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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 computationWed, 11 Mar 2015 15:49:52 +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/11/t1426089108uhqac970uc47l03.htm/, Retrieved Sun, 19 May 2024 13:08:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278200, Retrieved Sun, 19 May 2024 13:08:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101

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] [] [2015-03-11 15:49:52] [8e46ac5a02f6c72569c3bd9e9d260f29] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
58552
54955
65540
51570
51145
46641
35704
33253
35193
41668
34865
21210
56126
49231
59723
48103
47472
50497
40059
34149
36860
46356
36577
23872
57276
56389
57657
62300
48929
51168
39636
33213
38127
43291
30600
21956
48033
46148
50736
48114
38390
44112
36287
30333
35908
40005
35263
26591
49709
47840
64781
57802
48154
54353
39737
37732
37163
43782
40649
29412
53597
53588
64172
53955
55509
48908
35331
38073
41776
42717
40736
49020
45099
44114
60487
48760
41281
48346
37025
31514
33977
42060
36036
22012
51048
45834
53712
53577
45022
43740
34898
30103
35137
39752
32348
25198

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=278200&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=278200&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278200&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
144191.333333333312723.60460885344330
244085.416666666710099.370578572435851
345045.166666666712611.706472619640344
439993.33333333337562.755586464924145
545926.16666666679899.0099856990635369
648115.16666666678507.2236560074828841
740892.58333333339824.7376690246338475
840864.08333333339458.2322532310828514

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 44191.3333333333 & 12723.604608853 & 44330 \tabularnewline
2 & 44085.4166666667 & 10099.3705785724 & 35851 \tabularnewline
3 & 45045.1666666667 & 12611.7064726196 & 40344 \tabularnewline
4 & 39993.3333333333 & 7562.7555864649 & 24145 \tabularnewline
5 & 45926.1666666667 & 9899.00998569906 & 35369 \tabularnewline
6 & 48115.1666666667 & 8507.22365600748 & 28841 \tabularnewline
7 & 40892.5833333333 & 9824.73766902463 & 38475 \tabularnewline
8 & 40864.0833333333 & 9458.23225323108 & 28514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278200&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]44191.3333333333[/C][C]12723.604608853[/C][C]44330[/C][/ROW]
[ROW][C]2[/C][C]44085.4166666667[/C][C]10099.3705785724[/C][C]35851[/C][/ROW]
[ROW][C]3[/C][C]45045.1666666667[/C][C]12611.7064726196[/C][C]40344[/C][/ROW]
[ROW][C]4[/C][C]39993.3333333333[/C][C]7562.7555864649[/C][C]24145[/C][/ROW]
[ROW][C]5[/C][C]45926.1666666667[/C][C]9899.00998569906[/C][C]35369[/C][/ROW]
[ROW][C]6[/C][C]48115.1666666667[/C][C]8507.22365600748[/C][C]28841[/C][/ROW]
[ROW][C]7[/C][C]40892.5833333333[/C][C]9824.73766902463[/C][C]38475[/C][/ROW]
[ROW][C]8[/C][C]40864.0833333333[/C][C]9458.23225323108[/C][C]28514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278200&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278200&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
144191.333333333312723.60460885344330
244085.416666666710099.370578572435851
345045.166666666712611.706472619640344
439993.33333333337562.755586464924145
545926.16666666679899.0099856990635369
648115.16666666678507.2236560074828841
740892.58333333339824.7376690246338475
840864.08333333339458.2322532310828514






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2969.39843773163
beta0.163074455949807
S.D.0.25053353181424
T-STAT0.650908701796933
p-value0.539217986380341

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2969.39843773163 \tabularnewline
beta & 0.163074455949807 \tabularnewline
S.D. & 0.25053353181424 \tabularnewline
T-STAT & 0.650908701796933 \tabularnewline
p-value & 0.539217986380341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278200&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2969.39843773163[/C][/ROW]
[ROW][C]beta[/C][C]0.163074455949807[/C][/ROW]
[ROW][C]S.D.[/C][C]0.25053353181424[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.650908701796933[/C][/ROW]
[ROW][C]p-value[/C][C]0.539217986380341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278200&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278200&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)
alpha2969.39843773163
beta0.163074455949807
S.D.0.25053353181424
T-STAT0.650908701796933
p-value0.539217986380341






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.783839397345793
beta0.788372003446934
S.D.1.06517388004269
T-STAT0.740134562270091
p-value0.487158167548545
Lambda0.211627996553066

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.783839397345793 \tabularnewline
beta & 0.788372003446934 \tabularnewline
S.D. & 1.06517388004269 \tabularnewline
T-STAT & 0.740134562270091 \tabularnewline
p-value & 0.487158167548545 \tabularnewline
Lambda & 0.211627996553066 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278200&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.783839397345793[/C][/ROW]
[ROW][C]beta[/C][C]0.788372003446934[/C][/ROW]
[ROW][C]S.D.[/C][C]1.06517388004269[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.740134562270091[/C][/ROW]
[ROW][C]p-value[/C][C]0.487158167548545[/C][/ROW]
[ROW][C]Lambda[/C][C]0.211627996553066[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278200&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278200&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)
alpha0.783839397345793
beta0.788372003446934
S.D.1.06517388004269
T-STAT0.740134562270091
p-value0.487158167548545
Lambda0.211627996553066


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')