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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 computationFri, 18 Nov 2016 09:52:16 +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/2016/Nov/18/t1479462803ank46uosy54hr4t.htm/, Retrieved Fri, 03 May 2024 01:42:48 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 03 May 2024 01:42:48 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
75.99
76.31
76.51
76.75
77.23
77.22
77.25
77.36
77.57
77.88
78.29
78.42
78.96
79.85
80.05
80.16
80.29
80.36
80.48
80.95
82.3
84.81
85.4
86.13
87.02
87.38
87.5
87.91
88.06
88.09
88.16
88.33
88.52
88.96
89.26
89.34
89.09
89.25
89.31
89.28
89.32
89.47
89.59
89.62
89.71
89.9
90.04
90.05
90.18
90.5
90.63
90.75
90.76
90.67
90.5
90.8
91.22
92.19
92.51
92.67
93.75
94.1
94.96
95.21
95.33
95.43
95.44
95.64
95.8
95.87
95.98
96.07
96.23
96.32
96.55
96.73
96.61
96.64
96.86
97.02
97.22
98.1
98.46
98.6
98.78
99.13
99.48
99.62
99.68
99.95
100.12
100.25
100.47
100.7
100.88
100.95
100.92
101.12
101.19
101.28
101.28
101.3
101.3
101.36
101.45
101.58
101.73
101.84
102.01
102.14
102.16
102.32
102.41
102.4
102.43
102.42
102.3
102.65
102.72
102.86

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
177.23166666666670.7524485283916692.43000000000001
281.6452.434029580756987.17
388.21083333333330.7255650880311842.32000000000001
489.55250.3213642792844290.959999999999994
591.1150.8502994125066132.48999999999999
695.29833333333330.7229589870592242.31999999999999
797.11166666666670.8220134187506052.36999999999999
8100.0008333333330.6895117947878162.17
9101.36250.2565195367360410.920000000000002
10102.4016666666670.2470860480713450.849999999999994

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 77.2316666666667 & 0.752448528391669 & 2.43000000000001 \tabularnewline
2 & 81.645 & 2.43402958075698 & 7.17 \tabularnewline
3 & 88.2108333333333 & 0.725565088031184 & 2.32000000000001 \tabularnewline
4 & 89.5525 & 0.321364279284429 & 0.959999999999994 \tabularnewline
5 & 91.115 & 0.850299412506613 & 2.48999999999999 \tabularnewline
6 & 95.2983333333333 & 0.722958987059224 & 2.31999999999999 \tabularnewline
7 & 97.1116666666667 & 0.822013418750605 & 2.36999999999999 \tabularnewline
8 & 100.000833333333 & 0.689511794787816 & 2.17 \tabularnewline
9 & 101.3625 & 0.256519536736041 & 0.920000000000002 \tabularnewline
10 & 102.401666666667 & 0.247086048071345 & 0.849999999999994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]77.2316666666667[/C][C]0.752448528391669[/C][C]2.43000000000001[/C][/ROW]
[ROW][C]2[/C][C]81.645[/C][C]2.43402958075698[/C][C]7.17[/C][/ROW]
[ROW][C]3[/C][C]88.2108333333333[/C][C]0.725565088031184[/C][C]2.32000000000001[/C][/ROW]
[ROW][C]4[/C][C]89.5525[/C][C]0.321364279284429[/C][C]0.959999999999994[/C][/ROW]
[ROW][C]5[/C][C]91.115[/C][C]0.850299412506613[/C][C]2.48999999999999[/C][/ROW]
[ROW][C]6[/C][C]95.2983333333333[/C][C]0.722958987059224[/C][C]2.31999999999999[/C][/ROW]
[ROW][C]7[/C][C]97.1116666666667[/C][C]0.822013418750605[/C][C]2.36999999999999[/C][/ROW]
[ROW][C]8[/C][C]100.000833333333[/C][C]0.689511794787816[/C][C]2.17[/C][/ROW]
[ROW][C]9[/C][C]101.3625[/C][C]0.256519536736041[/C][C]0.920000000000002[/C][/ROW]
[ROW][C]10[/C][C]102.401666666667[/C][C]0.247086048071345[/C][C]0.849999999999994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
177.23166666666670.7524485283916692.43000000000001
281.6452.434029580756987.17
388.21083333333330.7255650880311842.32000000000001
489.55250.3213642792844290.959999999999994
591.1150.8502994125066132.48999999999999
695.29833333333330.7229589870592242.31999999999999
797.11166666666670.8220134187506052.36999999999999
8100.0008333333330.6895117947878162.17
9101.36250.2565195367360410.920000000000002
10102.4016666666670.2470860480713450.849999999999994






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4.61216913515316
beta-0.0414532428616408
S.D.0.0217246022689276
T-STAT-1.90812436280736
p-value0.0927990562602208

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4.61216913515316 \tabularnewline
beta & -0.0414532428616408 \tabularnewline
S.D. & 0.0217246022689276 \tabularnewline
T-STAT & -1.90812436280736 \tabularnewline
p-value & 0.0927990562602208 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.61216913515316[/C][/ROW]
[ROW][C]beta[/C][C]-0.0414532428616408[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0217246022689276[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.90812436280736[/C][/ROW]
[ROW][C]p-value[/C][C]0.0927990562602208[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)
alpha4.61216913515316
beta-0.0414532428616408
S.D.0.0217246022689276
T-STAT-1.90812436280736
p-value0.0927990562602208






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha19.0977647437776
beta-4.32628954707335
S.D.2.06693439027577
T-STAT-2.09309476267224
p-value0.069681910799587
Lambda5.32628954707335

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 19.0977647437776 \tabularnewline
beta & -4.32628954707335 \tabularnewline
S.D. & 2.06693439027577 \tabularnewline
T-STAT & -2.09309476267224 \tabularnewline
p-value & 0.069681910799587 \tabularnewline
Lambda & 5.32628954707335 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]19.0977647437776[/C][/ROW]
[ROW][C]beta[/C][C]-4.32628954707335[/C][/ROW]
[ROW][C]S.D.[/C][C]2.06693439027577[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.09309476267224[/C][/ROW]
[ROW][C]p-value[/C][C]0.069681910799587[/C][/ROW]
[ROW][C]Lambda[/C][C]5.32628954707335[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)
alpha19.0977647437776
beta-4.32628954707335
S.D.2.06693439027577
T-STAT-2.09309476267224
p-value0.069681910799587
Lambda5.32628954707335


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')