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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 computationMon, 21 Nov 2016 17:16:07 +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/2016/Nov/21/t1479748592fc49if1891kxts4.htm/, Retrieved Mon, 06 May 2024 13:59:00 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 06 May 2024 13:59:00 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.336
1.3649
1.3999
1.4442
1.4349
1.4388
1.4264
1.4343
1.377
1.3706
1.3556
1.3179
1.2905
1.3224
1.3201
1.3162
1.2789
1.2526
1.2288
1.24
1.2856
1.2974
1.2828
1.3119
1.3288
1.3359
1.2964
1.3026
1.2982
1.3189
1.308
1.331
1.3348
1.3635
1.3493
1.3704
1.361
1.3658
1.3823
1.3812
1.3732
1.3592
1.3539
1.3316
1.2901
1.2673
1.2472
1.2331
1.1621
1.135
1.0838
1.0779
1.115
1.1213
1.0996
1.1139
1.1221
1.1235
1.0736
1.0877

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

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






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11.391708333333330.04385789984470160.1263
21.28560.0313094815728980.0936000000000001
31.328150.02457694780961140.0740000000000001
41.3288250.05447618537239250.1492
51.1096250.0260794982174260.0884999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.39170833333333 & 0.0438578998447016 & 0.1263 \tabularnewline
2 & 1.2856 & 0.031309481572898 & 0.0936000000000001 \tabularnewline
3 & 1.32815 & 0.0245769478096114 & 0.0740000000000001 \tabularnewline
4 & 1.328825 & 0.0544761853723925 & 0.1492 \tabularnewline
5 & 1.109625 & 0.026079498217426 & 0.0884999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1.39170833333333[/C][C]0.0438578998447016[/C][C]0.1263[/C][/ROW]
[ROW][C]2[/C][C]1.2856[/C][C]0.031309481572898[/C][C]0.0936000000000001[/C][/ROW]
[ROW][C]3[/C][C]1.32815[/C][C]0.0245769478096114[/C][C]0.0740000000000001[/C][/ROW]
[ROW][C]4[/C][C]1.328825[/C][C]0.0544761853723925[/C][C]0.1492[/C][/ROW]
[ROW][C]5[/C][C]1.109625[/C][C]0.026079498217426[/C][C]0.0884999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
11.391708333333330.04385789984470160.1263
21.28560.0313094815728980.0936000000000001
31.328150.02457694780961140.0740000000000001
41.3288250.05447618537239250.1492
51.1096250.0260794982174260.0884999999999998






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.045199157230566
beta0.063051145043165
S.D.0.0585579464388122
T-STAT1.07673080901236
p-value0.360475131252478

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.045199157230566 \tabularnewline
beta & 0.063051145043165 \tabularnewline
S.D. & 0.0585579464388122 \tabularnewline
T-STAT & 1.07673080901236 \tabularnewline
p-value & 0.360475131252478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.045199157230566[/C][/ROW]
[ROW][C]beta[/C][C]0.063051145043165[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0585579464388122[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.07673080901236[/C][/ROW]
[ROW][C]p-value[/C][C]0.360475131252478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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-0.045199157230566
beta0.063051145043165
S.D.0.0585579464388122
T-STAT1.07673080901236
p-value0.360475131252478






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.90594452954753
beta2.13464055241794
S.D.1.91629029637715
T-STAT1.11394424761926
p-value0.346515980197941
Lambda-1.13464055241794

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.90594452954753 \tabularnewline
beta & 2.13464055241794 \tabularnewline
S.D. & 1.91629029637715 \tabularnewline
T-STAT & 1.11394424761926 \tabularnewline
p-value & 0.346515980197941 \tabularnewline
Lambda & -1.13464055241794 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.90594452954753[/C][/ROW]
[ROW][C]beta[/C][C]2.13464055241794[/C][/ROW]
[ROW][C]S.D.[/C][C]1.91629029637715[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.11394424761926[/C][/ROW]
[ROW][C]p-value[/C][C]0.346515980197941[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.13464055241794[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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-3.90594452954753
beta2.13464055241794
S.D.1.91629029637715
T-STAT1.11394424761926
p-value0.346515980197941
Lambda-1.13464055241794


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')