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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSat, 06 Dec 2008 10:47:18 -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/06/t1228585780x7t1rto7djm88wq.htm/, Retrieved Sun, 19 May 2024 11:29:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29767, Retrieved Sun, 19 May 2024 11:29:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact194

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]
F RMP   [Standard Deviation-Mean Plot] [step 1] [2008-12-06 09:05:45] [9f5bfe3b95f9ec3d2ed4c0a560a9648a]
F    D      [Standard Deviation-Mean Plot] [step 1] [2008-12-06 17:47:18] [a9e6d7cd6e144e8b311d9f96a24c5a25] [Current]
Feedback Forum
2008-12-13 11:01:48 [Sam De Cuyper] [reply] 
Juist maar Bèta is positief en significant verschillend van num omdat de p-waarde kleiner is dan 0,05.
De grafiek van SMP geeft het verband weer tussen de standaarddeviatie en het gemiddelde. Er treedt een positief lineair verband maar er moet wel opgepast worden met outliers die een sterke invloed hebben op het gemiddelde.
2008-12-13 11:19:08 [Ken Wright] [reply] 
Deze calculator gaat in dit geval de tijdreeks onderverdelen in de verschillende jaren. Hij berekent voor elk jaar het gemiddelde, de standaardafwijking en de range. Maar in jouw geval is het niet nodig om de lambda parameter te gebruiken, want de helling van de regressie rechte(beta) is niet significant van 0 (de p value is te hoog, groter als 0.005)
2008-12-16 18:49:57 [Kevin Vermeiren] [reply] 
Het antwoord van de student is correct maar zeer beperkt. Hij beargumenteert zijn antwoord niet. Hier had dus nog gesproken moeten worden over de waarschijnlijkheid waarmee de nul hypothese (beta=0) wordt verworpen. Dit doen we aan de hand van de p-waarde. We zien dat deze zeer klein is (0.01<0.05). Bijgevolg kunnen we dan concluderen dat de beta significant verschillend is van 0. Met andere woorden de nul hypothese wordt verworpen. De helling van de regressierechte is dus niet toe te schrijven aan toeval. We gaan dus de transformatie met lambda -0.11 uitvoeren.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2648,9
2669,6
3042,3
2604,2
2732,1
2621,7
2483,7
2479,3
2684,6
2834,7
2566,1
2251,2
2350
2299,8
2542,8
2530,2
2508,1
2616,8
2534,1
2181,8
2578,9
2841,9
2529,9
2103,2
2326,2
2452,6
2782,1
2727,3
2648,2
2760,7
2613
2225,4
2713,9
2923,3
2707
2473,9
2521
2531,8
3068,8
2826,9
2674,2
2966,6
2798,8
2629,6
3124,6
3115,7
3083
2863,9
2728,7
2789,4
3225,7
3148,2
2836,5
3153,5
2656,9
2834,7
3172,5
2998,8
3103,1
2735,6
2818,1
2874,4
3438,5
2949,1
3306,8
3530
3003,8
3206,4
3514,6
3522,6
3525,5
2996,2
3231,1
3030
3541,7
3113,2
3390,8
3424,2
3079,8
3123,4
3317,1
3579,9
3317,9
2668,1
3609,2
3535,2
3644,7
3925,7
3663,2
3905,3
3990
3695,8

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=29767&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=29767&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29767&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
12634.86666666667195.253091389022791.1
22468.125202.421410675847738.7
32612.8203.956550631390697.9
42850.40833333333224.434632955114603.6
52948.63333333333205.565346094986568.8
63223.83333333333281.917129452589711.9
73234.76666666667252.531907374938911.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2634.86666666667 & 195.253091389022 & 791.1 \tabularnewline
2 & 2468.125 & 202.421410675847 & 738.7 \tabularnewline
3 & 2612.8 & 203.956550631390 & 697.9 \tabularnewline
4 & 2850.40833333333 & 224.434632955114 & 603.6 \tabularnewline
5 & 2948.63333333333 & 205.565346094986 & 568.8 \tabularnewline
6 & 3223.83333333333 & 281.917129452589 & 711.9 \tabularnewline
7 & 3234.76666666667 & 252.531907374938 & 911.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29767&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]2634.86666666667[/C][C]195.253091389022[/C][C]791.1[/C][/ROW]
[ROW][C]2[/C][C]2468.125[/C][C]202.421410675847[/C][C]738.7[/C][/ROW]
[ROW][C]3[/C][C]2612.8[/C][C]203.956550631390[/C][C]697.9[/C][/ROW]
[ROW][C]4[/C][C]2850.40833333333[/C][C]224.434632955114[/C][C]603.6[/C][/ROW]
[ROW][C]5[/C][C]2948.63333333333[/C][C]205.565346094986[/C][C]568.8[/C][/ROW]
[ROW][C]6[/C][C]3223.83333333333[/C][C]281.917129452589[/C][C]711.9[/C][/ROW]
[ROW][C]7[/C][C]3234.76666666667[/C][C]252.531907374938[/C][C]911.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29767&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29767&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
12634.86666666667195.253091389022791.1
22468.125202.421410675847738.7
32612.8203.956550631390697.9
42850.40833333333224.434632955114603.6
52948.63333333333205.565346094986568.8
63223.83333333333281.917129452589711.9
73234.76666666667252.531907374938911.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-37.6387917753487
beta0.09159925489365
S.D.0.0243793062044199
T-STAT3.75725437490274
p-value0.0131947594470037

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -37.6387917753487 \tabularnewline
beta & 0.09159925489365 \tabularnewline
S.D. & 0.0243793062044199 \tabularnewline
T-STAT & 3.75725437490274 \tabularnewline
p-value & 0.0131947594470037 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29767&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-37.6387917753487[/C][/ROW]
[ROW][C]beta[/C][C]0.09159925489365[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0243793062044199[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.75725437490274[/C][/ROW]
[ROW][C]p-value[/C][C]0.0131947594470037[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29767&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29767&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-37.6387917753487
beta0.09159925489365
S.D.0.0243793062044199
T-STAT3.75725437490274
p-value0.0131947594470037






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.4030681160305
beta1.10736907917068
S.D.0.300545276556095
T-STAT3.68453329847624
p-value0.0142263107189296
Lambda-0.107369079170681

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.4030681160305 \tabularnewline
beta & 1.10736907917068 \tabularnewline
S.D. & 0.300545276556095 \tabularnewline
T-STAT & 3.68453329847624 \tabularnewline
p-value & 0.0142263107189296 \tabularnewline
Lambda & -0.107369079170681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29767&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.4030681160305[/C][/ROW]
[ROW][C]beta[/C][C]1.10736907917068[/C][/ROW]
[ROW][C]S.D.[/C][C]0.300545276556095[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.68453329847624[/C][/ROW]
[ROW][C]p-value[/C][C]0.0142263107189296[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.107369079170681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29767&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29767&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-3.4030681160305
beta1.10736907917068
S.D.0.300545276556095
T-STAT3.68453329847624
p-value0.0142263107189296
Lambda-0.107369079170681


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')