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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 computationWed, 29 Dec 2010 12:50:31 +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/29/t1293627092ktr6i9gwfolc4ui.htm/, Retrieved Fri, 03 May 2024 08:02:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116773, Retrieved Fri, 03 May 2024 08:02:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166

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] [] [2010-12-17 08:36:27] [9f0fea5f96e3630b8f903250153d0968]
-   PD    [Standard Deviation-Mean Plot] [Verband gemiddeld...] [2010-12-29 12:50:31] [be9b1effb945c5b0652fb49bcca5faef] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
45990
42904
49968
42831
42110
45002
42091
39457
44448
48208
49603
48093
43130
45599
52287
49732
49571
48933
49203
45018
49405
56007
61858
55740
48827
52043
60348
55615
56852
55630
56457
50013
56291
52477
59846
55732
49114
55382
61102
61219
55785
57941
58844
51479
59968
60747
61532
61292
55164
56292
66015
60829
57571
57619
55304
54181
61033
63886
67365
63707
53473
52531
62703
61004
60438
65272
64463
62449
67373
70307
75544
71966
66263
69550
75388
57716
55779
52927
45655
46487
48683
50010
48944
41341
32411
34763
39106
34472
32642
34248
32280
29990
29656
34071
34105
33717

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116773&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116773&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116773&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
145058.753352.1626974238610511
250540.255266.889320427818728
355010.91666666673550.9185612722611521
457867.08333333334139.2147577295512418
559913.83333333334528.1951819748913184
663960.256860.9383286836223013
754895.2510506.385799511734047
833455.08333333332444.819363408469450

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 45058.75 & 3352.16269742386 & 10511 \tabularnewline
2 & 50540.25 & 5266.8893204278 & 18728 \tabularnewline
3 & 55010.9166666667 & 3550.91856127226 & 11521 \tabularnewline
4 & 57867.0833333333 & 4139.21475772955 & 12418 \tabularnewline
5 & 59913.8333333333 & 4528.19518197489 & 13184 \tabularnewline
6 & 63960.25 & 6860.93832868362 & 23013 \tabularnewline
7 & 54895.25 & 10506.3857995117 & 34047 \tabularnewline
8 & 33455.0833333333 & 2444.81936340846 & 9450 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116773&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]45058.75[/C][C]3352.16269742386[/C][C]10511[/C][/ROW]
[ROW][C]2[/C][C]50540.25[/C][C]5266.8893204278[/C][C]18728[/C][/ROW]
[ROW][C]3[/C][C]55010.9166666667[/C][C]3550.91856127226[/C][C]11521[/C][/ROW]
[ROW][C]4[/C][C]57867.0833333333[/C][C]4139.21475772955[/C][C]12418[/C][/ROW]
[ROW][C]5[/C][C]59913.8333333333[/C][C]4528.19518197489[/C][C]13184[/C][/ROW]
[ROW][C]6[/C][C]63960.25[/C][C]6860.93832868362[/C][C]23013[/C][/ROW]
[ROW][C]7[/C][C]54895.25[/C][C]10506.3857995117[/C][C]34047[/C][/ROW]
[ROW][C]8[/C][C]33455.0833333333[/C][C]2444.81936340846[/C][C]9450[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116773&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116773&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
145058.753352.1626974238610511
250540.255266.889320427818728
355010.91666666673550.9185612722611521
457867.08333333334139.2147577295512418
559913.83333333334528.1951819748913184
663960.256860.9383286836223013
754895.2510506.385799511734047
833455.08333333332444.819363408469450






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1652.59205250158
beta0.128048678460067
S.D.0.0954372031690215
T-STAT1.34170610839559
p-value0.228238138735582

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1652.59205250158 \tabularnewline
beta & 0.128048678460067 \tabularnewline
S.D. & 0.0954372031690215 \tabularnewline
T-STAT & 1.34170610839559 \tabularnewline
p-value & 0.228238138735582 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116773&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1652.59205250158[/C][/ROW]
[ROW][C]beta[/C][C]0.128048678460067[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0954372031690215[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.34170610839559[/C][/ROW]
[ROW][C]p-value[/C][C]0.228238138735582[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116773&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116773&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)
alpha-1652.59205250158
beta0.128048678460067
S.D.0.0954372031690215
T-STAT1.34170610839559
p-value0.228238138735582






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.95544266848599
beta1.41832531597787
S.D.0.688795846231155
T-STAT2.05913744070677
p-value0.0851580567621087
Lambda-0.418325315977873

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.95544266848599 \tabularnewline
beta & 1.41832531597787 \tabularnewline
S.D. & 0.688795846231155 \tabularnewline
T-STAT & 2.05913744070677 \tabularnewline
p-value & 0.0851580567621087 \tabularnewline
Lambda & -0.418325315977873 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116773&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.95544266848599[/C][/ROW]
[ROW][C]beta[/C][C]1.41832531597787[/C][/ROW]
[ROW][C]S.D.[/C][C]0.688795846231155[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.05913744070677[/C][/ROW]
[ROW][C]p-value[/C][C]0.0851580567621087[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.418325315977873[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116773&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116773&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-6.95544266848599
beta1.41832531597787
S.D.0.688795846231155
T-STAT2.05913744070677
p-value0.0851580567621087
Lambda-0.418325315977873


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 4 ;
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')