
5.321
5.561
5.907
4.944
4.966
3.258
1.964
1.743
1.262
2.086
1.793
3.548
5.672
6.084
4.914
4.990
5.139
3.218
2.179
2.238
1.442
2.205
2.025
3.531
4.977
7.998
4.880
5.231
5.202
3.303
2.683
2.202
1.376
2.422
1.997
3.163
5.964
5.657
6.415
6.208
4.500
2.939
2.702
2.090
1.504
2.549
1.931
3.013
6.204
5.788
5.611
5.594
4.647
3.490
2.487
1.992
1.507
2.306
2.002
3.075
5.331
5.589
5.813
4.876
4.665
3.601
2.192
2.111
1.580
2.288
1.993
3.228
5.000
5.480
5.770
4.962
4.685
3.607
2.222
2.467
1.594
2.228
1.910
3.157
4.809
6.249
4.607
4.975
4.784
3.028
2.461
2.218
1.351
2.070
1.887
3.024
4.596
6.398
4.459
5.382
4.359
2.687
2.249
2.154
1.169
2.429
1.762
2.846
5.627
5.749
4.502
5.720
4.403
2.867
2.635
2.059
1.511
2.359
1.741
2.917
6.249
5.760
6.250
5.134
4.831
3.695
2.462
2.146
1.579

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317046&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=317046&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317046&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 time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13.513251.751029781429934.645
23.608583333333331.671338465168424.642
33.801083333333331.904047672165486.622
43.796751.832931339536364.911
53.734416666666671.729940222736734.697
63.595083333333331.578135059223874.233
73.6081.504044124110974.176
83.481416666666671.541658814885824.898
93.36951.621986296321445.229
103.509166666666671.598460954869534.238
113.760251.789635164699024.671

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3.51325 & 1.75102978142993 & 4.645 \tabularnewline
2 & 3.60858333333333 & 1.67133846516842 & 4.642 \tabularnewline
3 & 3.80108333333333 & 1.90404767216548 & 6.622 \tabularnewline
4 & 3.79675 & 1.83293133953636 & 4.911 \tabularnewline
5 & 3.73441666666667 & 1.72994022273673 & 4.697 \tabularnewline
6 & 3.59508333333333 & 1.57813505922387 & 4.233 \tabularnewline
7 & 3.608 & 1.50404412411097 & 4.176 \tabularnewline
8 & 3.48141666666667 & 1.54165881488582 & 4.898 \tabularnewline
9 & 3.3695 & 1.62198629632144 & 5.229 \tabularnewline
10 & 3.50916666666667 & 1.59846095486953 & 4.238 \tabularnewline
11 & 3.76025 & 1.78963516469902 & 4.671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317046&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]3.51325[/C][C]1.75102978142993[/C][C]4.645[/C][/ROW]
[ROW][C]2[/C][C]3.60858333333333[/C][C]1.67133846516842[/C][C]4.642[/C][/ROW]
[ROW][C]3[/C][C]3.80108333333333[/C][C]1.90404767216548[/C][C]6.622[/C][/ROW]
[ROW][C]4[/C][C]3.79675[/C][C]1.83293133953636[/C][C]4.911[/C][/ROW]
[ROW][C]5[/C][C]3.73441666666667[/C][C]1.72994022273673[/C][C]4.697[/C][/ROW]
[ROW][C]6[/C][C]3.59508333333333[/C][C]1.57813505922387[/C][C]4.233[/C][/ROW]
[ROW][C]7[/C][C]3.608[/C][C]1.50404412411097[/C][C]4.176[/C][/ROW]
[ROW][C]8[/C][C]3.48141666666667[/C][C]1.54165881488582[/C][C]4.898[/C][/ROW]
[ROW][C]9[/C][C]3.3695[/C][C]1.62198629632144[/C][C]5.229[/C][/ROW]
[ROW][C]10[/C][C]3.50916666666667[/C][C]1.59846095486953[/C][C]4.238[/C][/ROW]
[ROW][C]11[/C][C]3.76025[/C][C]1.78963516469902[/C][C]4.671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317046&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317046&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
13.513251.751029781429934.645
23.608583333333331.671338465168424.642
33.801083333333331.904047672165486.622
43.796751.832931339536364.911
53.734416666666671.729940222736734.697
63.595083333333331.578135059223874.233
73.6081.504044124110974.176
83.481416666666671.541658814885824.898
93.36951.621986296321445.229
103.509166666666671.598460954869534.238
113.760251.789635164699024.671






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.608058346526129
beta0.633821876863427
S.D.0.211673404325907
T-STAT2.99433874974464
p-value0.0150943113530639

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.608058346526129 \tabularnewline
beta & 0.633821876863427 \tabularnewline
S.D. & 0.211673404325907 \tabularnewline
T-STAT & 2.99433874974464 \tabularnewline
p-value & 0.0150943113530639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317046&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.608058346526129[/C][/ROW]
[ROW][C]beta[/C][C]0.633821876863427[/C][/ROW]
[ROW][C]S.D.[/C][C]0.211673404325907[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.99433874974464[/C][/ROW]
[ROW][C]p-value[/C][C]0.0150943113530639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317046&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317046&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-0.608058346526129
beta0.633821876863427
S.D.0.211673404325907
T-STAT2.99433874974464
p-value0.0150943113530639






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.17216468481041
beta1.31602228605555
S.D.0.462049016522975
T-STAT2.84823089974073
p-value0.0191443519178134
Lambda-0.316022286055552

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.17216468481041 \tabularnewline
beta & 1.31602228605555 \tabularnewline
S.D. & 0.462049016522975 \tabularnewline
T-STAT & 2.84823089974073 \tabularnewline
p-value & 0.0191443519178134 \tabularnewline
Lambda & -0.316022286055552 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=317046&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.17216468481041[/C][/ROW]
[ROW][C]beta[/C][C]1.31602228605555[/C][/ROW]
[ROW][C]S.D.[/C][C]0.462049016522975[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.84823089974073[/C][/ROW]
[ROW][C]p-value[/C][C]0.0191443519178134[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.316022286055552[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=317046&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=317046&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-1.17216468481041
beta1.31602228605555
S.D.0.462049016522975
T-STAT2.84823089974073
p-value0.0191443519178134
Lambda-0.316022286055552


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')