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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 computationTue, 02 Dec 2008 13:39:05 -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/02/t12282503968ns34okfsccassh.htm/, Retrieved Sat, 18 May 2024 05:45:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28410, Retrieved Sat, 18 May 2024 05:45:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact170

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD    [Standard Deviation-Mean Plot] [workshop, Q8] [2008-12-02 20:39:05] [a16dfd7e948381d8b6391003c5d09447] [Current]
Feedback Forum
2008-12-07 14:52:05 [Stephanie Vanderlinden] [reply] 
Correct verklaring.

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=28410&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=28410&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28410&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=28410&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=28410&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28410&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=28410&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=28410&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28410&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=28410&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=28410&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28410&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')