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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, 11 May 2015 08:32:42 +0100
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/May/11/t1431329987y471w3q55k0icb3.htm/, Retrieved Wed, 01 May 2024 14:37:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279071, Retrieved Wed, 01 May 2024 14:37:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172

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...] [2015-05-11 07:32:42] [e6344a6a1a33122c0bdf1792ef294740] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5
6
6
7
12
16
18
19
20
24
17
23
25
24
17
14
16
13
10
10
12
12
20
16
12
14
7
9
9
4
3
-1
1
2
-1
3
2
0
2
4
4
7
9
13
8
13
15
15
15
10
12
11
11
17
18
19
22
24
24
20
25
22
17
9
11
13
11
9
7
3
3
6
4
8
1
2
2
1
-1
-2
-2
1
-1
1
8
-1
-2
2
2
2
2
6
4
5
2
1

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279071&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279071&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279071&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'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
114.41666666666676.9473125390435319
215.755.0294586732027715
35.166666666666674.969604581550715
47.666666666666675.365433699886615
516.91666666666675.1071844820148514
611.33333333333336.9587529359966822
71.166666666666672.7906771199618910
82.583333333333332.8109633849474410

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14.4166666666667 & 6.94731253904353 & 19 \tabularnewline
2 & 15.75 & 5.02945867320277 & 15 \tabularnewline
3 & 5.16666666666667 & 4.9696045815507 & 15 \tabularnewline
4 & 7.66666666666667 & 5.3654336998866 & 15 \tabularnewline
5 & 16.9166666666667 & 5.10718448201485 & 14 \tabularnewline
6 & 11.3333333333333 & 6.95875293599668 & 22 \tabularnewline
7 & 1.16666666666667 & 2.79067711996189 & 10 \tabularnewline
8 & 2.58333333333333 & 2.81096338494744 & 10 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279071&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]14.4166666666667[/C][C]6.94731253904353[/C][C]19[/C][/ROW]
[ROW][C]2[/C][C]15.75[/C][C]5.02945867320277[/C][C]15[/C][/ROW]
[ROW][C]3[/C][C]5.16666666666667[/C][C]4.9696045815507[/C][C]15[/C][/ROW]
[ROW][C]4[/C][C]7.66666666666667[/C][C]5.3654336998866[/C][C]15[/C][/ROW]
[ROW][C]5[/C][C]16.9166666666667[/C][C]5.10718448201485[/C][C]14[/C][/ROW]
[ROW][C]6[/C][C]11.3333333333333[/C][C]6.95875293599668[/C][C]22[/C][/ROW]
[ROW][C]7[/C][C]1.16666666666667[/C][C]2.79067711996189[/C][C]10[/C][/ROW]
[ROW][C]8[/C][C]2.58333333333333[/C][C]2.81096338494744[/C][C]10[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279071&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279071&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
114.41666666666676.9473125390435319
215.755.0294586732027715
35.166666666666674.969604581550715
47.666666666666675.365433699886615
516.91666666666675.1071844820148514
611.33333333333336.9587529359966822
71.166666666666672.7906771199618910
82.583333333333332.8109633849474410






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.30299061135667
beta0.180739500343348
S.D.0.0755100694957361
T-STAT2.39358143291808
p-value0.0537631082325648

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.30299061135667 \tabularnewline
beta & 0.180739500343348 \tabularnewline
S.D. & 0.0755100694957361 \tabularnewline
T-STAT & 2.39358143291808 \tabularnewline
p-value & 0.0537631082325648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279071&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.30299061135667[/C][/ROW]
[ROW][C]beta[/C][C]0.180739500343348[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0755100694957361[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.39358143291808[/C][/ROW]
[ROW][C]p-value[/C][C]0.0537631082325648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279071&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279071&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)
alpha3.30299061135667
beta0.180739500343348
S.D.0.0755100694957361
T-STAT2.39358143291808
p-value0.0537631082325648






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.9504886023152
beta0.314514839787079
S.D.0.0770894906948135
T-STAT4.07986661933206
p-value0.00650306350776212
Lambda0.685485160212921

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.9504886023152 \tabularnewline
beta & 0.314514839787079 \tabularnewline
S.D. & 0.0770894906948135 \tabularnewline
T-STAT & 4.07986661933206 \tabularnewline
p-value & 0.00650306350776212 \tabularnewline
Lambda & 0.685485160212921 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279071&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.9504886023152[/C][/ROW]
[ROW][C]beta[/C][C]0.314514839787079[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0770894906948135[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.07986661933206[/C][/ROW]
[ROW][C]p-value[/C][C]0.00650306350776212[/C][/ROW]
[ROW][C]Lambda[/C][C]0.685485160212921[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279071&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279071&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)
alpha0.9504886023152
beta0.314514839787079
S.D.0.0770894906948135
T-STAT4.07986661933206
p-value0.00650306350776212
Lambda0.685485160212921


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 <- '12'
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')