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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 computationSun, 11 May 2008 06:56:50 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/11/t1210510634jlpa7o9vnt5i0pd.htm/, Retrieved Sun, 19 May 2024 20:28:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12258, Retrieved Sun, 19 May 2024 20:28:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact225

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] [aankoop nieuwe en...] [2008-05-11 12:56:50] [92ac00bd259cd41fd6a466a7e7f24e71] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
102.8
103.1
103.1
103.3
103.5
103.3
103.5
103.8
103.9
103.9
104.2
104.6
104.9
105.2
105.2
105.6
105.6
106.2
106.3
106.4
106.9
107.2
107.3
107.3
107.4
107.55
107.87
108.37
108.38
107.92
108.03
108.14
108.3
108.64
108.66
109.04
109.03
109.03
109.54
109.75
109.83
109.65
109.82
109.95
110.12
110.15
110.2
109.99
110.14
110.14
110.81
110.97
110.99
109.73
109.81
110.02
110.18
110.21
110.25
110.36
110.51
110.64
110.95
111.18
111.19
111.69
111.7
111.83
111.77
111.73
112.01
111.86
112.04

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12258&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12258&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12258&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1103.0750.2061552812808830.5
2103.5250.2061552812808830.5
3104.150.3316624790355350.699999999999989
4105.2250.2872281323268970.699999999999989
5106.1250.3593976442141340.800000000000011
6107.1750.1892969448600050.399999999999991
7107.79750.429059047995340.969999999999999
8108.11750.1967019742317440.459999999999994
9108.660.3024345659257040.740000000000009
10109.33750.3652738698565780.719999999999999
11109.81250.1233896267925290.299999999999997
12110.1150.08962886439832910.210000000000008
13110.5150.4379117110407830.829999999999998
14110.13750.5813418386227931.25999999999999
15110.250.07874007874011690.179999999999993
16110.820.3027650354097500.670000000000002
17111.60250.2822971247934830.64
18111.84250.1241974234837440.280000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 103.075 & 0.206155281280883 & 0.5 \tabularnewline
2 & 103.525 & 0.206155281280883 & 0.5 \tabularnewline
3 & 104.15 & 0.331662479035535 & 0.699999999999989 \tabularnewline
4 & 105.225 & 0.287228132326897 & 0.699999999999989 \tabularnewline
5 & 106.125 & 0.359397644214134 & 0.800000000000011 \tabularnewline
6 & 107.175 & 0.189296944860005 & 0.399999999999991 \tabularnewline
7 & 107.7975 & 0.42905904799534 & 0.969999999999999 \tabularnewline
8 & 108.1175 & 0.196701974231744 & 0.459999999999994 \tabularnewline
9 & 108.66 & 0.302434565925704 & 0.740000000000009 \tabularnewline
10 & 109.3375 & 0.365273869856578 & 0.719999999999999 \tabularnewline
11 & 109.8125 & 0.123389626792529 & 0.299999999999997 \tabularnewline
12 & 110.115 & 0.0896288643983291 & 0.210000000000008 \tabularnewline
13 & 110.515 & 0.437911711040783 & 0.829999999999998 \tabularnewline
14 & 110.1375 & 0.581341838622793 & 1.25999999999999 \tabularnewline
15 & 110.25 & 0.0787400787401169 & 0.179999999999993 \tabularnewline
16 & 110.82 & 0.302765035409750 & 0.670000000000002 \tabularnewline
17 & 111.6025 & 0.282297124793483 & 0.64 \tabularnewline
18 & 111.8425 & 0.124197423483744 & 0.280000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12258&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]103.075[/C][C]0.206155281280883[/C][C]0.5[/C][/ROW]
[ROW][C]2[/C][C]103.525[/C][C]0.206155281280883[/C][C]0.5[/C][/ROW]
[ROW][C]3[/C][C]104.15[/C][C]0.331662479035535[/C][C]0.699999999999989[/C][/ROW]
[ROW][C]4[/C][C]105.225[/C][C]0.287228132326897[/C][C]0.699999999999989[/C][/ROW]
[ROW][C]5[/C][C]106.125[/C][C]0.359397644214134[/C][C]0.800000000000011[/C][/ROW]
[ROW][C]6[/C][C]107.175[/C][C]0.189296944860005[/C][C]0.399999999999991[/C][/ROW]
[ROW][C]7[/C][C]107.7975[/C][C]0.42905904799534[/C][C]0.969999999999999[/C][/ROW]
[ROW][C]8[/C][C]108.1175[/C][C]0.196701974231744[/C][C]0.459999999999994[/C][/ROW]
[ROW][C]9[/C][C]108.66[/C][C]0.302434565925704[/C][C]0.740000000000009[/C][/ROW]
[ROW][C]10[/C][C]109.3375[/C][C]0.365273869856578[/C][C]0.719999999999999[/C][/ROW]
[ROW][C]11[/C][C]109.8125[/C][C]0.123389626792529[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]12[/C][C]110.115[/C][C]0.0896288643983291[/C][C]0.210000000000008[/C][/ROW]
[ROW][C]13[/C][C]110.515[/C][C]0.437911711040783[/C][C]0.829999999999998[/C][/ROW]
[ROW][C]14[/C][C]110.1375[/C][C]0.581341838622793[/C][C]1.25999999999999[/C][/ROW]
[ROW][C]15[/C][C]110.25[/C][C]0.0787400787401169[/C][C]0.179999999999993[/C][/ROW]
[ROW][C]16[/C][C]110.82[/C][C]0.302765035409750[/C][C]0.670000000000002[/C][/ROW]
[ROW][C]17[/C][C]111.6025[/C][C]0.282297124793483[/C][C]0.64[/C][/ROW]
[ROW][C]18[/C][C]111.8425[/C][C]0.124197423483744[/C][C]0.280000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12258&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12258&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
1103.0750.2061552812808830.5
2103.5250.2061552812808830.5
3104.150.3316624790355350.699999999999989
4105.2250.2872281323268970.699999999999989
5106.1250.3593976442141340.800000000000011
6107.1750.1892969448600050.399999999999991
7107.79750.429059047995340.969999999999999
8108.11750.1967019742317440.459999999999994
9108.660.3024345659257040.740000000000009
10109.33750.3652738698565780.719999999999999
11109.81250.1233896267925290.299999999999997
12110.1150.08962886439832910.210000000000008
13110.5150.4379117110407830.829999999999998
14110.13750.5813418386227931.25999999999999
15110.250.07874007874011690.179999999999993
16110.820.3027650354097500.670000000000002
17111.60250.2822971247934830.64
18111.84250.1241974234837440.280000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.353583980373684
beta-0.000754959674706867
S.D.0.0120447955124487
T-STAT-0.0626793268450754
p-value0.950798210810807

