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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, 09 Dec 2008 11:28:09 -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/09/t1228847331j8pzc12as41x9rs.htm/, Retrieved Fri, 17 May 2024 04:19:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31669, Retrieved Fri, 17 May 2024 04:19:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact188

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 15:53:54] [74be16979710d4c4e7c6647856088456]
F    D      [Standard Deviation-Mean Plot] [step 1] [2008-12-09 18:28:09] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-16 17:58:20 [6066575aa30c0611e452e930b1dff53d] [reply] 
Het is inderdaad zo dat er geen significant verband is, maar dit is om een totaal andere reden dan vermeld. Als we de eerste tabel bekijken Regression: S.E.(k) = alpha + beta * Mean(k) zien we dat beta positief is. We zien ook dat de p-value groter is dan 0,05. Dit houdt in dat er geen significant verband is tussen de spreiding en het gemiddelde niveau. We kunnen dus stellen dat lambda gelijk is aan 1.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
113438
109416
109406
105645
101328
97686
93093
91382
122257
139183
139887
131822
116805
113706
113012
110452
107005
102841
98173
98181
137277
147579
146571
138920
130340
128140
127059
122860
117702
113537
108366
111078
150739
159129
157928
147768
137507
136919
136151
133001
125554
119647
114158
116193
152803
161761
160942
149470
139208
134588
130322
126611
122401
117352
112135
112879
148729
157230
157221
146681
136524
132111
125326
122716
116615
113719
110737
112093
143565
149946
149147
134339
122683
115614
116566
111272
104609
101802
94542
93051
124129
130374
123946
114971
105531
104919
104782
101281
94545
93248
84031
87486
115867
120327
117008
108811
104519

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' @ 72.249.76.132

\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' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31669&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31669&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31669&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' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1112878.58333333316956.290334313048505
2119210.16666666718392.689446098049406
3131220.518260.617885095150763
4137008.83333333316501.689741760847603
5133779.7516201.791164307145095
6128903.16666666714176.56511695139209
7112796.58333333312059.225095399637323
810315311594.709561613936296

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 112878.583333333 & 16956.2903343130 & 48505 \tabularnewline
2 & 119210.166666667 & 18392.6894460980 & 49406 \tabularnewline
3 & 131220.5 & 18260.6178850951 & 50763 \tabularnewline
4 & 137008.833333333 & 16501.6897417608 & 47603 \tabularnewline
5 & 133779.75 & 16201.7911643071 & 45095 \tabularnewline
6 & 128903.166666667 & 14176.565116951 & 39209 \tabularnewline
7 & 112796.583333333 & 12059.2250953996 & 37323 \tabularnewline
8 & 103153 & 11594.7095616139 & 36296 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31669&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]112878.583333333[/C][C]16956.2903343130[/C][C]48505[/C][/ROW]
[ROW][C]2[/C][C]119210.166666667[/C][C]18392.6894460980[/C][C]49406[/C][/ROW]
[ROW][C]3[/C][C]131220.5[/C][C]18260.6178850951[/C][C]50763[/C][/ROW]
[ROW][C]4[/C][C]137008.833333333[/C][C]16501.6897417608[/C][C]47603[/C][/ROW]
[ROW][C]5[/C][C]133779.75[/C][C]16201.7911643071[/C][C]45095[/C][/ROW]
[ROW][C]6[/C][C]128903.166666667[/C][C]14176.565116951[/C][C]39209[/C][/ROW]
[ROW][C]7[/C][C]112796.583333333[/C][C]12059.2250953996[/C][C]37323[/C][/ROW]
[ROW][C]8[/C][C]103153[/C][C]11594.7095616139[/C][C]36296[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31669&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31669&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
1112878.58333333316956.290334313048505
2119210.16666666718392.689446098049406
3131220.518260.617885095150763
4137008.83333333316501.689741760847603
5133779.7516201.791164307145095
6128903.16666666714176.56511695139209
7112796.58333333312059.225095399637323
810315311594.709561613936296






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha797.672381141834
beta0.120294324658782
S.D.0.0738498615691353
T-STAT1.62890386119637
p-value0.154456412244776

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 797.672381141834 \tabularnewline
beta & 0.120294324658782 \tabularnewline
S.D. & 0.0738498615691353 \tabularnewline
T-STAT & 1.62890386119637 \tabularnewline
p-value & 0.154456412244776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31669&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]797.672381141834[/C][/ROW]
[ROW][C]beta[/C][C]0.120294324658782[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0738498615691353[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.62890386119637[/C][/ROW]
[ROW][C]p-value[/C][C]0.154456412244776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31669&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31669&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)
alpha797.672381141834
beta0.120294324658782
S.D.0.0738498615691353
T-STAT1.62890386119637
p-value0.154456412244776






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.82127727978241
beta1.06379936176305
S.D.0.579868486910502
T-STAT1.83455280943253
p-value0.116252403039710
Lambda-0.0637993617630492

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.82127727978241 \tabularnewline
beta & 1.06379936176305 \tabularnewline
S.D. & 0.579868486910502 \tabularnewline
T-STAT & 1.83455280943253 \tabularnewline
p-value & 0.116252403039710 \tabularnewline
Lambda & -0.0637993617630492 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31669&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.82127727978241[/C][/ROW]
[ROW][C]beta[/C][C]1.06379936176305[/C][/ROW]
[ROW][C]S.D.[/C][C]0.579868486910502[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.83455280943253[/C][/ROW]
[ROW][C]p-value[/C][C]0.116252403039710[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0637993617630492[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31669&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31669&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-2.82127727978241
beta1.06379936176305
S.D.0.579868486910502
T-STAT1.83455280943253
p-value0.116252403039710
Lambda-0.0637993617630492


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')