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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 computationTue, 29 Nov 2011 14:28:20 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/29/t1322594974olc98nussybsvgi.htm/, Retrieved Thu, 25 Apr 2024 21:10:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148695, Retrieved Thu, 25 Apr 2024 21:10:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact139

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] [Opgave 8 Oefening...] [2011-11-29 19:28:20] [b59b09b8e0844ceffdb892999921d72c] [Current]
- RMPD    [Classical Decomposition] [Multiplicatief de...] [2011-12-06 12:05:32] [74be16979710d4c4e7c6647856088456]
- RMP     [Classical Decomposition] [Oefening 2 opgave 9] [2011-12-06 12:16:42] [74be16979710d4c4e7c6647856088456]
- RMP     [Classical Decomposition] [Oefening 2 opgave 9] [2011-12-06 12:16:42] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14,5
15,1
17,4
16,2
15,6
17,2
14,9
13,8
17,5
16,2
17,5
16,6
16,2
16,6
19,6
15,9
18
18,3
16,3
14,9
18,2
18,4
18,5
16
17,4
17,2
19,6
17,2
18,3
19,3
18,1
16,2
18,4
20,5
19
16,5
18,7
19
19,2
20,5
19,3
20,6
20,1
16,1
20,4
19,7
15,6
14,4
13,7
14,1
15
14,2
13,6
15,4
14,8
12,5
16,2
16,1
16
15,8
14,9
15,4
18,6
17,1
16,8
19,5
17,3
15,8
19,3
18,8
18,5
17,3

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=148695&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=148695&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148695&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
115.81.278019300845392.9
215.3751.424488212189443.4
316.950.65574385243021.3
417.0751.707581135212423.7
516.8751.584034932274753.4
617.7751.189887949906772.5
717.851.170469991071962.4
817.9751.294539815275433.1
918.61.655294535724684
1019.350.7937253933193771.8
1119.0252.022168802713234.5
1217.5252.970269348055836
1314.250.5446711546122731.3
1414.0751.289379695822762.9
1516.0250.1707825127659930.399999999999999
1616.51.687206764645843.7
1717.351.563116545025783.7
1818.4750.852

