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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, 03 Dec 2008 09:28:46 -0700
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/Dec/03/t1228321756gsdeqeaqwpu9pxm.htm/, Retrieved Sun, 19 May 2024 07:09:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28769, Retrieved Sun, 19 May 2024 07:09:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact204

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] [Uitvoer.Nederland] [2008-12-03 15:11:10] [988ab43f527fc78aae41c84649095267]
-   P   [Univariate Data Series] [Export From Belgi...] [2008-12-03 15:52:29] [988ab43f527fc78aae41c84649095267]
- RMP     [Variance Reduction Matrix] [Variance Reductio...] [2008-12-03 15:56:08] [988ab43f527fc78aae41c84649095267]
- RMP         [Standard Deviation-Mean Plot] [standard deviatio...] [2008-12-03 16:28:46] [5d823194959040fa9b19b8c8302177e6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2236
2084.9
2409.5
2199.3
2203.5
2254.1
1975.8
1742.2
2520.6
2438.1
2126.3
2267.5
2201.1
2128.5
2596
2458.2
2210.5
2621.2
2231.4
2103.6
2685.8
2539.3
2462.4
2693.3
2307.7
2385.9
2737.6
2653.9
2545.4
2848.8
2359.5
2488.3
2861.1
2717.9
2844
2749
2652.9
2660.2
3187.1
2774.1
3158.2
3244.6
2665.5
2820.8
2983.4
3077.4
3024.8
2731.8
3046.2
2834.8
3292.8
2946.1
3196.9
3284.2
3003
2979
3137.4
3630.2
3270.7
2942.3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 & 0 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28769&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]0 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=28769&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28769&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 time0 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12232.425134.448537242570324.6
22043.9234.745748985294511.9
32338.125176.209957626312394.3
42345.95218.625318753341467.5
52291.675226.701997859157517.6
62595.2113.420486097824230.9
72521.275206.822441964116429.9
82560.5207.331248649755489.3
9279370.272374847209143.200000000000
102818.575251.872684439315534.2
112972.275274.338347969559579.1
122954.35153.271991353063345.6
133029.975195.336058712500458
143115.775148.743456438706305.2
153245.15289.968095946203687.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2232.425 & 134.448537242570 & 324.6 \tabularnewline
2 & 2043.9 & 234.745748985294 & 511.9 \tabularnewline
3 & 2338.125 & 176.209957626312 & 394.3 \tabularnewline
4 & 2345.95 & 218.625318753341 & 467.5 \tabularnewline
5 & 2291.675 & 226.701997859157 & 517.6 \tabularnewline
6 & 2595.2 & 113.420486097824 & 230.9 \tabularnewline
7 & 2521.275 & 206.822441964116 & 429.9 \tabularnewline
8 & 2560.5 & 207.331248649755 & 489.3 \tabularnewline
9 & 2793 & 70.272374847209 & 143.200000000000 \tabularnewline
10 & 2818.575 & 251.872684439315 & 534.2 \tabularnewline
11 & 2972.275 & 274.338347969559 & 579.1 \tabularnewline
12 & 2954.35 & 153.271991353063 & 345.6 \tabularnewline
13 & 3029.975 & 195.336058712500 & 458 \tabularnewline
14 & 3115.775 & 148.743456438706 & 305.2 \tabularnewline
15 & 3245.15 & 289.968095946203 & 687.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28769&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]2232.425[/C][C]134.448537242570[/C][C]324.6[/C][/ROW]
[ROW][C]2[/C][C]2043.9[/C][C]234.745748985294[/C][C]511.9[/C][/ROW]
[ROW][C]3[/C][C]2338.125[/C][C]176.209957626312[/C][C]394.3[/C][/ROW]
[ROW][C]4[/C][C]2345.95[/C][C]218.625318753341[/C][C]467.5[/C][/ROW]
[ROW][C]5[/C][C]2291.675[/C][C]226.701997859157[/C][C]517.6[/C][/ROW]
[ROW][C]6[/C][C]2595.2[/C][C]113.420486097824[/C][C]230.9[/C][/ROW]
[ROW][C]7[/C][C]2521.275[/C][C]206.822441964116[/C][C]429.9[/C][/ROW]
[ROW][C]8[/C][C]2560.5[/C][C]207.331248649755[/C][C]489.3[/C][/ROW]
[ROW][C]9[/C][C]2793[/C][C]70.272374847209[/C][C]143.200000000000[/C][/ROW]
[ROW][C]10[/C][C]2818.575[/C][C]251.872684439315[/C][C]534.2[/C][/ROW]
[ROW][C]11[/C][C]2972.275[/C][C]274.338347969559[/C][C]579.1[/C][/ROW]
[ROW][C]12[/C][C]2954.35[/C][C]153.271991353063[/C][C]345.6[/C][/ROW]
[ROW][C]13[/C][C]3029.975[/C][C]195.336058712500[/C][C]458[/C][/ROW]
[ROW][C]14[/C][C]3115.775[/C][C]148.743456438706[/C][C]305.2[/C][/ROW]
[ROW][C]15[/C][C]3245.15[/C][C]289.968095946203[/C][C]687.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28769&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28769&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
12232.425134.448537242570324.6
22043.9234.745748985294511.9
32338.125176.209957626312394.3
42345.95218.625318753341467.5
52291.675226.701997859157517.6
62595.2113.420486097824230.9
72521.275206.822441964116429.9
82560.5207.331248649755489.3
9279370.272374847209143.200000000000
102818.575251.872684439315534.2
112972.275274.338347969559579.1
122954.35153.271991353063345.6
133029.975195.336058712500458
143115.775148.743456438706305.2
153245.15289.968095946203687.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha149.973728204083
beta0.0163706249242296
S.D.0.0463353335263094
T-STAT0.353307587932529
p-value0.729521239224356

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 149.973728204083 \tabularnewline
beta & 0.0163706249242296 \tabularnewline
S.D. & 0.0463353335263094 \tabularnewline
T-STAT & 0.353307587932529 \tabularnewline
p-value & 0.729521239224356 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28769&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]149.973728204083[/C][/ROW]
[ROW][C]beta[/C][C]0.0163706249242296[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0463353335263094[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.353307587932529[/C][/ROW]
[ROW][C]p-value[/C][C]0.729521239224356[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28769&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28769&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)
alpha149.973728204083
beta0.0163706249242296
S.D.0.0463353335263094
T-STAT0.353307587932529
p-value0.729521239224356






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha5.07250918358382
beta0.0171538220566986
S.D.0.750436571112978
T-STAT0.0228584569529409
p-value0.98211031860507
Lambda0.982846177943301

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.07250918358382 \tabularnewline
beta & 0.0171538220566986 \tabularnewline
S.D. & 0.750436571112978 \tabularnewline
T-STAT & 0.0228584569529409 \tabularnewline
p-value & 0.98211031860507 \tabularnewline
Lambda & 0.982846177943301 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28769&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.07250918358382[/C][/ROW]
[ROW][C]beta[/C][C]0.0171538220566986[/C][/ROW]
[ROW][C]S.D.[/C][C]0.750436571112978[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0228584569529409[/C][/ROW]
[ROW][C]p-value[/C][C]0.98211031860507[/C][/ROW]
[ROW][C]Lambda[/C][C]0.982846177943301[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28769&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28769&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)
alpha5.07250918358382
beta0.0171538220566986
S.D.0.750436571112978
T-STAT0.0228584569529409
p-value0.98211031860507
Lambda0.982846177943301


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')