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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 computationMon, 27 Dec 2010 13:35:47 +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/2010/Dec/27/t129345686855gpfv91jze990c.htm/, Retrieved Mon, 06 May 2024 17:18:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115974, Retrieved Mon, 06 May 2024 17:18:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2010-12-14 13:47:21] [acfa3f91ce5598ec4ba98aad4cfba2f0]
- RMPD  [(Partial) Autocorrelation Function] [] [2010-12-27 13:27:22] [acfa3f91ce5598ec4ba98aad4cfba2f0]
- RMP       [Standard Deviation-Mean Plot] [] [2010-12-27 13:35:47] [c474a97a96075919a678ad3d2290b00b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
35.36
31.19
35.29
33.80
36.38
37.77
34.88
37.07
35.56
34.18
32.05
32.35
34.79
33.75
33.76
36.80
36.57
34.14
33.85
35.10
33.92
33.34
30.69
32.32
32.47
34.71
37.19
35.58
36.04
35.63
32.74
33.31
28.40
27.37
28.20
29.23
28.05
27.70
28.05
28.01
30.73
30.82
30.48
30.92
31.20
31.41
31.96
36.95
35.64
37.18
38.69
39.97
40.36
40.79
42.92
41.21
44.15
44.70
47.42
45.14
46.08
50.59
48.63
47.46
47.30
49.02
51.77
54.15
56.10
52.58
52.56
51.27
57.72
53.46
55.48
59.33
57.32
56.44
58.80
55.64
53.62
54.87
56.15
55.35
52.38
51.27
53.95
56.09
56.34
60.65
58.35
57.18
58.87
66.20
62.25
62.62
54.73
56.20
52.54
63.06
63.53
60.95
53.83
51.20
44.57
44.15
44.04
42.28
38.42
35.41
37.01
39.19
46.50
44.79
47.01
49.15
50.85
54.09
55.40
56.16
54.37
52.34
56.13
51.29
42.95
28.88
38.47
34.83
41.17
40.80
40.00
44.00

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115974&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115974&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115974&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
134.65666666666672.030290321081896.58
234.08583333333331.667150308615026.11
332.57253.459590425049039.82
430.52333333333332.548134195600369.25
541.51416666666673.4732653180684311.78
650.62583333333333.0148374246333210.02
756.18166666666671.850434019522465.87
858.01254.4200249382266414.93
952.597.5992260371459121.25
1046.1657.3217415960958420.75
1143.76916666666678.2867346988845427.25

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 34.6566666666667 & 2.03029032108189 & 6.58 \tabularnewline
2 & 34.0858333333333 & 1.66715030861502 & 6.11 \tabularnewline
3 & 32.5725 & 3.45959042504903 & 9.82 \tabularnewline
4 & 30.5233333333333 & 2.54813419560036 & 9.25 \tabularnewline
5 & 41.5141666666667 & 3.47326531806843 & 11.78 \tabularnewline
6 & 50.6258333333333 & 3.01483742463332 & 10.02 \tabularnewline
7 & 56.1816666666667 & 1.85043401952246 & 5.87 \tabularnewline
8 & 58.0125 & 4.42002493822664 & 14.93 \tabularnewline
9 & 52.59 & 7.59922603714591 & 21.25 \tabularnewline
10 & 46.165 & 7.32174159609584 & 20.75 \tabularnewline
11 & 43.7691666666667 & 8.28673469888454 & 27.25 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115974&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]34.6566666666667[/C][C]2.03029032108189[/C][C]6.58[/C][/ROW]
[ROW][C]2[/C][C]34.0858333333333[/C][C]1.66715030861502[/C][C]6.11[/C][/ROW]
[ROW][C]3[/C][C]32.5725[/C][C]3.45959042504903[/C][C]9.82[/C][/ROW]
[ROW][C]4[/C][C]30.5233333333333[/C][C]2.54813419560036[/C][C]9.25[/C][/ROW]
[ROW][C]5[/C][C]41.5141666666667[/C][C]3.47326531806843[/C][C]11.78[/C][/ROW]
[ROW][C]6[/C][C]50.6258333333333[/C][C]3.01483742463332[/C][C]10.02[/C][/ROW]
[ROW][C]7[/C][C]56.1816666666667[/C][C]1.85043401952246[/C][C]5.87[/C][/ROW]
[ROW][C]8[/C][C]58.0125[/C][C]4.42002493822664[/C][C]14.93[/C][/ROW]
[ROW][C]9[/C][C]52.59[/C][C]7.59922603714591[/C][C]21.25[/C][/ROW]
[ROW][C]10[/C][C]46.165[/C][C]7.32174159609584[/C][C]20.75[/C][/ROW]
[ROW][C]11[/C][C]43.7691666666667[/C][C]8.28673469888454[/C][C]27.25[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115974&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115974&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
134.65666666666672.030290321081896.58
234.08583333333331.667150308615026.11
332.57253.459590425049039.82
430.52333333333332.548134195600369.25
541.51416666666673.4732653180684311.78
650.62583333333333.0148374246333210.02
756.18166666666671.850434019522465.87
858.01254.4200249382266414.93
952.597.5992260371459121.25
1046.1657.3217415960958420.75
1143.76916666666678.2867346988845427.25






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.576486376452651
beta0.0818189138166362
S.D.0.0781913481571156
T-STAT1.04639344051507
p-value0.322667547852175

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.576486376452651 \tabularnewline
beta & 0.0818189138166362 \tabularnewline
S.D. & 0.0781913481571156 \tabularnewline
T-STAT & 1.04639344051507 \tabularnewline
p-value & 0.322667547852175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115974&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.576486376452651[/C][/ROW]
[ROW][C]beta[/C][C]0.0818189138166362[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0781913481571156[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.04639344051507[/C][/ROW]
[ROW][C]p-value[/C][C]0.322667547852175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115974&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115974&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)
alpha0.576486376452651
beta0.0818189138166362
S.D.0.0781913481571156
T-STAT1.04639344051507
p-value0.322667547852175






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.29157496534439
beta0.949070491107067
S.D.0.771870892417966
T-STAT1.22957155196513
p-value0.250031282819526
Lambda0.0509295088929329

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.29157496534439 \tabularnewline
beta & 0.949070491107067 \tabularnewline
S.D. & 0.771870892417966 \tabularnewline
T-STAT & 1.22957155196513 \tabularnewline
p-value & 0.250031282819526 \tabularnewline
Lambda & 0.0509295088929329 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115974&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.29157496534439[/C][/ROW]
[ROW][C]beta[/C][C]0.949070491107067[/C][/ROW]
[ROW][C]S.D.[/C][C]0.771870892417966[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.22957155196513[/C][/ROW]
[ROW][C]p-value[/C][C]0.250031282819526[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0509295088929329[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115974&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115974&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-2.29157496534439
beta0.949070491107067
S.D.0.771870892417966
T-STAT1.22957155196513
p-value0.250031282819526
Lambda0.0509295088929329


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')