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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 computationThu, 05 Dec 2013 15:36:20 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/05/t1386275787nw253itgqh58kl8.htm/, Retrieved Thu, 25 Apr 2024 04:53:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=231245, Retrieved Thu, 25 Apr 2024 04:53:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77

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] [] [2013-12-05 20:36:20] [354a1e9bb909abf3036d55f04d250334] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204
25739
26434
27525
30695
32436
30160
30236
31293
31077
32226
33865
32810
32242
32700
32819
33947
34148
35261
39506
41591
39148
41216
40225
41126
42362
40740
40256
39804
41002
41702
42254
43605
43271
43221
41373

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231245&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]3 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=231245&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231245&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
116322775.6835109056462166
219107.9166666667703.2356980200142069
3224801260.966944992474147
429740.83333333332835.123945770068661
536301.08333333333704.161626611439349
641726.33333333331231.130694881253801

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 16322 & 775.683510905646 & 2166 \tabularnewline
2 & 19107.9166666667 & 703.235698020014 & 2069 \tabularnewline
3 & 22480 & 1260.96694499247 & 4147 \tabularnewline
4 & 29740.8333333333 & 2835.12394577006 & 8661 \tabularnewline
5 & 36301.0833333333 & 3704.16162661143 & 9349 \tabularnewline
6 & 41726.3333333333 & 1231.13069488125 & 3801 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231245&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]16322[/C][C]775.683510905646[/C][C]2166[/C][/ROW]
[ROW][C]2[/C][C]19107.9166666667[/C][C]703.235698020014[/C][C]2069[/C][/ROW]
[ROW][C]3[/C][C]22480[/C][C]1260.96694499247[/C][C]4147[/C][/ROW]
[ROW][C]4[/C][C]29740.8333333333[/C][C]2835.12394577006[/C][C]8661[/C][/ROW]
[ROW][C]5[/C][C]36301.0833333333[/C][C]3704.16162661143[/C][C]9349[/C][/ROW]
[ROW][C]6[/C][C]41726.3333333333[/C][C]1231.13069488125[/C][C]3801[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231245&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231245&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
116322775.6835109056462166
219107.9166666667703.2356980200142069
3224801260.966944992474147
429740.83333333332835.123945770068661
536301.08333333333704.161626611439349
641726.33333333331231.130694881253801






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-126.67644996942
beta0.068025626718049
S.D.0.0507724539373266
T-STAT1.33981364781028
p-value0.251357200512038

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -126.67644996942 \tabularnewline
beta & 0.068025626718049 \tabularnewline
S.D. & 0.0507724539373266 \tabularnewline
T-STAT & 1.33981364781028 \tabularnewline
p-value & 0.251357200512038 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231245&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-126.67644996942[/C][/ROW]
[ROW][C]beta[/C][C]0.068025626718049[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0507724539373266[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.33981364781028[/C][/ROW]
[ROW][C]p-value[/C][C]0.251357200512038[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231245&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231245&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)
alpha-126.67644996942
beta0.068025626718049
S.D.0.0507724539373266
T-STAT1.33981364781028
p-value0.251357200512038






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.48376001695735
beta1.25430662071899
S.D.0.664364179052804
T-STAT1.88798050868317
p-value0.132058124846142
Lambda-0.254306620718988

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.48376001695735 \tabularnewline
beta & 1.25430662071899 \tabularnewline
S.D. & 0.664364179052804 \tabularnewline
T-STAT & 1.88798050868317 \tabularnewline
p-value & 0.132058124846142 \tabularnewline
Lambda & -0.254306620718988 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231245&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.48376001695735[/C][/ROW]
[ROW][C]beta[/C][C]1.25430662071899[/C][/ROW]
[ROW][C]S.D.[/C][C]0.664364179052804[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.88798050868317[/C][/ROW]
[ROW][C]p-value[/C][C]0.132058124846142[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.254306620718988[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231245&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231245&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-5.48376001695735
beta1.25430662071899
S.D.0.664364179052804
T-STAT1.88798050868317
p-value0.132058124846142
Lambda-0.254306620718988


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')