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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 computationTue, 10 Mar 2015 13:26:28 +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/Mar/10/t14259941930j9dt1ejzc3s32e.htm/, Retrieved Sun, 19 May 2024 09:25:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278134, Retrieved Sun, 19 May 2024 09:25:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145

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] [] [2015-03-10 13:26:28] [9cc41cf98ef45bbf4afe09924481aae1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
50
45
43
40
43
47
44
41
31
41
40
31
43
22
17
21
29
23
15
24
24
27
17
22
26
12
13
20
15
23
27
17
22
16
20
8
24
18
28
25
11
33
34
23
13
23
26
15
29
23
26
17
32
25
26
32
24
24
28
26
27
45
47
29
40
25
35
26
32
21
32
16
35
19
28
29
29
26
35
38
27
28
29
26
40
20
28
34
38
32
51
27
23
44
37
26

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'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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278134&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278134&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278134&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
141.33333333333335.6461303455364819
223.66666666666677.3278216201658228
318.255.7859547809564419
422.757.3376364785201223
5264.0898988651643615
631.259.3237234076209231
729.08333333333335.0173939873446719
833.33333333333339.1187452619050231

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 41.3333333333333 & 5.64613034553648 & 19 \tabularnewline
2 & 23.6666666666667 & 7.32782162016582 & 28 \tabularnewline
3 & 18.25 & 5.78595478095644 & 19 \tabularnewline
4 & 22.75 & 7.33763647852012 & 23 \tabularnewline
5 & 26 & 4.08989886516436 & 15 \tabularnewline
6 & 31.25 & 9.32372340762092 & 31 \tabularnewline
7 & 29.0833333333333 & 5.01739398734467 & 19 \tabularnewline
8 & 33.3333333333333 & 9.11874526190502 & 31 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278134&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]41.3333333333333[/C][C]5.64613034553648[/C][C]19[/C][/ROW]
[ROW][C]2[/C][C]23.6666666666667[/C][C]7.32782162016582[/C][C]28[/C][/ROW]
[ROW][C]3[/C][C]18.25[/C][C]5.78595478095644[/C][C]19[/C][/ROW]
[ROW][C]4[/C][C]22.75[/C][C]7.33763647852012[/C][C]23[/C][/ROW]
[ROW][C]5[/C][C]26[/C][C]4.08989886516436[/C][C]15[/C][/ROW]
[ROW][C]6[/C][C]31.25[/C][C]9.32372340762092[/C][C]31[/C][/ROW]
[ROW][C]7[/C][C]29.0833333333333[/C][C]5.01739398734467[/C][C]19[/C][/ROW]
[ROW][C]8[/C][C]33.3333333333333[/C][C]9.11874526190502[/C][C]31[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278134&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278134&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
141.33333333333335.6461303455364819
223.66666666666677.3278216201658228
318.255.7859547809564419
422.757.3376364785201223
5264.0898988651643615
631.259.3237234076209231
729.08333333333335.0173939873446719
833.33333333333339.1187452619050231






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.6485845046381
beta0.0374828450964948
S.D.0.10630634187591
T-STAT0.352592746914836
p-value0.736449134203145

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.6485845046381 \tabularnewline
beta & 0.0374828450964948 \tabularnewline
S.D. & 0.10630634187591 \tabularnewline
T-STAT & 0.352592746914836 \tabularnewline
p-value & 0.736449134203145 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278134&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.6485845046381[/C][/ROW]
[ROW][C]beta[/C][C]0.0374828450964948[/C][/ROW]
[ROW][C]S.D.[/C][C]0.10630634187591[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.352592746914836[/C][/ROW]
[ROW][C]p-value[/C][C]0.736449134203145[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278134&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278134&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)
alpha5.6485845046381
beta0.0374828450964948
S.D.0.10630634187591
T-STAT0.352592746914836
p-value0.736449134203145






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.3399054658927
beta0.159153357987184
S.D.0.461225525478544
T-STAT0.345066240256444
p-value0.741819450025944
Lambda0.840846642012816

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.3399054658927 \tabularnewline
beta & 0.159153357987184 \tabularnewline
S.D. & 0.461225525478544 \tabularnewline
T-STAT & 0.345066240256444 \tabularnewline
p-value & 0.741819450025944 \tabularnewline
Lambda & 0.840846642012816 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278134&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.3399054658927[/C][/ROW]
[ROW][C]beta[/C][C]0.159153357987184[/C][/ROW]
[ROW][C]S.D.[/C][C]0.461225525478544[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.345066240256444[/C][/ROW]
[ROW][C]p-value[/C][C]0.741819450025944[/C][/ROW]
[ROW][C]Lambda[/C][C]0.840846642012816[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278134&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278134&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)
alpha1.3399054658927
beta0.159153357987184
S.D.0.461225525478544
T-STAT0.345066240256444
p-value0.741819450025944
Lambda0.840846642012816


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')