FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationSun, 07 Dec 2008 09:07:52 -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/t12286661423yw3su9dvhqjwa8.htm/, Retrieved Wed, 22 May 2024 16:23:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30130, Retrieved Wed, 22 May 2024 16:23:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact181

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 RMPD    [Standard Deviation-Mean Plot] [workshop8, Q1] [2008-12-07 16:07:52] [a16dfd7e948381d8b6391003c5d09447] [Current]
Feedback Forum
2008-12-15 18:25:32 [Peter Van Doninck] [reply] 
De studente merk correct op dat er zowel links als rechts zich outliers voordoen. Dit vormt een probleem om de transformatie toe te passen. De studente had beter gebruik gemaakt van de p-waarde. Deze bedraagt hier 0,50. Hieruit kunnen we afleiden dat er 50% kans is dat we ons vergissen bij het verwerpen van de nulhypothese. In dit geval hebben we geen transformatie nodig en stellen we lambda gelijk aan 1, zoals gezegd werd tijdens het college.
2008-12-15 18:43:00 [Lana Van Wesemael] [reply] 
Door de SMP te berekenen kunnen we besluiten of dat een lambda transformatie nodig is en waaraan deze dan gelijk moet zijn. De studente merkt goed op dat de lambda tranformatie hier niet nodig is. De beta waarde is immers niet significant verschillend van nul (de p-waarde is te groot) en bovendien vertoont de eerste scatterplot geen verband tussen het gemiddelde en de standaardafwijking. Het is hier dus niet nodig om de lamda transformatie toe te passen en zal deze dus gedurende de volgende stappen gelijk blijven aan 1.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7,5
7,2
6,9
6,7
6,4
6,3
6,8
7,3
7,1
7,1
6,8
6,5
6,3
6,1
6,1
6,3
6,3
6
6,2
6,4
6,8
7,5
7,5
7,6
7,6
7,4
7,3
7,1
6,9
6,8
7,5
7,6
7,8
8
8,1
8,2
8,3
8,2
8
7,9
7,6
7,6
8,2
8,3
8,4
8,4
8,4
8,6
8,9
8,8
8,3
7,5
7,2
7,5
8,8
9,3
9,3
8,7
8,2
8,3
8,5
8,6
8,6
8,2
8,1
8
8,6
8,7
8,8
8,5
8,4
8,5
8,7
8,7
8,6
8,5
8,3
8,1
8,2
8,1
8,1
7,9
7,9
7,9
8
8
7,9
8
7,7
7,2
7,5
7,3
7
7
7
7,2
7,3
7,1
6,8
6,6
6,2
6,2
6,8
6,9
6,8
6,7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30130&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30130&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30130&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
16.883333333333330.3713203305486891.2
26.591666666666670.6022055422789761.6
37.5250.4535215741084631.4
48.158333333333330.3203927514028921
58.40.7006490497453712.1
68.458333333333330.2429303429280740.8
78.250.3060005941764880.799999999999999
87.483333333333330.4174235549683611

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.88333333333333 & 0.371320330548689 & 1.2 \tabularnewline
2 & 6.59166666666667 & 0.602205542278976 & 1.6 \tabularnewline
3 & 7.525 & 0.453521574108463 & 1.4 \tabularnewline
4 & 8.15833333333333 & 0.320392751402892 & 1 \tabularnewline
5 & 8.4 & 0.700649049745371 & 2.1 \tabularnewline
6 & 8.45833333333333 & 0.242930342928074 & 0.8 \tabularnewline
7 & 8.25 & 0.306000594176488 & 0.799999999999999 \tabularnewline
8 & 7.48333333333333 & 0.417423554968361 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30130&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]6.88333333333333[/C][C]0.371320330548689[/C][C]1.2[/C][/ROW]
[ROW][C]2[/C][C]6.59166666666667[/C][C]0.602205542278976[/C][C]1.6[/C][/ROW]
[ROW][C]3[/C][C]7.525[/C][C]0.453521574108463[/C][C]1.4[/C][/ROW]
[ROW][C]4[/C][C]8.15833333333333[/C][C]0.320392751402892[/C][C]1[/C][/ROW]
[ROW][C]5[/C][C]8.4[/C][C]0.700649049745371[/C][C]2.1[/C][/ROW]
[ROW][C]6[/C][C]8.45833333333333[/C][C]0.242930342928074[/C][C]0.8[/C][/ROW]
[ROW][C]7[/C][C]8.25[/C][C]0.306000594176488[/C][C]0.799999999999999[/C][/ROW]
[ROW][C]8[/C][C]7.48333333333333[/C][C]0.417423554968361[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30130&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30130&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
16.883333333333330.3713203305486891.2
26.591666666666670.6022055422789761.6
37.5250.4535215741084631.4
48.158333333333330.3203927514028921
58.40.7006490497453712.1
68.458333333333330.2429303429280740.8
78.250.3060005941764880.799999999999999
87.483333333333330.4174235549683611






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.893912349681398
beta-0.0605158713731802
S.D.0.0857089864679134
T-STAT-0.706062151322198
p-value0.506625918829552

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.893912349681398 \tabularnewline
beta & -0.0605158713731802 \tabularnewline
S.D. & 0.0857089864679134 \tabularnewline
T-STAT & -0.706062151322198 \tabularnewline
p-value & 0.506625918829552 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30130&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.893912349681398[/C][/ROW]
[ROW][C]beta[/C][C]-0.0605158713731802[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0857089864679134[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.706062151322198[/C][/ROW]
[ROW][C]p-value[/C][C]0.506625918829552[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30130&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30130&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)
alpha0.893912349681398
beta-0.0605158713731802
S.D.0.0857089864679134
T-STAT-0.706062151322198
p-value0.506625918829552






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.98325630459511
beta-1.41688459323719
S.D.1.41191910589233
T-STAT-1.003516835578
p-value0.354350933178103
Lambda2.41688459323719

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.98325630459511 \tabularnewline
beta & -1.41688459323719 \tabularnewline
S.D. & 1.41191910589233 \tabularnewline
T-STAT & -1.003516835578 \tabularnewline
p-value & 0.354350933178103 \tabularnewline
Lambda & 2.41688459323719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30130&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.98325630459511[/C][/ROW]
[ROW][C]beta[/C][C]-1.41688459323719[/C][/ROW]
[ROW][C]S.D.[/C][C]1.41191910589233[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.003516835578[/C][/ROW]
[ROW][C]p-value[/C][C]0.354350933178103[/C][/ROW]
[ROW][C]Lambda[/C][C]2.41688459323719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30130&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30130&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)
alpha1.98325630459511
beta-1.41688459323719
S.D.1.41191910589233
T-STAT-1.003516835578
p-value0.354350933178103
Lambda2.41688459323719


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')