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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 computationFri, 16 Dec 2016 14:10:25 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/16/t1481893902chw91hsg7jqrjwe.htm/, Retrieved Thu, 02 May 2024 23:59:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300240, Retrieved Thu, 02 May 2024 23:59:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56

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] [standard deviatio...] [2016-12-16 13:10:25] [a7a7548920aea9a2d444ee0f03dc394a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3800
1650
4250
3200
2050
3600
3700
6000
8550
9050
6000
8550
6700
3850
2950
2900
2200
3500
4900
6650
10050
8300
7650
5750
4600
5250
3250
1150
1950
2850
2950
4950
6000
6650
6150
4300
4450
1250
3000
2600
1200
2050
2000
5050
4050
5150
6450
3700
3300
2000
2650
900
1350
4550
1850
3650
3250
5950
4050
3250
2200
1050
2250
2650
650
1100
2900
6450
3100
6050
4200
1800
2100
1550
1050
900
1800
1700
1700
2250
4000
3500
3300
1550
2750
1900
1200
1150
1150
2200
1500
3850
2950
3750
4600
3350
2300
1400
900
1250
1650
1600
1200
2300
2950
5650
4000
3300

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300240&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300240&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300240&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
15033.333333333332565.712140494097400
254502471.565569358097850
34170.833333333331745.703600444845500
43412.51671.842342501775250
53062.51426.235509049165050
62866.666666666671862.346190517045800
72116.66666666667981.0322331219513100
82529.166666666671189.243138481043450
923751396.830828567434750

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5033.33333333333 & 2565.71214049409 & 7400 \tabularnewline
2 & 5450 & 2471.56556935809 & 7850 \tabularnewline
3 & 4170.83333333333 & 1745.70360044484 & 5500 \tabularnewline
4 & 3412.5 & 1671.84234250177 & 5250 \tabularnewline
5 & 3062.5 & 1426.23550904916 & 5050 \tabularnewline
6 & 2866.66666666667 & 1862.34619051704 & 5800 \tabularnewline
7 & 2116.66666666667 & 981.032233121951 & 3100 \tabularnewline
8 & 2529.16666666667 & 1189.24313848104 & 3450 \tabularnewline
9 & 2375 & 1396.83082856743 & 4750 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300240&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]5033.33333333333[/C][C]2565.71214049409[/C][C]7400[/C][/ROW]
[ROW][C]2[/C][C]5450[/C][C]2471.56556935809[/C][C]7850[/C][/ROW]
[ROW][C]3[/C][C]4170.83333333333[/C][C]1745.70360044484[/C][C]5500[/C][/ROW]
[ROW][C]4[/C][C]3412.5[/C][C]1671.84234250177[/C][C]5250[/C][/ROW]
[ROW][C]5[/C][C]3062.5[/C][C]1426.23550904916[/C][C]5050[/C][/ROW]
[ROW][C]6[/C][C]2866.66666666667[/C][C]1862.34619051704[/C][C]5800[/C][/ROW]
[ROW][C]7[/C][C]2116.66666666667[/C][C]981.032233121951[/C][C]3100[/C][/ROW]
[ROW][C]8[/C][C]2529.16666666667[/C][C]1189.24313848104[/C][C]3450[/C][/ROW]
[ROW][C]9[/C][C]2375[/C][C]1396.83082856743[/C][C]4750[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300240&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300240&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
15033.333333333332565.712140494097400
254502471.565569358097850
34170.833333333331745.703600444845500
43412.51671.842342501775250
53062.51426.235509049165050
62866.666666666671862.346190517045800
72116.66666666667981.0322331219513100
82529.166666666671189.243138481043450
923751396.830828567434750






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha263.396548870402
beta0.417193206212847
S.D.0.0667047933613237
T-STAT6.25432124424721
p-value0.000422381766328853

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 263.396548870402 \tabularnewline
beta & 0.417193206212847 \tabularnewline
S.D. & 0.0667047933613237 \tabularnewline
T-STAT & 6.25432124424721 \tabularnewline
p-value & 0.000422381766328853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300240&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]263.396548870402[/C][/ROW]
[ROW][C]beta[/C][C]0.417193206212847[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0667047933613237[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.25432124424721[/C][/ROW]
[ROW][C]p-value[/C][C]0.000422381766328853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300240&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300240&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)
alpha263.396548870402
beta0.417193206212847
S.D.0.0667047933613237
T-STAT6.25432124424721
p-value0.000422381766328853






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.381589502962485
beta0.866397173962382
S.D.0.14755195928061
T-STAT5.87181070442238
p-value0.000616808690569167
Lambda0.133602826037618

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.381589502962485 \tabularnewline
beta & 0.866397173962382 \tabularnewline
S.D. & 0.14755195928061 \tabularnewline
T-STAT & 5.87181070442238 \tabularnewline
p-value & 0.000616808690569167 \tabularnewline
Lambda & 0.133602826037618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300240&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.381589502962485[/C][/ROW]
[ROW][C]beta[/C][C]0.866397173962382[/C][/ROW]
[ROW][C]S.D.[/C][C]0.14755195928061[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.87181070442238[/C][/ROW]
[ROW][C]p-value[/C][C]0.000616808690569167[/C][/ROW]
[ROW][C]Lambda[/C][C]0.133602826037618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300240&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300240&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)
alpha0.381589502962485
beta0.866397173962382
S.D.0.14755195928061
T-STAT5.87181070442238
p-value0.000616808690569167
Lambda0.133602826037618


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')