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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 computationSat, 03 Jan 2015 09:24:54 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Jan/03/t1420277136ip488krnc2655dw.htm/, Retrieved Tue, 14 May 2024 07:59:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271878, Retrieved Tue, 14 May 2024 07:59:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129

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] [] [2015-01-03 09:24:54] [062c419fa600f620f2df94d64c8876ba] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
53
47
49
44
48
51
47
44
33
47
41
36
46
24
17
22
30
24
18
24
24
28
19
22
26
14
16
21
15
23
29
17
24
18
22
8
26
22
34
25
20
35
38
24
14
25
31
17
32
27
30
19
36
27
28
38
26
25
30
27
30
50
48
34
41
26
39
33
38
28
36
20
39
22
32
32
31
28
44
40
32
35
32
31
41
23
36
36
42
36
64
30
25
51
38
27

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' @ yule.wessa.net

\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' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271878&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271878&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271878&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' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1455.8775381364525920
224.83333333333337.6613947618543829
319.41666666666675.8536442935278821
425.91666666666677.3664884113905724
528.755.0294586732027719
635.258.7399292695286530
733.16666666666675.7813702894938722
837.416666666666711.508560713528441

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 45 & 5.87753813645259 & 20 \tabularnewline
2 & 24.8333333333333 & 7.66139476185438 & 29 \tabularnewline
3 & 19.4166666666667 & 5.85364429352788 & 21 \tabularnewline
4 & 25.9166666666667 & 7.36648841139057 & 24 \tabularnewline
5 & 28.75 & 5.02945867320277 & 19 \tabularnewline
6 & 35.25 & 8.73992926952865 & 30 \tabularnewline
7 & 33.1666666666667 & 5.78137028949387 & 22 \tabularnewline
8 & 37.4166666666667 & 11.5085607135284 & 41 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271878&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]45[/C][C]5.87753813645259[/C][C]20[/C][/ROW]
[ROW][C]2[/C][C]24.8333333333333[/C][C]7.66139476185438[/C][C]29[/C][/ROW]
[ROW][C]3[/C][C]19.4166666666667[/C][C]5.85364429352788[/C][C]21[/C][/ROW]
[ROW][C]4[/C][C]25.9166666666667[/C][C]7.36648841139057[/C][C]24[/C][/ROW]
[ROW][C]5[/C][C]28.75[/C][C]5.02945867320277[/C][C]19[/C][/ROW]
[ROW][C]6[/C][C]35.25[/C][C]8.73992926952865[/C][C]30[/C][/ROW]
[ROW][C]7[/C][C]33.1666666666667[/C][C]5.78137028949387[/C][C]22[/C][/ROW]
[ROW][C]8[/C][C]37.4166666666667[/C][C]11.5085607135284[/C][C]41[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271878&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271878&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
1455.8775381364525920
224.83333333333337.6613947618543829
319.41666666666675.8536442935278821
425.91666666666677.3664884113905724
528.755.0294586732027719
635.258.7399292695286530
733.16666666666675.7813702894938722
837.416666666666711.508560713528441






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.24731054846305
beta0.0634230236687675
S.D.0.103252220699927
T-STAT0.614253361708204
p-value0.561600715162211

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.24731054846305 \tabularnewline
beta & 0.0634230236687675 \tabularnewline
S.D. & 0.103252220699927 \tabularnewline
T-STAT & 0.614253361708204 \tabularnewline
p-value & 0.561600715162211 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271878&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.24731054846305[/C][/ROW]
[ROW][C]beta[/C][C]0.0634230236687675[/C][/ROW]
[ROW][C]S.D.[/C][C]0.103252220699927[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.614253361708204[/C][/ROW]
[ROW][C]p-value[/C][C]0.561600715162211[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271878&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271878&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)
alpha5.24731054846305
beta0.0634230236687675
S.D.0.103252220699927
T-STAT0.614253361708204
p-value0.561600715162211






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.09916569252327
beta0.24772034048244
S.D.0.403418481330134
T-STAT0.614053029166308
p-value0.561724596296131
Lambda0.75227965951756

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.09916569252327 \tabularnewline
beta & 0.24772034048244 \tabularnewline
S.D. & 0.403418481330134 \tabularnewline
T-STAT & 0.614053029166308 \tabularnewline
p-value & 0.561724596296131 \tabularnewline
Lambda & 0.75227965951756 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271878&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.09916569252327[/C][/ROW]
[ROW][C]beta[/C][C]0.24772034048244[/C][/ROW]
[ROW][C]S.D.[/C][C]0.403418481330134[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.614053029166308[/C][/ROW]
[ROW][C]p-value[/C][C]0.561724596296131[/C][/ROW]
[ROW][C]Lambda[/C][C]0.75227965951756[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271878&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271878&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)
alpha1.09916569252327
beta0.24772034048244
S.D.0.403418481330134
T-STAT0.614053029166308
p-value0.561724596296131
Lambda0.75227965951756


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')