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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 computationSat, 30 May 2015 14:38:31 +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/30/t14329931285hpegc1wj6nktvr.htm/, Retrieved Mon, 29 Apr 2024 13:04:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279506, Retrieved Mon, 29 Apr 2024 13:04:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variability] [] [2015-05-30 11:19:07] [b30bdcc44403aed8ab60f5e6bd04fee3]
- RMPD    [Standard Deviation-Mean Plot] [] [2015-05-30 13:38:31] [d3245c242fac7b2d7caab09de558415e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20
23
27
23
21
18
16
11
14
-3
2
26
11
11
11
3
8
8
7
3
4
-7
0
-5
5
-1
-4
4
7
6
13
20
21
37
52
59
66
73
71
69
63
68
58
50
50
50
47
60
62
63
56
38
45
39
26
25
19
14
6
4
5
-3
-5
0
-6
4
-3
14
16
17
25
25
30
51
31
31
25
35
39
48
41
47
61
55
63
45
62
55
50
52
45
36
40
32
29
24
28
27
33
33
24
26
38
32
30
26
21
21

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=279506&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=279506&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279506&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
116.59.2785186905512630
24.56.0677987621691818
318.2520.693103813941163
460.41666666666679.2976862550297826
533.083333333333320.703352092808359
67.4166666666666711.48483849044131
741.166666666666711.27211630797936
844.416666666666712.630830486863439
928.255.1544332198779917

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 16.5 & 9.27851869055126 & 30 \tabularnewline
2 & 4.5 & 6.06779876216918 & 18 \tabularnewline
3 & 18.25 & 20.6931038139411 & 63 \tabularnewline
4 & 60.4166666666667 & 9.29768625502978 & 26 \tabularnewline
5 & 33.0833333333333 & 20.7033520928083 & 59 \tabularnewline
6 & 7.41666666666667 & 11.484838490441 & 31 \tabularnewline
7 & 41.1666666666667 & 11.272116307979 & 36 \tabularnewline
8 & 44.4166666666667 & 12.6308304868634 & 39 \tabularnewline
9 & 28.25 & 5.15443321987799 & 17 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279506&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]16.5[/C][C]9.27851869055126[/C][C]30[/C][/ROW]
[ROW][C]2[/C][C]4.5[/C][C]6.06779876216918[/C][C]18[/C][/ROW]
[ROW][C]3[/C][C]18.25[/C][C]20.6931038139411[/C][C]63[/C][/ROW]
[ROW][C]4[/C][C]60.4166666666667[/C][C]9.29768625502978[/C][C]26[/C][/ROW]
[ROW][C]5[/C][C]33.0833333333333[/C][C]20.7033520928083[/C][C]59[/C][/ROW]
[ROW][C]6[/C][C]7.41666666666667[/C][C]11.484838490441[/C][C]31[/C][/ROW]
[ROW][C]7[/C][C]41.1666666666667[/C][C]11.272116307979[/C][C]36[/C][/ROW]
[ROW][C]8[/C][C]44.4166666666667[/C][C]12.6308304868634[/C][C]39[/C][/ROW]
[ROW][C]9[/C][C]28.25[/C][C]5.15443321987799[/C][C]17[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279506&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279506&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
116.59.2785186905512630
24.56.0677987621691818
318.2520.693103813941163
460.41666666666679.2976862550297826
533.083333333333320.703352092808359
67.4166666666666711.48483849044131
741.166666666666711.27211630797936
844.416666666666712.630830486863439
928.255.1544332198779917






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha11.2975685642084
beta0.0193092954400999
S.D.0.114085729389749
T-STAT0.169252504615489
p-value0.870385219821407

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 11.2975685642084 \tabularnewline
beta & 0.0193092954400999 \tabularnewline
S.D. & 0.114085729389749 \tabularnewline
T-STAT & 0.169252504615489 \tabularnewline
p-value & 0.870385219821407 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279506&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]11.2975685642084[/C][/ROW]
[ROW][C]beta[/C][C]0.0193092954400999[/C][/ROW]
[ROW][C]S.D.[/C][C]0.114085729389749[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.169252504615489[/C][/ROW]
[ROW][C]p-value[/C][C]0.870385219821407[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279506&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279506&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)
alpha11.2975685642084
beta0.0193092954400999
S.D.0.114085729389749
T-STAT0.169252504615489
p-value0.870385219821407






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.94181300405984
beta0.14036450767783
S.D.0.201042962294567
T-STAT0.698181652696549
p-value0.507586404832016
Lambda0.85963549232217

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.94181300405984 \tabularnewline
beta & 0.14036450767783 \tabularnewline
S.D. & 0.201042962294567 \tabularnewline
T-STAT & 0.698181652696549 \tabularnewline
p-value & 0.507586404832016 \tabularnewline
Lambda & 0.85963549232217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279506&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.94181300405984[/C][/ROW]
[ROW][C]beta[/C][C]0.14036450767783[/C][/ROW]
[ROW][C]S.D.[/C][C]0.201042962294567[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.698181652696549[/C][/ROW]
[ROW][C]p-value[/C][C]0.507586404832016[/C][/ROW]
[ROW][C]Lambda[/C][C]0.85963549232217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279506&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279506&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)
alpha1.94181300405984
beta0.14036450767783
S.D.0.201042962294567
T-STAT0.698181652696549
p-value0.507586404832016
Lambda0.85963549232217


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')