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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, 08 May 2011 16:47:16 +0000
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/May/08/t1304873063gdqq73rbm6lqkkv.htm/, Retrieved Mon, 13 May 2024 00:49:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121205, Retrieved Mon, 13 May 2024 00:49:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact156

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] [Standard Deviatio...] [2011-05-08 16:47:16] [8b50cbc1ebd04aa753862408f533fbe8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.2638
1.2640
1.2261
1.1989
1.2000
1.2146
1.2266
1.2191
1.2224
1.2507
1.2997
1.3406
1.3123
1.3013
1.3185
1.2943
1.2697
1.2155
1.2041
1.2295
1.2234
1.2022
1.1789
1.1861
1.2126
1.1940
1.2028
1.2273
1.2767
1.2661
1.2681
1.2810
1.2722
1.2617
1.2888
1.3205
1.2993
1.3080
1.3246
1.3513
1.3518
1.3421
1.3726
1.3626
1.3910
1.4233
1.4683
1.4559
1.4728
1.4759
1.5520
1.5754
1.5554
1.5562
1.5759
1.4955
1.4342
1.3266
1.2744
1.3511
1.3244
1.2797
1.3050
1.3199
1.3646
1.4014
1.4092
1.4266
1.4575
1.4821
1.4908
1.4579
1.4266
1.3680
1.3570
1.3417
1.2563
1.2223
1.2811
1.2903
1.3103
1.3901
1.3654
1.3221

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 0 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121205&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121205&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121205&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 time0 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11.2438750.04244237001779320.1417
21.244650.05139903607161240.1396
31.255983333333330.03839320094480110.1265
41.37090.05455470982084280.169
51.470450.103880967720490.3015
61.393258333333330.07309650480803790.2111
71.32760.05868736893682720.2043

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.243875 & 0.0424423700177932 & 0.1417 \tabularnewline
2 & 1.24465 & 0.0513990360716124 & 0.1396 \tabularnewline
3 & 1.25598333333333 & 0.0383932009448011 & 0.1265 \tabularnewline
4 & 1.3709 & 0.0545547098208428 & 0.169 \tabularnewline
5 & 1.47045 & 0.10388096772049 & 0.3015 \tabularnewline
6 & 1.39325833333333 & 0.0730965048080379 & 0.2111 \tabularnewline
7 & 1.3276 & 0.0586873689368272 & 0.2043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121205&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]1.243875[/C][C]0.0424423700177932[/C][C]0.1417[/C][/ROW]
[ROW][C]2[/C][C]1.24465[/C][C]0.0513990360716124[/C][C]0.1396[/C][/ROW]
[ROW][C]3[/C][C]1.25598333333333[/C][C]0.0383932009448011[/C][C]0.1265[/C][/ROW]
[ROW][C]4[/C][C]1.3709[/C][C]0.0545547098208428[/C][C]0.169[/C][/ROW]
[ROW][C]5[/C][C]1.47045[/C][C]0.10388096772049[/C][C]0.3015[/C][/ROW]
[ROW][C]6[/C][C]1.39325833333333[/C][C]0.0730965048080379[/C][C]0.2111[/C][/ROW]
[ROW][C]7[/C][C]1.3276[/C][C]0.0586873689368272[/C][C]0.2043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121205&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121205&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
11.2438750.04244237001779320.1417
21.244650.05139903607161240.1396
31.255983333333330.03839320094480110.1265
41.37090.05455470982084280.169
51.470450.103880967720490.3015
61.393258333333330.07309650480803790.2111
71.32760.05868736893682720.2043






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.249349317227482
beta0.23293922621255
S.D.0.0469852031176016
T-STAT4.95771457302238
p-value0.00425653731705115

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.249349317227482 \tabularnewline
beta & 0.23293922621255 \tabularnewline
S.D. & 0.0469852031176016 \tabularnewline
T-STAT & 4.95771457302238 \tabularnewline
p-value & 0.00425653731705115 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121205&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.249349317227482[/C][/ROW]
[ROW][C]beta[/C][C]0.23293922621255[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0469852031176016[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.95771457302238[/C][/ROW]
[ROW][C]p-value[/C][C]0.00425653731705115[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121205&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121205&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-0.249349317227482
beta0.23293922621255
S.D.0.0469852031176016
T-STAT4.95771457302238
p-value0.00425653731705115






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.19923177484781
beta4.73607270502192
S.D.0.938380656207997
T-STAT5.04706983641417
p-value0.00394309680438794
Lambda-3.73607270502192

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.19923177484781 \tabularnewline
beta & 4.73607270502192 \tabularnewline
S.D. & 0.938380656207997 \tabularnewline
T-STAT & 5.04706983641417 \tabularnewline
p-value & 0.00394309680438794 \tabularnewline
Lambda & -3.73607270502192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121205&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.19923177484781[/C][/ROW]
[ROW][C]beta[/C][C]4.73607270502192[/C][/ROW]
[ROW][C]S.D.[/C][C]0.938380656207997[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.04706983641417[/C][/ROW]
[ROW][C]p-value[/C][C]0.00394309680438794[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.73607270502192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121205&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121205&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-4.19923177484781
beta4.73607270502192
S.D.0.938380656207997
T-STAT5.04706983641417
p-value0.00394309680438794
Lambda-3.73607270502192


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')