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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, 30 Jul 2017 14:28:11 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Jul/30/t1501417701ipv8nfmc3ryz2g0.htm/, Retrieved Thu, 16 May 2024 00:08:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=306816, Retrieved Thu, 16 May 2024 00:08:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130

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] [] [2017-07-30 12:28:11] [1a8cec710a8245ea2c14b5d40c333c7c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
247832.00
246909.00
245973.00
244036.00
263198.00
262184.00
247832.00
238290.00
239213.00
239213.00
240240.00
242086.00
244959.00
244959.00
243113.00
238290.00
263198.00
266994.00
261261.00
247832.00
253578.00
244959.00
248846.00
250705.00
252642.00
247832.00
248846.00
242086.00
263198.00
269867.00
264134.00
253578.00
265057.00
252642.00
264134.00
263198.00
266071.00
255515.00
266994.00
266071.00
283296.00
279409.00
264134.00
256438.00
266994.00
252642.00
263198.00
265057.00
268944.00
260338.00
265057.00
267930.00
278486.00
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258388.00
245973.00
257465.00
225875.00
241163.00
249769.00
258388.00
245973.00
245973.00
245973.00
252642.00
243113.00
230607.00
220142.00
227734.00
198094.00
216255.00
226811.00
228748.00
218192.00
219115.00
216255.00
225875.00
219115.00
205790.00
196157.00
212446.00
177073.00
200044.00
210509.00
210509.00
198094.00
186615.00
185692.00
196157.00
186615.00
168467.00
155961.00
169390.00
137813.00
166517.00
181792.00
186615.00
176059.00
162721.00
172263.00
176059.00
173186.00
144469.00
131144.00
140673.00
111969.00
141609.00
152165.00
160771.00
146419.00
132990.00
140673.00
144469.00
136877.00
108173.00
95667.00
107146.00
75569.00
110019.00
131144.00

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=306816&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=306816&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306816&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
1246417.1666666678350.6630747431524908
2250724.58860.6152002709628704
3257267.8333333338691.1354508051727781
4265484.9166666678892.1873928065630654
5257437.91666666714643.301959092152611
6234308.7517458.747992833660294
7210776.58333333314357.672953121251675
8178635.16666666720011.36920413672696
9155744.33333333322345.37800625574646
10124159.7524730.170885433285202

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 246417.166666667 & 8350.66307474315 & 24908 \tabularnewline
2 & 250724.5 & 8860.61520027096 & 28704 \tabularnewline
3 & 257267.833333333 & 8691.13545080517 & 27781 \tabularnewline
4 & 265484.916666667 & 8892.18739280656 & 30654 \tabularnewline
5 & 257437.916666667 & 14643.3019590921 & 52611 \tabularnewline
6 & 234308.75 & 17458.7479928336 & 60294 \tabularnewline
7 & 210776.583333333 & 14357.6729531212 & 51675 \tabularnewline
8 & 178635.166666667 & 20011.369204136 & 72696 \tabularnewline
9 & 155744.333333333 & 22345.378006255 & 74646 \tabularnewline
10 & 124159.75 & 24730.1708854332 & 85202 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306816&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]246417.166666667[/C][C]8350.66307474315[/C][C]24908[/C][/ROW]
[ROW][C]2[/C][C]250724.5[/C][C]8860.61520027096[/C][C]28704[/C][/ROW]
[ROW][C]3[/C][C]257267.833333333[/C][C]8691.13545080517[/C][C]27781[/C][/ROW]
[ROW][C]4[/C][C]265484.916666667[/C][C]8892.18739280656[/C][C]30654[/C][/ROW]
[ROW][C]5[/C][C]257437.916666667[/C][C]14643.3019590921[/C][C]52611[/C][/ROW]
[ROW][C]6[/C][C]234308.75[/C][C]17458.7479928336[/C][C]60294[/C][/ROW]
[ROW][C]7[/C][C]210776.583333333[/C][C]14357.6729531212[/C][C]51675[/C][/ROW]
[ROW][C]8[/C][C]178635.166666667[/C][C]20011.369204136[/C][C]72696[/C][/ROW]
[ROW][C]9[/C][C]155744.333333333[/C][C]22345.378006255[/C][C]74646[/C][/ROW]
[ROW][C]10[/C][C]124159.75[/C][C]24730.1708854332[/C][C]85202[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306816&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306816&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
1246417.1666666678350.6630747431524908
2250724.58860.6152002709628704
3257267.8333333338691.1354508051727781
4265484.9166666678892.1873928065630654
5257437.91666666714643.301959092152611
6234308.7517458.747992833660294
7210776.58333333314357.672953121251675
8178635.16666666720011.36920413672696
9155744.33333333322345.37800625574646
10124159.7524730.170885433285202






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha39512.0425993164
beta-0.113151792219188
S.D.0.0185894327362385
T-STAT-6.08688784777213
p-value0.000293686871073617

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 39512.0425993164 \tabularnewline
beta & -0.113151792219188 \tabularnewline
S.D. & 0.0185894327362385 \tabularnewline
T-STAT & -6.08688784777213 \tabularnewline
p-value & 0.000293686871073617 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306816&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]39512.0425993164[/C][/ROW]
[ROW][C]beta[/C][C]-0.113151792219188[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0185894327362385[/C][/ROW]
[ROW][C]T-STAT[/C][C]-6.08688784777213[/C][/ROW]
[ROW][C]p-value[/C][C]0.000293686871073617[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306816&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306816&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)
alpha39512.0425993164
beta-0.113151792219188
S.D.0.0185894327362385
T-STAT-6.08688784777213
p-value0.000293686871073617






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha26.523301175685
beta-1.38589065989076
S.D.0.316605261909547
T-STAT-4.37734563074541
p-value0.00235715681397512
Lambda2.38589065989076

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 26.523301175685 \tabularnewline
beta & -1.38589065989076 \tabularnewline
S.D. & 0.316605261909547 \tabularnewline
T-STAT & -4.37734563074541 \tabularnewline
p-value & 0.00235715681397512 \tabularnewline
Lambda & 2.38589065989076 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306816&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]26.523301175685[/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]0.00235715681397512[/C][/ROW]
[ROW][C]Lambda[/C][C]2.38589065989076[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306816&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306816&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)
alpha26.523301175685
beta-1.38589065989076
S.D.0.316605261909547
T-STAT-4.37734563074541
p-value0.00235715681397512
Lambda2.38589065989076


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')