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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 computationWed, 29 Jul 2015 15:31:23 +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/Jul/29/t1438180299adkm8u08djzht91.htm/, Retrieved Fri, 17 May 2024 06:26:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279743, Retrieved Fri, 17 May 2024 06:26:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact175

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] [] [2015-07-29 14:31:23] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
228768.00
227916.00
227052.00
225264.00
242952.00
242016.00
228768.00
219960.00
220812.00
220812.00
221760.00
223464.00
226116.00
226116.00
224412.00
219960.00
242952.00
246456.00
241164.00
228768.00
234072.00
226116.00
229704.00
231420.00
233208.00
228768.00
229704.00
223464.00
242952.00
249108.00
243816.00
234072.00
244668.00
233208.00
243816.00
242952.00
245604.00
235860.00
246456.00
245604.00
261504.00
257916.00
243816.00
236712.00
246456.00
233208.00
242952.00
244668.00
248256.00
240312.00
244668.00
247320.00
257064.00
249108.00
238512.00
227052.00
237660.00
208500.00
222612.00
230556.00
238512.00
227052.00
227052.00
227052.00
233208.00
224412.00
212868.00
203208.00
210216.00
182856.00
199620.00
209364.00
211152.00
201408.00
202260.00
199620.00
208500.00
202260.00
189960.00
181068.00
196104.00
163452.00
184656.00
194316.00
194316.00
182856.00
172260.00
171408.00
181068.00
172260.00
155508.00
143964.00
156360.00
127212.00
153708.00
167808.00
172260.00
162516.00
150204.00
159012.00
162516.00
159864.00
133356.00
121056.00
129852.00
103356.00
130716.00
140460.00
148404.00
135156.00
122760.00
129852.00
133356.00
126348.00
99852.00
88308.00
98904.00
69756.00
101556.00
121056.00

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279743&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279743&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279743&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'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12274627708.3043766859922992
22314388179.0294156347326496
32374788022.5865699740125644
42450638208.1729779752828296
523763513516.89411608548564
621628516115.767378000355656
719456313253.236572111947700
816489418472.033111510167104
914376420626.502775004668904
1011460922827.850048092278648

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 227462 & 7708.30437668599 & 22992 \tabularnewline
2 & 231438 & 8179.02941563473 & 26496 \tabularnewline
3 & 237478 & 8022.58656997401 & 25644 \tabularnewline
4 & 245063 & 8208.17297797528 & 28296 \tabularnewline
5 & 237635 & 13516.894116085 & 48564 \tabularnewline
6 & 216285 & 16115.7673780003 & 55656 \tabularnewline
7 & 194563 & 13253.2365721119 & 47700 \tabularnewline
8 & 164894 & 18472.0331115101 & 67104 \tabularnewline
9 & 143764 & 20626.5027750046 & 68904 \tabularnewline
10 & 114609 & 22827.8500480922 & 78648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279743&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]227462[/C][C]7708.30437668599[/C][C]22992[/C][/ROW]
[ROW][C]2[/C][C]231438[/C][C]8179.02941563473[/C][C]26496[/C][/ROW]
[ROW][C]3[/C][C]237478[/C][C]8022.58656997401[/C][C]25644[/C][/ROW]
[ROW][C]4[/C][C]245063[/C][C]8208.17297797528[/C][C]28296[/C][/ROW]
[ROW][C]5[/C][C]237635[/C][C]13516.894116085[/C][C]48564[/C][/ROW]
[ROW][C]6[/C][C]216285[/C][C]16115.7673780003[/C][C]55656[/C][/ROW]
[ROW][C]7[/C][C]194563[/C][C]13253.2365721119[/C][C]47700[/C][/ROW]
[ROW][C]8[/C][C]164894[/C][C]18472.0331115101[/C][C]67104[/C][/ROW]
[ROW][C]9[/C][C]143764[/C][C]20626.5027750046[/C][C]68904[/C][/ROW]
[ROW][C]10[/C][C]114609[/C][C]22827.8500480922[/C][C]78648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279743&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279743&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
12274627708.3043766859922992
22314388179.0294156347326496
32374788022.5865699740125644
42450638208.1729779752828296
523763513516.89411608548564
621628516115.767378000355656
719456313253.236572111947700
816489418472.033111510167104
914376420626.502775004668904
1011460922827.850048092278648






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha36472.6547070613
beta-0.113151792219188
S.D.0.0185894327362386
T-STAT-6.08688784777213
p-value0.000293686871073618

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 36472.6547070613 \tabularnewline
beta & -0.113151792219188 \tabularnewline
S.D. & 0.0185894327362386 \tabularnewline
T-STAT & -6.08688784777213 \tabularnewline
p-value & 0.000293686871073618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279743&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]36472.6547070613[/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]0.000293686871073618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279743&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279743&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)
alpha36472.6547070613
beta-0.113151792219188
S.D.0.0185894327362386
T-STAT-6.08688784777213
p-value0.000293686871073618






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha26.3323280270543
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 & 26.3323280270543 \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=279743&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]26.3323280270543[/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=279743&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279743&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)
alpha26.3323280270543
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):
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')