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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 computationSun, 23 Nov 2014 09:29:02 +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/2014/Nov/23/t1416734954b9nzf4ug96jg9ul.htm/, Retrieved Sun, 19 May 2024 13:37:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=257932, Retrieved Sun, 19 May 2024 13:37:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103

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] [] [2014-11-23 09:29:02] [3bbf952604bb7b6db5ab93a0a8bc191d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1,4718
1,4748
1,5527
1,5751
1,5557
1,5553
1,577
1,4975
1,437
1,3322
1,2732
1,3449
1,3239
1,2785
1,305
1,319
1,365
1,4016
1,4088
1,4268
1,4562
1,4816
1,4914
1,4614
1,4272
1,3686
1,3569
1,3406
1,2565
1,2209
1,277
1,2894
1,3067
1,3898
1,3661
1,322
1,336
1,3649
1,3999
1,4442
1,4349
1,4388
1,4264
1,4343
1,377
1,3706
1,3556
1,3179
1,2905
1,3224
1,3201
1,3162
1,2789
1,2526
1,2288
1,24
1,2856
1,2974
1,2828
1,3119
1,3288
1,3359
1,2964
1,3026
1,2982
1,3189
1,308
1,331
1,3348
1,3635
1,3493
1,3704

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 Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257932&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257932&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257932&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 Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11.47060.1040940047177640.3038
21.393266666666670.07358332732763630.2129
31.326808333333330.05946740066981440.2063
41.391708333333330.04385789984470160.1263
51.28560.0313094815728980.0936000000000001
61.328150.02457694780961140.0740000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.4706 & 0.104094004717764 & 0.3038 \tabularnewline
2 & 1.39326666666667 & 0.0735833273276363 & 0.2129 \tabularnewline
3 & 1.32680833333333 & 0.0594674006698144 & 0.2063 \tabularnewline
4 & 1.39170833333333 & 0.0438578998447016 & 0.1263 \tabularnewline
5 & 1.2856 & 0.031309481572898 & 0.0936000000000001 \tabularnewline
6 & 1.32815 & 0.0245769478096114 & 0.0740000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257932&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]1.4706[/C][C]0.104094004717764[/C][C]0.3038[/C][/ROW]
[ROW][C]2[/C][C]1.39326666666667[/C][C]0.0735833273276363[/C][C]0.2129[/C][/ROW]
[ROW][C]3[/C][C]1.32680833333333[/C][C]0.0594674006698144[/C][C]0.2063[/C][/ROW]
[ROW][C]4[/C][C]1.39170833333333[/C][C]0.0438578998447016[/C][C]0.1263[/C][/ROW]
[ROW][C]5[/C][C]1.2856[/C][C]0.031309481572898[/C][C]0.0936000000000001[/C][/ROW]
[ROW][C]6[/C][C]1.32815[/C][C]0.0245769478096114[/C][C]0.0740000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257932&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257932&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
11.47060.1040940047177640.3038
21.393266666666670.07358332732763630.2129
31.326808333333330.05946740066981440.2063
41.391708333333330.04385789984470160.1263
51.28560.0313094815728980.0936000000000001
61.328150.02457694780961140.0740000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.460476827815502
beta0.378196632823051
S.D.0.120435241537236
T-STAT3.14024888392922
p-value0.0348393856317039

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.460476827815502 \tabularnewline
beta & 0.378196632823051 \tabularnewline
S.D. & 0.120435241537236 \tabularnewline
T-STAT & 3.14024888392922 \tabularnewline
p-value & 0.0348393856317039 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257932&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.460476827815502[/C][/ROW]
[ROW][C]beta[/C][C]0.378196632823051[/C][/ROW]
[ROW][C]S.D.[/C][C]0.120435241537236[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.14024888392922[/C][/ROW]
[ROW][C]p-value[/C][C]0.0348393856317039[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257932&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257932&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-0.460476827815502
beta0.378196632823051
S.D.0.120435241537236
T-STAT3.14024888392922
p-value0.0348393856317039






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.77370454709073
beta8.92535521827228
S.D.3.43383863456261
T-STAT2.59923548195769
p-value0.0600964676780357
Lambda-7.92535521827228

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.77370454709073 \tabularnewline
beta & 8.92535521827228 \tabularnewline
S.D. & 3.43383863456261 \tabularnewline
T-STAT & 2.59923548195769 \tabularnewline
p-value & 0.0600964676780357 \tabularnewline
Lambda & -7.92535521827228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=257932&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.77370454709073[/C][/ROW]
[ROW][C]beta[/C][C]8.92535521827228[/C][/ROW]
[ROW][C]S.D.[/C][C]3.43383863456261[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.59923548195769[/C][/ROW]
[ROW][C]p-value[/C][C]0.0600964676780357[/C][/ROW]
[ROW][C]Lambda[/C][C]-7.92535521827228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=257932&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=257932&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-5.77370454709073
beta8.92535521827228
S.D.3.43383863456261
T-STAT2.59923548195769
p-value0.0600964676780357
Lambda-7.92535521827228


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')