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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 computationSun, 16 Aug 2015 19:58:36 +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/2015/Aug/16/t143975181780gsrmxdvqc0dmh.htm/, Retrieved Sat, 18 May 2024 06:32:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280201, Retrieved Sat, 18 May 2024 06:32:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variability] [] [2014-11-24 12:14:04] [46d78fa4bef23992fc20db72a2a0da97]
- RMPD  [(Partial) Autocorrelation Function] [] [2015-08-16 18:29:51] [46d78fa4bef23992fc20db72a2a0da97]
- RMP       [Standard Deviation-Mean Plot] [] [2015-08-16 18:58:36] [fced41568b3cc41e6659ad201d611503] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
95320.00
94965.00
94605.00
93860.00
101230.00
100840.00
95320.00
91650.00
92005.00
92005.00
92400.00
93110.00
94215.00
94215.00
93505.00
91650.00
101230.00
102690.00
100485.00
95320.00
97530.00
94215.00
95710.00
96425.00
97170.00
95320.00
95710.00
93110.00
101230.00
103795.00
101590.00
97530.00
101945.00
97170.00
101590.00
101230.00
102335.00
98275.00
102690.00
102335.00
108960.00
107465.00
101590.00
98630.00
102690.00
97170.00
101230.00
101945.00
103440.00
100130.00
101945.00
103050.00
107110.00
103795.00
99380.00
94605.00
99025.00
86875.00
92755.00
96065.00
99380.00
94605.00
94605.00
94605.00
97170.00
93505.00
88695.00
84670.00
87590.00
76190.00
83175.00
87235.00
87980.00
83920.00
84275.00
83175.00
86875.00
84275.00
79150.00
75445.00
81710.00
68105.00
76940.00
80965.00
80965.00
76190.00
71775.00
71420.00
75445.00
71775.00
64795.00
59985.00
65150.00
53005.00
64045.00
69920.00
71775.00
67715.00
62585.00
66255.00
67715.00
66610.00
55565.00
50440.00
54105.00
43065.00
54465.00
58525.00
61835.00
56315.00
51150.00
54105.00
55565.00
52645.00
41605.00
36795.00
41210.00
29065.00
42315.00
50440.00

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280201&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280201&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280201&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
194775.83333333333211.793490285839580
296432.53407.9289231811411040
398949.16666666673342.7444041558410685
4102109.5833333333420.0720741563711790
599014.58333333335632.0392150354420235
690118.756714.9030741667923190
781067.91666666675522.1819050466119875
868705.83333333337696.6804631292327960
959901.66666666678594.3761562519228710
1047753.759511.6041867050732770

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 94775.8333333333 & 3211.79349028583 & 9580 \tabularnewline
2 & 96432.5 & 3407.92892318114 & 11040 \tabularnewline
3 & 98949.1666666667 & 3342.74440415584 & 10685 \tabularnewline
4 & 102109.583333333 & 3420.07207415637 & 11790 \tabularnewline
5 & 99014.5833333333 & 5632.03921503544 & 20235 \tabularnewline
6 & 90118.75 & 6714.90307416679 & 23190 \tabularnewline
7 & 81067.9166666667 & 5522.18190504661 & 19875 \tabularnewline
8 & 68705.8333333333 & 7696.68046312923 & 27960 \tabularnewline
9 & 59901.6666666667 & 8594.37615625192 & 28710 \tabularnewline
10 & 47753.75 & 9511.60418670507 & 32770 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280201&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]94775.8333333333[/C][C]3211.79349028583[/C][C]9580[/C][/ROW]
[ROW][C]2[/C][C]96432.5[/C][C]3407.92892318114[/C][C]11040[/C][/ROW]
[ROW][C]3[/C][C]98949.1666666667[/C][C]3342.74440415584[/C][C]10685[/C][/ROW]
[ROW][C]4[/C][C]102109.583333333[/C][C]3420.07207415637[/C][C]11790[/C][/ROW]
[ROW][C]5[/C][C]99014.5833333333[/C][C]5632.03921503544[/C][C]20235[/C][/ROW]
[ROW][C]6[/C][C]90118.75[/C][C]6714.90307416679[/C][C]23190[/C][/ROW]
[ROW][C]7[/C][C]81067.9166666667[/C][C]5522.18190504661[/C][C]19875[/C][/ROW]
[ROW][C]8[/C][C]68705.8333333333[/C][C]7696.68046312923[/C][C]27960[/C][/ROW]
[ROW][C]9[/C][C]59901.6666666667[/C][C]8594.37615625192[/C][C]28710[/C][/ROW]
[ROW][C]10[/C][C]47753.75[/C][C]9511.60418670507[/C][C]32770[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280201&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280201&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
194775.83333333333211.793490285839580
296432.53407.9289231811411040
398949.16666666673342.7444041558410685
4102109.5833333333420.0720741563711790
599014.58333333335632.0392150354420235
690118.756714.9030741667923190
781067.91666666675522.1819050466119875
868705.83333333337696.6804631292327960
959901.66666666678594.3761562519228710
1047753.759511.6041867050732770






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha15196.9394612756
beta-0.113151792219188
S.D.0.0185894327362386
T-STAT-6.08688784777213
p-value0.000293686871073616

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 15196.9394612756 \tabularnewline
beta & -0.113151792219188 \tabularnewline
S.D. & 0.0185894327362386 \tabularnewline
T-STAT & -6.08688784777213 \tabularnewline
p-value & 0.000293686871073616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280201&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]15196.9394612756[/C][/ROW]
[ROW][C]beta[/C][C]-0.113151792219188[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0185894327362386[/C][/ROW]
[ROW][C]T-STAT[/C][C]-6.08688784777213[/C][/ROW]
[ROW][C]p-value[/C][C]0.000293686871073616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280201&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280201&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)
alpha15196.9394612756
beta-0.113151792219188
S.D.0.0185894327362386
T-STAT-6.08688784777213
p-value0.000293686871073616






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha24.2435553435753
beta-1.38589065989076
S.D.0.316605261909547
T-STAT-4.37734563074541
p-value0.00235715681397514
Lambda2.38589065989076

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 24.2435553435753 \tabularnewline
beta & -1.38589065989076 \tabularnewline
S.D. & 0.316605261909547 \tabularnewline
T-STAT & -4.37734563074541 \tabularnewline
p-value & 0.00235715681397514 \tabularnewline
Lambda & 2.38589065989076 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280201&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]24.2435553435753[/C][/ROW]
[ROW][C]beta[/C][C]-1.38589065989076[/C][/ROW]
[ROW][C]S.D.[/C][C]0.316605261909547[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.37734563074541[/C][/ROW]
[ROW][C]p-value[/C][C]0.00235715681397514[/C][/ROW]
[ROW][C]Lambda[/C][C]2.38589065989076[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280201&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280201&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)
alpha24.2435553435753
beta-1.38589065989076
S.D.0.316605261909547
T-STAT-4.37734563074541
p-value0.00235715681397514
Lambda2.38589065989076


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')