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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, 07 Dec 2008 10:56:35 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/07/t1228672617snh74h7uzlj024t.htm/, Retrieved Fri, 17 May 2024 05:03:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30198, Retrieved Fri, 17 May 2024 05:03:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact190

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
-   PD  [Univariate Data Series] [part 1] [2008-12-07 17:49:27] [74be16979710d4c4e7c6647856088456]
F RMPD      [Standard Deviation-Mean Plot] [part1] [2008-12-07 17:56:35] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-14 17:13:57 [Jasmine Hendrikx] [reply] 
Evaluatie stap 1:
De student heeft stap 1 correct berekend, maar geen interpretatie gegeven. Hier zou je dus het volgende aan kunnen toevoegen:
In de eerste tabel die de output geeft krijgen we voor het eerste jaar en voor de volgende jaren steeds het gemiddelde en de standaardafwijking. In de laatste kolom zien we de range (dit is het verschil tussen de grootste en kleinste waarde). De grafiek geeft het verband weer tussen het gemiddelde niveau en de standaardafwijking. Op de x-as zien we het gemiddelde en op de y-as de standaardafwijking. We moeten hier goed opletten op outliers, zeker wanneer deze zich links of rechts bevinden, aangezien zij de helling dan sterk zullen beïnvloeden. Uit de grafiek kunnen we afleiden dat de punten vrij verspreid zijn en dat er niet meteen een verband op te merken valt. We kunnen dus niet van een verband spreken tussen het gemiddelde en de standaardafwijking. We zien uit de tweede tabel (die echter niet in het document wordt weergegeven) dat bèta gelijk is aan 0,014. Dit getal is niet significant verschillend van 0, doordat de p-waarde afgerond 0.64 bedraagt. De p-waarde is dus groter dan 5% waardoor we kunnen zeggen dat er geen significant verschil is. Het eventuele verband tussen het gemiddelde en de standaardafwijking is aan het toeval te wijten. In de derde tabel vind je een theoretische lambda die je eventueel kan gebruiken in de transformatie. We zien uit de vorige tabel dat er geen significant verband bestaat tussen het gemiddelde en de standaardafwijking (p-waarde is groter dan 5%), daarom mogen we deze lambda niet gebruiken en gebruiken we dus gewoon als lambda 1.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2174.56
2196.72
2350.44
2440.25
2408.64
2472.81
2407.6
2454.62
2448.05
2497.84
2645.64
2756.76
2849.27
2921.44
2981.85
3080.58
3106.22
3119.31
3061.26
3097.31
3161.69
3257.16
3277.01
3295.32
3363.99
3494.17
3667.03
3813.06
3917.96
3895.51
3801.06
3570.12
3701.61
3862.27
3970.1
4138.52
4199.75
4290.89
4443.91
4502.64
4356.98
4591.27
4696.96
4621.4
4562.84
4202.52
4296.49
4435.23
4105.18
4116.68
3844.49
3720.98
3674.4
3857.62
3801.06
3504.37
3032.6
3047.03
2962.34

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30198&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30198&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30198&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12437.8275161.517349595808582.2
23100.70166666667137.836137815447446.05
33766.28333333333217.593686252542774.53
44433.40666666667166.292423614292497.21

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2437.8275 & 161.517349595808 & 582.2 \tabularnewline
2 & 3100.70166666667 & 137.836137815447 & 446.05 \tabularnewline
3 & 3766.28333333333 & 217.593686252542 & 774.53 \tabularnewline
4 & 4433.40666666667 & 166.292423614292 & 497.21 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30198&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]2437.8275[/C][C]161.517349595808[/C][C]582.2[/C][/ROW]
[ROW][C]2[/C][C]3100.70166666667[/C][C]137.836137815447[/C][C]446.05[/C][/ROW]
[ROW][C]3[/C][C]3766.28333333333[/C][C]217.593686252542[/C][C]774.53[/C][/ROW]
[ROW][C]4[/C][C]4433.40666666667[/C][C]166.292423614292[/C][C]497.21[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30198&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30198&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
12437.8275161.517349595808582.2
23100.70166666667137.836137815447446.05
33766.28333333333217.593686252542774.53
44433.40666666667166.292423614292497.21






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha122.259922490437
beta0.0141357409545142
S.D.0.0257777888592458
T-STAT0.548369025431136
p-value0.638471858240454

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 122.259922490437 \tabularnewline
beta & 0.0141357409545142 \tabularnewline
S.D. & 0.0257777888592458 \tabularnewline
T-STAT & 0.548369025431136 \tabularnewline
p-value & 0.638471858240454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30198&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]122.259922490437[/C][/ROW]
[ROW][C]beta[/C][C]0.0141357409545142[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0257777888592458[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.548369025431136[/C][/ROW]
[ROW][C]p-value[/C][C]0.638471858240454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30198&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30198&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)
alpha122.259922490437
beta0.0141357409545142
S.D.0.0257777888592458
T-STAT0.548369025431136
p-value0.638471858240454






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.87627604278964
beta0.277247450624091
S.D.0.481476721425074
T-STAT0.575827321004211
p-value0.622890584446824
Lambda0.722752549375909

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.87627604278964 \tabularnewline
beta & 0.277247450624091 \tabularnewline
S.D. & 0.481476721425074 \tabularnewline
T-STAT & 0.575827321004211 \tabularnewline
p-value & 0.622890584446824 \tabularnewline
Lambda & 0.722752549375909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30198&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.87627604278964[/C][/ROW]
[ROW][C]beta[/C][C]0.277247450624091[/C][/ROW]
[ROW][C]S.D.[/C][C]0.481476721425074[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.575827321004211[/C][/ROW]
[ROW][C]p-value[/C][C]0.622890584446824[/C][/ROW]
[ROW][C]Lambda[/C][C]0.722752549375909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30198&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30198&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)
alpha2.87627604278964
beta0.277247450624091
S.D.0.481476721425074
T-STAT0.575827321004211
p-value0.622890584446824
Lambda0.722752549375909


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')