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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 computationThu, 19 Nov 2015 13:24:37 +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/19/t1447940140v53901moocqa3oq.htm/, Retrieved Tue, 14 May 2024 13:33:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283620, Retrieved Tue, 14 May 2024 13:33:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106

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] [opdracht 8 oefeni...] [2015-11-19 13:24:37] [cd0005da8c1be4acc9acd7984e542112] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
85.13
85.54
85.47
85.78
86.07
86.05
86.32
86.43
86.41
86.38
86.59
86.68
86.87
87.32
87.13
87.42
87.22
87.17
87.52
87.49
87.53
87.93
88.54
88.96
89.3
90.01
90.52
90.64
91.25
91.59
92.09
91.81
92.03
92.15
91.98
92.11
92.28
92.53
91.97
92.05
91.87
91.49
91.48
91.63
91.46
91.61
91.7
91.87
92.21
92.65
92.83
93.02
93.33
93.35
93.45
93.51
93.8
93.94
94.02
94.26
94.71
95.26
95.54
95.69
96.03
96.4
96.55
96.45
96.65
96.84
97.21
97.31
97.91
98.51
98.54
98.52
98.66
98.53
98.71
98.92
98.96
99.25
99.32
99.41
99.36
99.58
99.77
99.77
100.03
100.2
100.24
100.1
100.03
100.18
100.29
100.41
100.6
100.75
100.79
100.44
100.29
100.34
100.46
100.12
100.06
100.28
100.28
100.4

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' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283620&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283620&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283620&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' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
186.07083333333330.491314717380981.55000000000001
287.59166666666670.607421275607472.08999999999999
391.290.95591935757252.85000000000001
491.82833333333330.3362854126896971.07000000000001
593.36416666666670.6052866838919972.05000000000001
696.220.7927397830539122.60000000000001
798.770.4260815116212551.5
899.99666666666670.3141607386306731.05
9100.4008333333330.2252860135001450.730000000000004

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 86.0708333333333 & 0.49131471738098 & 1.55000000000001 \tabularnewline
2 & 87.5916666666667 & 0.60742127560747 & 2.08999999999999 \tabularnewline
3 & 91.29 & 0.9559193575725 & 2.85000000000001 \tabularnewline
4 & 91.8283333333333 & 0.336285412689697 & 1.07000000000001 \tabularnewline
5 & 93.3641666666667 & 0.605286683891997 & 2.05000000000001 \tabularnewline
6 & 96.22 & 0.792739783053912 & 2.60000000000001 \tabularnewline
7 & 98.77 & 0.426081511621255 & 1.5 \tabularnewline
8 & 99.9966666666667 & 0.314160738630673 & 1.05 \tabularnewline
9 & 100.400833333333 & 0.225286013500145 & 0.730000000000004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283620&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]86.0708333333333[/C][C]0.49131471738098[/C][C]1.55000000000001[/C][/ROW]
[ROW][C]2[/C][C]87.5916666666667[/C][C]0.60742127560747[/C][C]2.08999999999999[/C][/ROW]
[ROW][C]3[/C][C]91.29[/C][C]0.9559193575725[/C][C]2.85000000000001[/C][/ROW]
[ROW][C]4[/C][C]91.8283333333333[/C][C]0.336285412689697[/C][C]1.07000000000001[/C][/ROW]
[ROW][C]5[/C][C]93.3641666666667[/C][C]0.605286683891997[/C][C]2.05000000000001[/C][/ROW]
[ROW][C]6[/C][C]96.22[/C][C]0.792739783053912[/C][C]2.60000000000001[/C][/ROW]
[ROW][C]7[/C][C]98.77[/C][C]0.426081511621255[/C][C]1.5[/C][/ROW]
[ROW][C]8[/C][C]99.9966666666667[/C][C]0.314160738630673[/C][C]1.05[/C][/ROW]
[ROW][C]9[/C][C]100.400833333333[/C][C]0.225286013500145[/C][C]0.730000000000004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283620&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283620&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
186.07083333333330.491314717380981.55000000000001
287.59166666666670.607421275607472.08999999999999
391.290.95591935757252.85000000000001
491.82833333333330.3362854126896971.07000000000001
593.36416666666670.6052866838919972.05000000000001
696.220.7927397830539122.60000000000001
798.770.4260815116212551.5
899.99666666666670.3141607386306731.05
9100.4008333333330.2252860135001450.730000000000004






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.28351423185653
beta-0.0186830578277714
S.D.0.0155529554703135
T-STAT-1.20125450519244
p-value0.268715199999749

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.28351423185653 \tabularnewline
beta & -0.0186830578277714 \tabularnewline
S.D. & 0.0155529554703135 \tabularnewline
T-STAT & -1.20125450519244 \tabularnewline
p-value & 0.268715199999749 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283620&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.28351423185653[/C][/ROW]
[ROW][C]beta[/C][C]-0.0186830578277714[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0155529554703135[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.20125450519244[/C][/ROW]
[ROW][C]p-value[/C][C]0.268715199999749[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283620&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283620&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)
alpha2.28351423185653
beta-0.0186830578277714
S.D.0.0155529554703135
T-STAT-1.20125450519244
p-value0.268715199999749






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha17.6079247898047
beta-4.03823680021112
S.D.2.72426667863067
T-STAT-1.48232066702108
p-value0.181814465746784
Lambda5.03823680021112

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 17.6079247898047 \tabularnewline
beta & -4.03823680021112 \tabularnewline
S.D. & 2.72426667863067 \tabularnewline
T-STAT & -1.48232066702108 \tabularnewline
p-value & 0.181814465746784 \tabularnewline
Lambda & 5.03823680021112 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283620&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]17.6079247898047[/C][/ROW]
[ROW][C]beta[/C][C]-4.03823680021112[/C][/ROW]
[ROW][C]S.D.[/C][C]2.72426667863067[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.48232066702108[/C][/ROW]
[ROW][C]p-value[/C][C]0.181814465746784[/C][/ROW]
[ROW][C]Lambda[/C][C]5.03823680021112[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283620&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283620&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)
alpha17.6079247898047
beta-4.03823680021112
S.D.2.72426667863067
T-STAT-1.48232066702108
p-value0.181814465746784
Lambda5.03823680021112


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')