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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 computationSun, 26 Dec 2010 18:01:17 +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/26/t1293386472nyyb2mb079rdx0u.htm/, Retrieved Mon, 06 May 2024 12:20:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115751, Retrieved Mon, 06 May 2024 12:20:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Standard Deviation-Mean Plot] [Births] [2010-11-29 10:52:49] [b98453cac15ba1066b407e146608df68]
- RMP           [(Partial) Autocorrelation Function] [WS6 - autocorrelatie] [2010-12-14 19:09:35] [8ed0bd3560b9ca2814a2ed0a29182575]
- RMP             [Standard Deviation-Mean Plot] [WS6 - stdev mean ...] [2010-12-14 19:56:43] [8ed0bd3560b9ca2814a2ed0a29182575]
-   PD                [Standard Deviation-Mean Plot] [Stdev mean plot D...] [2010-12-26 18:01:17] [c9d5faca36bd2ada281161976df30bf1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,8973
0,9383
0,9217
0,9095
0,892
0,8742
0,8532
0,8607
0,9005
0,9111
0,9059
0,8883
0,8924
0,8833
0,87
0,8758
0,8858
0,917
0,9554
0,9922
0,9778
0,9808
0,9811
1,0014
1,0183
1,0622
1,0773
1,0807
1,0848
1,1582
1,1663
1,1372
1,1139
1,1222
1,1692
1,1702
1,2286
1,2613
1,2646
1,2262
1,1985
1,2007
1,2138
1,2266
1,2176
1,2218
1,249
1,2991
1,3408
1,3119
1,3014
1,3201
1,2938
1,2694
1,2165
1,2037
1,2292
1,2256
1,2015
1,1786
1,1856
1,2103
1,1938
1,202
1,2271
1,277
1,265
1,2684
1,2811
1,2727
1,2611
1,2881
1,3213
1,2999
1,3074
1,3242
1,3516
1,3511
1,3419
1,3716
1,3622
1,3896
1,4227
1,4684
1,457
1,4718
1,4748
1,5527
1,575
1,5557
1,5553
1,577
1,4975
1,4369
1,3322
1,2732
1,3449
1,3239
1,2785
1,305
1,319
1,365
1,4016
1,4088
1,4268
1,4562
1,4816
1,4914
1,4614
1,4272
1,3686
1,3569
1,3406
1,2565
1,2208
1,277
1,2894
1,3067
1,3898
1,3661

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'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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115751&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115751&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115751&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
10.8960583333333330.02451049713279950.0851
20.9344166666666670.05144237435021720.1314
31.1133750.04921692474970560.1519
41.233983333333330.02936354676785280.1006
51.257708333333330.05473751345090380.1622
61.244350.03775171278474420.1025
71.3593250.04892240841837760.1685
81.4799250.09653921600713730.3038
91.383558333333330.07143065878984680.2129
101.338416666666670.07096480348266550.2406

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 0.896058333333333 & 0.0245104971327995 & 0.0851 \tabularnewline
2 & 0.934416666666667 & 0.0514423743502172 & 0.1314 \tabularnewline
3 & 1.113375 & 0.0492169247497056 & 0.1519 \tabularnewline
4 & 1.23398333333333 & 0.0293635467678528 & 0.1006 \tabularnewline
5 & 1.25770833333333 & 0.0547375134509038 & 0.1622 \tabularnewline
6 & 1.24435 & 0.0377517127847442 & 0.1025 \tabularnewline
7 & 1.359325 & 0.0489224084183776 & 0.1685 \tabularnewline
8 & 1.479925 & 0.0965392160071373 & 0.3038 \tabularnewline
9 & 1.38355833333333 & 0.0714306587898468 & 0.2129 \tabularnewline
10 & 1.33841666666667 & 0.0709648034826655 & 0.2406 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115751&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]0.896058333333333[/C][C]0.0245104971327995[/C][C]0.0851[/C][/ROW]
[ROW][C]2[/C][C]0.934416666666667[/C][C]0.0514423743502172[/C][C]0.1314[/C][/ROW]
[ROW][C]3[/C][C]1.113375[/C][C]0.0492169247497056[/C][C]0.1519[/C][/ROW]
[ROW][C]4[/C][C]1.23398333333333[/C][C]0.0293635467678528[/C][C]0.1006[/C][/ROW]
[ROW][C]5[/C][C]1.25770833333333[/C][C]0.0547375134509038[/C][C]0.1622[/C][/ROW]
[ROW][C]6[/C][C]1.24435[/C][C]0.0377517127847442[/C][C]0.1025[/C][/ROW]
[ROW][C]7[/C][C]1.359325[/C][C]0.0489224084183776[/C][C]0.1685[/C][/ROW]
[ROW][C]8[/C][C]1.479925[/C][C]0.0965392160071373[/C][C]0.3038[/C][/ROW]
[ROW][C]9[/C][C]1.38355833333333[/C][C]0.0714306587898468[/C][C]0.2129[/C][/ROW]
[ROW][C]10[/C][C]1.33841666666667[/C][C]0.0709648034826655[/C][C]0.2406[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115751&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115751&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
10.8960583333333330.02451049713279950.0851
20.9344166666666670.05144237435021720.1314
31.1133750.04921692474970560.1519
41.233983333333330.02936354676785280.1006
51.257708333333330.05473751345090380.1622
61.244350.03775171278474420.1025
71.3593250.04892240841837760.1685
81.4799250.09653921600713730.3038
91.383558333333330.07143065878984680.2129
101.338416666666670.07096480348266550.2406






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.0410756445413832
beta0.0772508037541305
S.D.0.0292303476294625
T-STAT2.64282877280139
p-value0.0295831697056815

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0410756445413832 \tabularnewline
beta & 0.0772508037541305 \tabularnewline
S.D. & 0.0292303476294625 \tabularnewline
T-STAT & 2.64282877280139 \tabularnewline
p-value & 0.0295831697056815 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115751&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0410756445413832[/C][/ROW]
[ROW][C]beta[/C][C]0.0772508037541305[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0292303476294625[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.64282877280139[/C][/ROW]
[ROW][C]p-value[/C][C]0.0295831697056815[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115751&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115751&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-0.0410756445413832
beta0.0772508037541305
S.D.0.0292303476294625
T-STAT2.64282877280139
p-value0.0295831697056815






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.31450045326889
beta1.63296613612359
S.D.0.671920630785513
T-STAT2.43029617086554
p-value0.0411832114456356
Lambda-0.632966136123592

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.31450045326889 \tabularnewline
beta & 1.63296613612359 \tabularnewline
S.D. & 0.671920630785513 \tabularnewline
T-STAT & 2.43029617086554 \tabularnewline
p-value & 0.0411832114456356 \tabularnewline
Lambda & -0.632966136123592 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115751&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.31450045326889[/C][/ROW]
[ROW][C]beta[/C][C]1.63296613612359[/C][/ROW]
[ROW][C]S.D.[/C][C]0.671920630785513[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.43029617086554[/C][/ROW]
[ROW][C]p-value[/C][C]0.0411832114456356[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.632966136123592[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115751&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115751&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-3.31450045326889
beta1.63296613612359
S.D.0.671920630785513
T-STAT2.43029617086554
p-value0.0411832114456356
Lambda-0.632966136123592


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')