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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 20:03:17 +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/t1447877074chr2o0137peumnj.htm/, Retrieved Tue, 14 May 2024 09:54:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283552, Retrieved Tue, 14 May 2024 09:54:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114

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 20:03:17] [663b8bcb3523d59827bca0af0b37f04c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
91.99
92.17
92.19
92.24
92.19
92.21
92.22
92.14
92.43
92.93
93.01
93.07
93.08
93.11
93.21
93.49
93.48
93.51
93.52
93.49
93.76
94.25
94.42
94.45
94.45
94.53
94.78
95.05
95.21
95.23
95.23
95.34
95.93
96.75
97.15
97.21
97.21
97.35
97.44
97.34
97.44
97.43
97.43
97.47
97.69
98.54
98.64
98.72
98.72
98.73
98.68
98.75
98.73
98.74
98.75
98.85
99.14
99.83
99.93
100
100
100.08
100.25
100.4
100.33
100.29
100.29
100.32
100.82
101.42
101.46
101.55
101.56
101.56
101.6
101.66
101.82
101.94
101.95
101.93
102.26
102.65
102.9
102.94
99.14
99.18
99.23
99.32
99.46
99.5
99.95
100.13
100.43
101.09
101.27
101.29
101.04
101.14
101.11
101.01
101.08
101.06
101.26
101.32
101.4
101.85
102.12
102.15

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'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283552&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283552&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283552&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
192.39916666666670.3782365381449551.08
293.64750.4797371439368951.37
395.57166666666670.9701062109924152.75999999999999
497.7250.5598944705762141.51000000000001
599.07083333333330.5269890171933611.31999999999999
6100.6008333333330.5640189928029221.55
7102.0641666666670.5081599306827691.38
899.99916666666670.8354798113368852.15000000000001
9101.3783333333330.4215950951356341.14

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 92.3991666666667 & 0.378236538144955 & 1.08 \tabularnewline
2 & 93.6475 & 0.479737143936895 & 1.37 \tabularnewline
3 & 95.5716666666667 & 0.970106210992415 & 2.75999999999999 \tabularnewline
4 & 97.725 & 0.559894470576214 & 1.51000000000001 \tabularnewline
5 & 99.0708333333333 & 0.526989017193361 & 1.31999999999999 \tabularnewline
6 & 100.600833333333 & 0.564018992802922 & 1.55 \tabularnewline
7 & 102.064166666667 & 0.508159930682769 & 1.38 \tabularnewline
8 & 99.9991666666667 & 0.835479811336885 & 2.15000000000001 \tabularnewline
9 & 101.378333333333 & 0.421595095135634 & 1.14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283552&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]92.3991666666667[/C][C]0.378236538144955[/C][C]1.08[/C][/ROW]
[ROW][C]2[/C][C]93.6475[/C][C]0.479737143936895[/C][C]1.37[/C][/ROW]
[ROW][C]3[/C][C]95.5716666666667[/C][C]0.970106210992415[/C][C]2.75999999999999[/C][/ROW]
[ROW][C]4[/C][C]97.725[/C][C]0.559894470576214[/C][C]1.51000000000001[/C][/ROW]
[ROW][C]5[/C][C]99.0708333333333[/C][C]0.526989017193361[/C][C]1.31999999999999[/C][/ROW]
[ROW][C]6[/C][C]100.600833333333[/C][C]0.564018992802922[/C][C]1.55[/C][/ROW]
[ROW][C]7[/C][C]102.064166666667[/C][C]0.508159930682769[/C][C]1.38[/C][/ROW]
[ROW][C]8[/C][C]99.9991666666667[/C][C]0.835479811336885[/C][C]2.15000000000001[/C][/ROW]
[ROW][C]9[/C][C]101.378333333333[/C][C]0.421595095135634[/C][C]1.14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283552&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283552&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
192.39916666666670.3782365381449551.08
293.64750.4797371439368951.37
395.57166666666670.9701062109924152.75999999999999
497.7250.5598944705762141.51000000000001
599.07083333333330.5269890171933611.31999999999999
6100.6008333333330.5640189928029221.55
7102.0641666666670.5081599306827691.38
899.99916666666670.8354798113368852.15000000000001
9101.3783333333330.4215950951356341.14






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.369724027663147
beta0.00217200575873458
S.D.0.0211675971080008
T-STAT0.102609934781573
p-value0.921150197141432

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.369724027663147 \tabularnewline
beta & 0.00217200575873458 \tabularnewline
S.D. & 0.0211675971080008 \tabularnewline
T-STAT & 0.102609934781573 \tabularnewline
p-value & 0.921150197141432 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283552&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.369724027663147[/C][/ROW]
[ROW][C]beta[/C][C]0.00217200575873458[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0211675971080008[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.102609934781573[/C][/ROW]
[ROW][C]p-value[/C][C]0.921150197141432[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283552&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283552&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)
alpha0.369724027663147
beta0.00217200575873458
S.D.0.0211675971080008
T-STAT0.102609934781573
p-value0.921150197141432






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.25608652934153
beta1.01913761790416
S.D.3.18579732192088
T-STAT0.319900331038532
p-value0.758380458018571
Lambda-0.0191376179041556

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.25608652934153 \tabularnewline
beta & 1.01913761790416 \tabularnewline
S.D. & 3.18579732192088 \tabularnewline
T-STAT & 0.319900331038532 \tabularnewline
p-value & 0.758380458018571 \tabularnewline
Lambda & -0.0191376179041556 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283552&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.25608652934153[/C][/ROW]
[ROW][C]beta[/C][C]1.01913761790416[/C][/ROW]
[ROW][C]S.D.[/C][C]3.18579732192088[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.319900331038532[/C][/ROW]
[ROW][C]p-value[/C][C]0.758380458018571[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0191376179041556[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283552&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283552&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-5.25608652934153
beta1.01913761790416
S.D.3.18579732192088
T-STAT0.319900331038532
p-value0.758380458018571
Lambda-0.0191376179041556


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')