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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 computationThu, 22 Dec 2011 14:14:46 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/22/t13245812947zymjmiwugqd46r.htm/, Retrieved Fri, 03 May 2024 03:50:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159875, Retrieved Fri, 03 May 2024 03:50:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMPD    [Standard Deviation-Mean Plot] [] [2011-12-22 19:14:46] [aedc5b8e4f26bdca34b1a0cf88d6dfa2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.2613
1.2646
1.2262
1.1985
1.2007
1.2138
1.2266
1.2176
1.2218
1.249
1.2991
1.3408
1.3119
1.3014
1.3201
1.2938
1.2694
1.2165
1.2037
1.2292
1.2256
1.2015
1.1786
1.1856
1.2103
1.1938
1.202
1.2271
1.277
1.265
1.2684
1.2811
1.2727
1.2611
1.2881
1.3213
1.2999
1.3074
1.3242
1.3516
1.3511
1.3419
1.3716
1.3622
1.3896
1.4227
1.4684
1.457
1.4718
1.4748
1.5527
1.575
1.5557
1.5553
1.577
1.4975
1.437
1.3322
1.2732
1.3449
1.3239
1.2785
1.305
1.319
1.365
1.4016
1.4088
1.4268
1.4562
1.4816
1.4914
1.4614
1.4272
1.3686
1.3569
1.3406
1.2565
1.2208
1.277
1.2894
1.3067
1.3898
1.3661
1.322
1.336
1.3649
1.3999
1.4442
1.4349
1.4388
1.4264
1.4343
1.377
1.3706
1.3556

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=159875&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=159875&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159875&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
11.243333333333330.0424437024632380.1423
21.2447750.05156309682850180.1415
31.255658333333330.03886141948311230.1275
41.370633333333330.05467872003112750.1685
51.470591666666670.1040848819546580.3038
61.393266666666670.07358332732763630.2129
71.32680.05948359590524250.2064

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.24333333333333 & 0.042443702463238 & 0.1423 \tabularnewline
2 & 1.244775 & 0.0515630968285018 & 0.1415 \tabularnewline
3 & 1.25565833333333 & 0.0388614194831123 & 0.1275 \tabularnewline
4 & 1.37063333333333 & 0.0546787200311275 & 0.1685 \tabularnewline
5 & 1.47059166666667 & 0.104084881954658 & 0.3038 \tabularnewline
6 & 1.39326666666667 & 0.0735833273276363 & 0.2129 \tabularnewline
7 & 1.3268 & 0.0594835959052425 & 0.2064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159875&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]1.24333333333333[/C][C]0.042443702463238[/C][C]0.1423[/C][/ROW]
[ROW][C]2[/C][C]1.244775[/C][C]0.0515630968285018[/C][C]0.1415[/C][/ROW]
[ROW][C]3[/C][C]1.25565833333333[/C][C]0.0388614194831123[/C][C]0.1275[/C][/ROW]
[ROW][C]4[/C][C]1.37063333333333[/C][C]0.0546787200311275[/C][C]0.1685[/C][/ROW]
[ROW][C]5[/C][C]1.47059166666667[/C][C]0.104084881954658[/C][C]0.3038[/C][/ROW]
[ROW][C]6[/C][C]1.39326666666667[/C][C]0.0735833273276363[/C][C]0.2129[/C][/ROW]
[ROW][C]7[/C][C]1.3268[/C][C]0.0594835959052425[/C][C]0.2064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159875&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159875&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
11.243333333333330.0424437024632380.1423
21.2447750.05156309682850180.1415
31.255658333333330.03886141948311230.1275
41.370633333333330.05467872003112750.1685
51.470591666666670.1040848819546580.3038
61.393266666666670.07358332732763630.2129
71.32680.05948359590524250.2064






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.249159321431644
beta0.233079032534995
S.D.0.046551423505014
T-STAT5.00691525598331
p-value0.00408049353049434

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.249159321431644 \tabularnewline
beta & 0.233079032534995 \tabularnewline
S.D. & 0.046551423505014 \tabularnewline
T-STAT & 5.00691525598331 \tabularnewline
p-value & 0.00408049353049434 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159875&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.249159321431644[/C][/ROW]
[ROW][C]beta[/C][C]0.233079032534995[/C][/ROW]
[ROW][C]S.D.[/C][C]0.046551423505014[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.00691525598331[/C][/ROW]
[ROW][C]p-value[/C][C]0.00408049353049434[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159875&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159875&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)
alpha-0.249159321431644
beta0.233079032534995
S.D.0.046551423505014
T-STAT5.00691525598331
p-value0.00408049353049434






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.18850617873102
beta4.72127837088453
S.D.0.926109643922314
T-STAT5.09796912478817
p-value0.00377662878552226
Lambda-3.72127837088453

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.18850617873102 \tabularnewline
beta & 4.72127837088453 \tabularnewline
S.D. & 0.926109643922314 \tabularnewline
T-STAT & 5.09796912478817 \tabularnewline
p-value & 0.00377662878552226 \tabularnewline
Lambda & -3.72127837088453 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159875&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.18850617873102[/C][/ROW]
[ROW][C]beta[/C][C]4.72127837088453[/C][/ROW]
[ROW][C]S.D.[/C][C]0.926109643922314[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.09796912478817[/C][/ROW]
[ROW][C]p-value[/C][C]0.00377662878552226[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.72127837088453[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159875&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159875&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)
alpha-4.18850617873102
beta4.72127837088453
S.D.0.926109643922314
T-STAT5.09796912478817
p-value0.00377662878552226
Lambda-3.72127837088453


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')