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15.8 & 1.27801930084539 & 2.9 \tabularnewline
2 & 15.375 & 1.42448821218944 & 3.4 \tabularnewline
3 & 16.95 & 0.6557438524302 & 1.3 \tabularnewline
4 & 17.075 & 1.70758113521242 & 3.7 \tabularnewline
5 & 16.875 & 1.58403493227475 & 3.4 \tabularnewline
6 & 17.775 & 1.18988794990677 & 2.5 \tabularnewline
7 & 17.85 & 1.17046999107196 & 2.4 \tabularnewline
8 & 17.975 & 1.29453981527543 & 3.1 \tabularnewline
9 & 18.6 & 1.65529453572468 & 4 \tabularnewline
10 & 19.35 & 0.793725393319377 & 1.8 \tabularnewline
11 & 19.025 & 2.02216880271323 & 4.5 \tabularnewline
12 & 17.525 & 2.97026934805583 & 6 \tabularnewline
13 & 14.25 & 0.544671154612273 & 1.3 \tabularnewline
14 & 14.075 & 1.28937969582276 & 2.9 \tabularnewline
15 & 16.025 & 0.170782512765993 & 0.399999999999999 \tabularnewline
16 & 16.5 & 1.68720676464584 & 3.7 \tabularnewline
17 & 17.35 & 1.56311654502578 & 3.7 \tabularnewline
18 & 18.475 & 0.85 & 2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148695&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]15.8[/C][C]1.27801930084539[/C][C]2.9[/C][/ROW]
[ROW][C]2[/C][C]15.375[/C][C]1.42448821218944[/C][C]3.4[/C][/ROW]
[ROW][C]3[/C][C]16.95[/C][C]0.6557438524302[/C][C]1.3[/C][/ROW]
[ROW][C]4[/C][C]17.075[/C][C]1.70758113521242[/C][C]3.7[/C][/ROW]
[ROW][C]5[/C][C]16.875[/C][C]1.58403493227475[/C][C]3.4[/C][/ROW]
[ROW][C]6[/C][C]17.775[/C][C]1.18988794990677[/C][C]2.5[/C][/ROW]
[ROW][C]7[/C][C]17.85[/C][C]1.17046999107196[/C][C]2.4[/C][/ROW]
[ROW][C]8[/C][C]17.975[/C][C]1.29453981527543[/C][C]3.1[/C][/ROW]
[ROW][C]9[/C][C]18.6[/C][C]1.65529453572468[/C][C]4[/C][/ROW]
[ROW][C]10[/C][C]19.35[/C][C]0.793725393319377[/C][C]1.8[/C][/ROW]
[ROW][C]11[/C][C]19.025[/C][C]2.02216880271323[/C][C]4.5[/C][/ROW]
[ROW][C]12[/C][C]17.525[/C][C]2.97026934805583[/C][C]6[/C][/ROW]
[ROW][C]13[/C][C]14.25[/C][C]0.544671154612273[/C][C]1.3[/C][/ROW]
[ROW][C]14[/C][C]14.075[/C][C]1.28937969582276[/C][C]2.9[/C][/ROW]
[ROW][C]15[/C][C]16.025[/C][C]0.170782512765993[/C][C]0.399999999999999[/C][/ROW]
[ROW][C]16[/C][C]16.5[/C][C]1.68720676464584[/C][C]3.7[/C][/ROW]
[ROW][C]17[/C][C]17.35[/C][C]1.56311654502578[/C][C]3.7[/C][/ROW]
[ROW][C]18[/C][C]18.475[/C][C]0.85[/C][C]2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148695&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148695&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
115.81.278019300845392.9
215.3751.424488212189443.4
316.950.65574385243021.3
417.0751.707581135212423.7
516.8751.584034932274753.4
617.7751.189887949906772.5
717.851.170469991071962.4
817.9751.294539815275433.1
918.61.655294535724684
1019.350.7937253933193771.8
1119.0252.022168802713234.5
1217.5252.970269348055836
1314.250.5446711546122731.3
1414.0751.289379695822762.9
1516.0250.1707825127659930.399999999999999
1616.51.687206764645843.7
1717.351.563116545025783.7
1818.4750.852






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.357401294173403
beta0.0986951384618328
S.D.0.101103586402409
T-STAT0.976178412395874
p-value0.343505433865728

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.357401294173403 \tabularnewline
beta & 0.0986951384618328 \tabularnewline
S.D. & 0.101103586402409 \tabularnewline
T-STAT & 0.976178412395874 \tabularnewline
p-value & 0.343505433865728 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148695&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.357401294173403[/C][/ROW]
[ROW][C]beta[/C][C]0.0986951384618328[/C][/ROW]
[ROW][C]S.D.[/C][C]0.101103586402409[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.976178412395874[/C][/ROW]
[ROW][C]p-value[/C][C]0.343505433865728[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148695&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148695&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-0.357401294173403
beta0.0986951384618328
S.D.0.101103586402409
T-STAT0.976178412395874
p-value0.343505433865728






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.92961144813542
beta1.78988549620052
S.D.1.66787068462858
T-STAT1.07315603823273
p-value0.299120672154098
Lambda-0.78988549620052

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.92961144813542 \tabularnewline
beta & 1.78988549620052 \tabularnewline
S.D. & 1.66787068462858 \tabularnewline
T-STAT & 1.07315603823273 \tabularnewline
p-value & 0.299120672154098 \tabularnewline
Lambda & -0.78988549620052 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148695&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.92961144813542[/C][/ROW]
[ROW][C]beta[/C][C]1.78988549620052[/C][/ROW]
[ROW][C]S.D.[/C][C]1.66787068462858[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.07315603823273[/C][/ROW]
[ROW][C]p-value[/C][C]0.299120672154098[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.78988549620052[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148695&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148695&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-4.92961144813542
beta1.78988549620052
S.D.1.66787068462858
T-STAT1.07315603823273
p-value0.299120672154098
Lambda-0.78988549620052


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')