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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 computationWed, 18 Nov 2015 14:28:41 +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/2015/Nov/18/t14478571471aw308b4bm7lmt8.htm/, Retrieved Tue, 14 May 2024 04:01:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283493, Retrieved Tue, 14 May 2024 04:01:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120

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] [] [2015-11-18 14:28:41] [bfd47bf74fe11b18de27163a0fd6b465] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
83.36
83.61
83.41
83.64
84.06
83.93
84.1
84.37
84.18
84.11
84.56
84.2
84.45
84.28
84.28
84.7
85.04
85.31
85.18
85.02
86.31
86.56
86.4
86.84
87.42
87.28
87.27
87.73
87.32
87.15
87.5
87.43
88.81
89.38
88.83
88.91
89.34
89.56
89.32
89.31
89.45
88.92
89.35
88.89
90.1
90.49
89.96
89.93
90.32
90.24
90.61
91.06
90.81
91.09
91.17
90.87
91.92
92.67
92.03
92.09
92.61
92.19
92.68
92.66
92.77
92.21
92.58
91.9
93.81
94.05
94.51
94.49
94.36
94.72
95.57
95.87
95.93
96.09
95.82
96.06
97.09
97.67
98.53
98.12
98.84
98.98
100.04
99.47
99.84
99.52
99.81
99.55
100.21
101.44
101
101.32
101.84
101.81
101.83
102.18
101.97
101.8
101.69
101.91
102.27
102.73
102.61
102.89

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283493&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283493&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283493&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
183.96083333333330.3783326658651181.2
285.36416666666670.9275427785609712.56
387.91916666666670.8101342013780322.22999999999999
489.55166666666670.4801294017494041.59999999999999
591.240.7674515086843082.43000000000001
693.03833333333330.921005708533622.61
796.31916666666671.287304854290084.17
8100.0016666666670.8540367602619832.59999999999999
9102.12750.4093259425845471.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 83.9608333333333 & 0.378332665865118 & 1.2 \tabularnewline
2 & 85.3641666666667 & 0.927542778560971 & 2.56 \tabularnewline
3 & 87.9191666666667 & 0.810134201378032 & 2.22999999999999 \tabularnewline
4 & 89.5516666666667 & 0.480129401749404 & 1.59999999999999 \tabularnewline
5 & 91.24 & 0.767451508684308 & 2.43000000000001 \tabularnewline
6 & 93.0383333333333 & 0.92100570853362 & 2.61 \tabularnewline
7 & 96.3191666666667 & 1.28730485429008 & 4.17 \tabularnewline
8 & 100.001666666667 & 0.854036760261983 & 2.59999999999999 \tabularnewline
9 & 102.1275 & 0.409325942584547 & 1.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283493&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]83.9608333333333[/C][C]0.378332665865118[/C][C]1.2[/C][/ROW]
[ROW][C]2[/C][C]85.3641666666667[/C][C]0.927542778560971[/C][C]2.56[/C][/ROW]
[ROW][C]3[/C][C]87.9191666666667[/C][C]0.810134201378032[/C][C]2.22999999999999[/C][/ROW]
[ROW][C]4[/C][C]89.5516666666667[/C][C]0.480129401749404[/C][C]1.59999999999999[/C][/ROW]
[ROW][C]5[/C][C]91.24[/C][C]0.767451508684308[/C][C]2.43000000000001[/C][/ROW]
[ROW][C]6[/C][C]93.0383333333333[/C][C]0.92100570853362[/C][C]2.61[/C][/ROW]
[ROW][C]7[/C][C]96.3191666666667[/C][C]1.28730485429008[/C][C]4.17[/C][/ROW]
[ROW][C]8[/C][C]100.001666666667[/C][C]0.854036760261983[/C][C]2.59999999999999[/C][/ROW]
[ROW][C]9[/C][C]102.1275[/C][C]0.409325942584547[/C][C]1.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283493&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283493&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
183.96083333333330.3783326658651181.2
285.36416666666670.9275427785609712.56
387.91916666666670.8101342013780322.22999999999999
489.55166666666670.4801294017494041.59999999999999
591.240.7674515086843082.43000000000001
693.03833333333330.921005708533622.61
796.31916666666671.287304854290084.17
8100.0016666666670.8540367602619832.59999999999999
9102.12750.4093259425845471.2






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.157114499497136
beta0.0065353662214513
S.D.0.0174385810068993
T-STAT0.374764794157604
p-value0.718931325873073

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.157114499497136 \tabularnewline
beta & 0.0065353662214513 \tabularnewline
S.D. & 0.0174385810068993 \tabularnewline
T-STAT & 0.374764794157604 \tabularnewline
p-value & 0.718931325873073 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283493&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.157114499497136[/C][/ROW]
[ROW][C]beta[/C][C]0.0065353662214513[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0174385810068993[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.374764794157604[/C][/ROW]
[ROW][C]p-value[/C][C]0.718931325873073[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283493&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283493&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)
alpha0.157114499497136
beta0.0065353662214513
S.D.0.0174385810068993
T-STAT0.374764794157604
p-value0.718931325873073






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.97031842231371
beta0.801000070056966
S.D.2.31054086899253
T-STAT0.346672106434641
p-value0.739025335845183
Lambda0.198999929943034

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.97031842231371 \tabularnewline
beta & 0.801000070056966 \tabularnewline
S.D. & 2.31054086899253 \tabularnewline
T-STAT & 0.346672106434641 \tabularnewline
p-value & 0.739025335845183 \tabularnewline
Lambda & 0.198999929943034 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283493&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.97031842231371[/C][/ROW]
[ROW][C]beta[/C][C]0.801000070056966[/C][/ROW]
[ROW][C]S.D.[/C][C]2.31054086899253[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.346672106434641[/C][/ROW]
[ROW][C]p-value[/C][C]0.739025335845183[/C][/ROW]
[ROW][C]Lambda[/C][C]0.198999929943034[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283493&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283493&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-3.97031842231371
beta0.801000070056966
S.D.2.31054086899253
T-STAT0.346672106434641
p-value0.739025335845183
Lambda0.198999929943034


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')