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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 computationFri, 11 Dec 2015 16:11:16 +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/2015/Dec/11/t1449850321avp71gsy1pgo26z.htm/, Retrieved Sat, 18 May 2024 14:21:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285989, Retrieved Sat, 18 May 2024 14:21:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact46

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...] [2015-12-11 16:11:16] [42f75ab47e982481f307588c9de28675] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6
8.7
8.5
8.3
8
8
8.8
8.7
8.5
8.1
7.8
7.7
7.5
7.2
6.9
6.6
6.5
6.6
7.7
8
7.7
7.3
7
7
7.3
7.3
7.1
7.1
7
7
7.5
7.8
7.9
8.1
8.3
8.4
8.6
8.5
8.4
8.3
8
8
8.7
8.7
8.6
8.5
8.5
8.6
8.8
8.7
8.6
8.4
8.1
8.1
8.7
8.7
8.6
8.6
8.5
8.6
8.8
8.8
8.7
8.5
8.3
8.3
8.9
9
8.8

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285989&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285989&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285989&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'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
18.383333333333330.2405801069888940.699999999999999
27.70.3592922335521731
37.041666666666670.5333570070503411.8
47.583333333333330.5589492306321231.7
58.350.331662479035540.9
67.358333333333330.5759708536396821.6
77.2750.3137022328723390.9
88.383333333333330.2516611478423580.699999999999999
98.5250.2261335084333230.700000000000001
108.650.2236067977499790.699999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.38333333333333 & 0.240580106988894 & 0.699999999999999 \tabularnewline
2 & 7.7 & 0.359292233552173 & 1 \tabularnewline
3 & 7.04166666666667 & 0.533357007050341 & 1.8 \tabularnewline
4 & 7.58333333333333 & 0.558949230632123 & 1.7 \tabularnewline
5 & 8.35 & 0.33166247903554 & 0.9 \tabularnewline
6 & 7.35833333333333 & 0.575970853639682 & 1.6 \tabularnewline
7 & 7.275 & 0.313702232872339 & 0.9 \tabularnewline
8 & 8.38333333333333 & 0.251661147842358 & 0.699999999999999 \tabularnewline
9 & 8.525 & 0.226133508433323 & 0.700000000000001 \tabularnewline
10 & 8.65 & 0.223606797749979 & 0.699999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285989&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]8.38333333333333[/C][C]0.240580106988894[/C][C]0.699999999999999[/C][/ROW]
[ROW][C]2[/C][C]7.7[/C][C]0.359292233552173[/C][C]1[/C][/ROW]
[ROW][C]3[/C][C]7.04166666666667[/C][C]0.533357007050341[/C][C]1.8[/C][/ROW]
[ROW][C]4[/C][C]7.58333333333333[/C][C]0.558949230632123[/C][C]1.7[/C][/ROW]
[ROW][C]5[/C][C]8.35[/C][C]0.33166247903554[/C][C]0.9[/C][/ROW]
[ROW][C]6[/C][C]7.35833333333333[/C][C]0.575970853639682[/C][C]1.6[/C][/ROW]
[ROW][C]7[/C][C]7.275[/C][C]0.313702232872339[/C][C]0.9[/C][/ROW]
[ROW][C]8[/C][C]8.38333333333333[/C][C]0.251661147842358[/C][C]0.699999999999999[/C][/ROW]
[ROW][C]9[/C][C]8.525[/C][C]0.226133508433323[/C][C]0.700000000000001[/C][/ROW]
[ROW][C]10[/C][C]8.65[/C][C]0.223606797749979[/C][C]0.699999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285989&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285989&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
18.383333333333330.2405801069888940.699999999999999
27.70.3592922335521731
37.041666666666670.5333570070503411.8
47.583333333333330.5589492306321231.7
58.350.331662479035540.9
67.358333333333330.5759708536396821.6
77.2750.3137022328723390.9
88.383333333333330.2516611478423580.699999999999999
98.5250.2261335084333230.700000000000001
108.650.2236067977499790.699999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.88001946820772
beta-0.191612354375778
S.D.0.0505876481784638
T-STAT-3.78773003441088
p-value0.0053290507351402

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.88001946820772 \tabularnewline
beta & -0.191612354375778 \tabularnewline
S.D. & 0.0505876481784638 \tabularnewline
T-STAT & -3.78773003441088 \tabularnewline
p-value & 0.0053290507351402 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285989&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.88001946820772[/C][/ROW]
[ROW][C]beta[/C][C]-0.191612354375778[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0505876481784638[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.78773003441088[/C][/ROW]
[ROW][C]p-value[/C][C]0.0053290507351402[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285989&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285989&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)
alpha1.88001946820772
beta-0.191612354375778
S.D.0.0505876481784638
T-STAT-3.78773003441088
p-value0.0053290507351402






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha7.46674191056617
beta-4.13574011156091
S.D.0.994900581981609
T-STAT-4.1569380764895
p-value0.00317854526053378
Lambda5.13574011156091

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.46674191056617 \tabularnewline
beta & -4.13574011156091 \tabularnewline
S.D. & 0.994900581981609 \tabularnewline
T-STAT & -4.1569380764895 \tabularnewline
p-value & 0.00317854526053378 \tabularnewline
Lambda & 5.13574011156091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285989&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.46674191056617[/C][/ROW]
[ROW][C]beta[/C][C]-4.13574011156091[/C][/ROW]
[ROW][C]S.D.[/C][C]0.994900581981609[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.1569380764895[/C][/ROW]
[ROW][C]p-value[/C][C]0.00317854526053378[/C][/ROW]
[ROW][C]Lambda[/C][C]5.13574011156091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285989&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285989&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)
alpha7.46674191056617
beta-4.13574011156091
S.D.0.994900581981609
T-STAT-4.1569380764895
p-value0.00317854526053378
Lambda5.13574011156091


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')