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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 computationMon, 01 Jun 2009 05:38:22 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/01/t12438564033w93p79fy7bkmwi.htm/, Retrieved Sun, 12 May 2024 19:09:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40909, Retrieved Sun, 12 May 2024 19:09:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [ben eysackers, op...] [2009-06-01 11:38:22] [2b08e9b5345c911f5a04c663d4ad43d5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
46
33
34
25
33
18
26
21
23
24
26
32
47
45
47
43
48
48
43
44
46
36
32
18
31
37
32
29
29
40
26
29
19
30
12
24
40
43
49
49
48
33
6
46
43
44
38
38
39
47
41
36
38
11
24
30
18
21
22
15
15
16
26
39
28
25
25
13
20
13
10
19
31
36
26
33
42
44
45
42
60
42
63
71

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=40909&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=40909&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40909&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
128.41666666666677.5733784142917828
241.41666666666678.8467593792954230
328.16666666666677.4691283820723528
439.7511.709553209394343
528.511.579762911688236
620.758.2255146288296729
744.583333333333313.594506466238745

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 28.4166666666667 & 7.57337841429178 & 28 \tabularnewline
2 & 41.4166666666667 & 8.84675937929542 & 30 \tabularnewline
3 & 28.1666666666667 & 7.46912838207235 & 28 \tabularnewline
4 & 39.75 & 11.7095532093943 & 43 \tabularnewline
5 & 28.5 & 11.5797629116882 & 36 \tabularnewline
6 & 20.75 & 8.22551462882967 & 29 \tabularnewline
7 & 44.5833333333333 & 13.5945064662387 & 45 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40909&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]28.4166666666667[/C][C]7.57337841429178[/C][C]28[/C][/ROW]
[ROW][C]2[/C][C]41.4166666666667[/C][C]8.84675937929542[/C][C]30[/C][/ROW]
[ROW][C]3[/C][C]28.1666666666667[/C][C]7.46912838207235[/C][C]28[/C][/ROW]
[ROW][C]4[/C][C]39.75[/C][C]11.7095532093943[/C][C]43[/C][/ROW]
[ROW][C]5[/C][C]28.5[/C][C]11.5797629116882[/C][C]36[/C][/ROW]
[ROW][C]6[/C][C]20.75[/C][C]8.22551462882967[/C][C]29[/C][/ROW]
[ROW][C]7[/C][C]44.5833333333333[/C][C]13.5945064662387[/C][C]45[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40909&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40909&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
128.41666666666677.5733784142917828
241.41666666666678.8467593792954230
328.16666666666677.4691283820723528
439.7511.709553209394343
528.511.579762911688236
620.758.2255146288296729
744.583333333333313.594506466238745






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4.05850798059298
beta0.17526756758975
S.D.0.0942842749617298
T-STAT1.85892682168783
p-value0.122139129075406

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4.05850798059298 \tabularnewline
beta & 0.17526756758975 \tabularnewline
S.D. & 0.0942842749617298 \tabularnewline
T-STAT & 1.85892682168783 \tabularnewline
p-value & 0.122139129075406 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40909&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.05850798059298[/C][/ROW]
[ROW][C]beta[/C][C]0.17526756758975[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0942842749617298[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.85892682168783[/C][/ROW]
[ROW][C]p-value[/C][C]0.122139129075406[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40909&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40909&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)
alpha4.05850798059298
beta0.17526756758975
S.D.0.0942842749617298
T-STAT1.85892682168783
p-value0.122139129075406






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.413091584746314
beta0.533570172214804
S.D.0.308050628588879
T-STAT1.73208597125410
p-value0.143804291101603
Lambda0.466429827785196

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.413091584746314 \tabularnewline
beta & 0.533570172214804 \tabularnewline
S.D. & 0.308050628588879 \tabularnewline
T-STAT & 1.73208597125410 \tabularnewline
p-value & 0.143804291101603 \tabularnewline
Lambda & 0.466429827785196 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40909&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.413091584746314[/C][/ROW]
[ROW][C]beta[/C][C]0.533570172214804[/C][/ROW]
[ROW][C]S.D.[/C][C]0.308050628588879[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.73208597125410[/C][/ROW]
[ROW][C]p-value[/C][C]0.143804291101603[/C][/ROW]
[ROW][C]Lambda[/C][C]0.466429827785196[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40909&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40909&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)
alpha0.413091584746314
beta0.533570172214804
S.D.0.308050628588879
T-STAT1.73208597125410
p-value0.143804291101603
Lambda0.466429827785196


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')