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.353583980373684 \tabularnewline
beta & -0.000754959674706867 \tabularnewline
S.D. & 0.0120447955124487 \tabularnewline
T-STAT & -0.0626793268450754 \tabularnewline
p-value & 0.950798210810807 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12258&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.353583980373684[/C][/ROW]
[ROW][C]beta[/C][C]-0.000754959674706867[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0120447955124487[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0626793268450754[/C][/ROW]
[ROW][C]p-value[/C][C]0.950798210810807[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12258&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12258&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)
alpha0.353583980373684
beta-0.000754959674706867
S.D.0.0120447955124487
T-STAT-0.0626793268450754
p-value0.950798210810807






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha13.4553292800805
beta-3.17899077225721
S.D.5.33915638876761
T-STAT-0.595410686779111
p-value0.559897259835078
Lambda4.1789907722572

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 13.4553292800805 \tabularnewline
beta & -3.17899077225721 \tabularnewline
S.D. & 5.33915638876761 \tabularnewline
T-STAT & -0.595410686779111 \tabularnewline
p-value & 0.559897259835078 \tabularnewline
Lambda & 4.1789907722572 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12258&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]13.4553292800805[/C][/ROW]
[ROW][C]beta[/C][C]-3.17899077225721[/C][/ROW]
[ROW][C]S.D.[/C][C]5.33915638876761[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.595410686779111[/C][/ROW]
[ROW][C]p-value[/C][C]0.559897259835078[/C][/ROW]
[ROW][C]Lambda[/C][C]4.1789907722572[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12258&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12258&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)
alpha13.4553292800805
beta-3.17899077225721
S.D.5.33915638876761
T-STAT-0.595410686779111
p-value0.559897259835078
Lambda4.1789907722572


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')