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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 computationWed, 10 Dec 2008 07:03:52 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/10/t1228917891le65kp6b48mo5bv.htm/, Retrieved Sun, 19 May 2024 07:09:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31963, Retrieved Sun, 19 May 2024 07:09:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136

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] [SDMP] [2008-12-10 14:03:52] [5f3e73ccf1ddc75508eed47fa51813d3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
632
1270
1211
1469
2570
2765
2487
3644
2501
1629
987
1100
690
1378
1376
1736
2800
2671
2508
3590
2691
1629
1020
1224
787
1424
1232
2021
2782
2682
3284
3194
2736
1701
1089
1240
799
1163
1180
1960
2914
2658
3254
3222
2987
1604
1032
1283
774
1109
1453
1849
2800
3310
3060
3422
3448
1670
1022
1391
767
1172
1498
1623
2646
3439

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31963&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31963&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31963&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11855.41666666667911.1827935893733012
21942.75883.0128306490852900
32014.33333333333883.2019570685392497
42004.66666666667940.6461351194462455
521091022.970185293782674

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1855.41666666667 & 911.182793589373 & 3012 \tabularnewline
2 & 1942.75 & 883.012830649085 & 2900 \tabularnewline
3 & 2014.33333333333 & 883.201957068539 & 2497 \tabularnewline
4 & 2004.66666666667 & 940.646135119446 & 2455 \tabularnewline
5 & 2109 & 1022.97018529378 & 2674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31963&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]1855.41666666667[/C][C]911.182793589373[/C][C]3012[/C][/ROW]
[ROW][C]2[/C][C]1942.75[/C][C]883.012830649085[/C][C]2900[/C][/ROW]
[ROW][C]3[/C][C]2014.33333333333[/C][C]883.201957068539[/C][C]2497[/C][/ROW]
[ROW][C]4[/C][C]2004.66666666667[/C][C]940.646135119446[/C][C]2455[/C][/ROW]
[ROW][C]5[/C][C]2109[/C][C]1022.97018529378[/C][C]2674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31963&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31963&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
11855.41666666667911.1827935893733012
21942.75883.0128306490852900
32014.33333333333883.2019570685392497
42004.66666666667940.6461351194462455
521091022.970185293782674






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha94.0270655721143
beta0.420190262154876
S.D.0.26252224299109
T-STAT1.60058918195795
p-value0.207778712912687

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 94.0270655721143 \tabularnewline
beta & 0.420190262154876 \tabularnewline
S.D. & 0.26252224299109 \tabularnewline
T-STAT & 1.60058918195795 \tabularnewline
p-value & 0.207778712912687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31963&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]94.0270655721143[/C][/ROW]
[ROW][C]beta[/C][C]0.420190262154876[/C][/ROW]
[ROW][C]S.D.[/C][C]0.26252224299109[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.60058918195795[/C][/ROW]
[ROW][C]p-value[/C][C]0.207778712912687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31963&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31963&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)
alpha94.0270655721143
beta0.420190262154876
S.D.0.26252224299109
T-STAT1.60058918195795
p-value0.207778712912687






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.412601988279452
beta0.845446489261212
S.D.0.56056926161875
T-STAT1.50819273753938
p-value0.228626506984978
Lambda0.154553510738788

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.412601988279452 \tabularnewline
beta & 0.845446489261212 \tabularnewline
S.D. & 0.56056926161875 \tabularnewline
T-STAT & 1.50819273753938 \tabularnewline
p-value & 0.228626506984978 \tabularnewline
Lambda & 0.154553510738788 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31963&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.412601988279452[/C][/ROW]
[ROW][C]beta[/C][C]0.845446489261212[/C][/ROW]
[ROW][C]S.D.[/C][C]0.56056926161875[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.50819273753938[/C][/ROW]
[ROW][C]p-value[/C][C]0.228626506984978[/C][/ROW]
[ROW][C]Lambda[/C][C]0.154553510738788[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31963&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31963&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)
alpha0.412601988279452
beta0.845446489261212
S.D.0.56056926161875
T-STAT1.50819273753938
p-value0.228626506984978
Lambda0.154553510738788


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')