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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 computationThu, 22 Dec 2011 20:52:28 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/22/t1324605162ljg1eb6x7owgtvr.htm/, Retrieved Fri, 03 May 2024 08:06:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160153, Retrieved Fri, 03 May 2024 08:06:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64

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         [Spectral Analysis] [Births] [2010-11-29 09:38:20] [b98453cac15ba1066b407e146608df68]
- R  D          [Spectral Analysis] [WS9 3.2 CP d=0, D=0] [2010-12-07 10:39:32] [afe9379cca749d06b3d6872e02cc47ed]
- RMPD              [Standard Deviation-Mean Plot] [PAPER: inflatie] [2011-12-23 01:52:28] [6baf48ba14bcb50d9e72b77bece8a45b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,0213
0,0218
0,0290
0,0263
0,0267
0,0181
0,0133
0,0088
0,0128
0,0126
0,0126
0,0129
0,0110
0,0137
0,0121
0,0174
0,0176
0,0148
0,0104
0,0162
0,0149
0,0179
0,0180
0,0158
0,0186
0,0174
0,0159
0,0126
0,0113
0,0192
0,0261
0,0226
0,0241
0,0226
0,0203
0,0286
0,0255
0,0227
0,0226
0,0257
0,0307
0,0276
0,0251
0,0287
0,0314
0,0311
0,0316
0,0247
0,0257
0,0289
0,0263
0,0238
0,0169
0,0196
0,0219
0,0187
0,0160
0,0163
0,0122
0,0121
0,0149
0,0164
0,0166
0,0177
0,0182
0,0178
0,0128
0,0129
0,0137
0,0112
0,0151
0,0224
0,0294
0,0309
0,0346
0,0364
0,0439
0,0415
0,0521
0,0580
0,0591
0,0539
0,0546
0,0472
0,0314
0,0263
0,0232
0,0193
0,0062
0,0060
-0,0037
-0,0110
-0,0168
-0,0078
-0,0119
-0,0097
-0,0012
0,0026
0,0062
0,0070
0,0166
0,0180
0,0227
0,0246
0,0257
0,0232
0,0291
0,0301
0,0286
0,0310
0,0322
0,0339
0,0352
0,0341
0,0335
0,0367
0,0375
0,0360
0,0355
0,0357

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'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 & 0 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160153&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160153&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160153&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
10.01801666666666670.006802517359348850.0202
20.01498333333333330.002685257168430250.0076
30.01994166666666670.005206369932955960.0173
40.02728333333333330.00335744311082470.009
50.01986666666666670.005507240413282950.0168
60.01580833333333330.003048235952849190.0112
70.04513333333333330.0105828620749290.0297
80.004291666666666670.0169364297157090.0482
90.017050.01078201364225710.0313
100.03415833333333330.002549316604801210.0089

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 0.0180166666666667 & 0.00680251735934885 & 0.0202 \tabularnewline
2 & 0.0149833333333333 & 0.00268525716843025 & 0.0076 \tabularnewline
3 & 0.0199416666666667 & 0.00520636993295596 & 0.0173 \tabularnewline
4 & 0.0272833333333333 & 0.0033574431108247 & 0.009 \tabularnewline
5 & 0.0198666666666667 & 0.00550724041328295 & 0.0168 \tabularnewline
6 & 0.0158083333333333 & 0.00304823595284919 & 0.0112 \tabularnewline
7 & 0.0451333333333333 & 0.010582862074929 & 0.0297 \tabularnewline
8 & 0.00429166666666667 & 0.016936429715709 & 0.0482 \tabularnewline
9 & 0.01705 & 0.0107820136422571 & 0.0313 \tabularnewline
10 & 0.0341583333333333 & 0.00254931660480121 & 0.0089 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160153&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]0.0180166666666667[/C][C]0.00680251735934885[/C][C]0.0202[/C][/ROW]
[ROW][C]2[/C][C]0.0149833333333333[/C][C]0.00268525716843025[/C][C]0.0076[/C][/ROW]
[ROW][C]3[/C][C]0.0199416666666667[/C][C]0.00520636993295596[/C][C]0.0173[/C][/ROW]
[ROW][C]4[/C][C]0.0272833333333333[/C][C]0.0033574431108247[/C][C]0.009[/C][/ROW]
[ROW][C]5[/C][C]0.0198666666666667[/C][C]0.00550724041328295[/C][C]0.0168[/C][/ROW]
[ROW][C]6[/C][C]0.0158083333333333[/C][C]0.00304823595284919[/C][C]0.0112[/C][/ROW]
[ROW][C]7[/C][C]0.0451333333333333[/C][C]0.010582862074929[/C][C]0.0297[/C][/ROW]
[ROW][C]8[/C][C]0.00429166666666667[/C][C]0.016936429715709[/C][C]0.0482[/C][/ROW]
[ROW][C]9[/C][C]0.01705[/C][C]0.0107820136422571[/C][C]0.0313[/C][/ROW]
[ROW][C]10[/C][C]0.0341583333333333[/C][C]0.00254931660480121[/C][C]0.0089[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160153&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160153&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
10.01801666666666670.006802517359348850.0202
20.01498333333333330.002685257168430250.0076
30.01994166666666670.005206369932955960.0173
40.02728333333333330.00335744311082470.009
50.01986666666666670.005507240413282950.0168
60.01580833333333330.003048235952849190.0112
70.04513333333333330.0105828620749290.0297
80.004291666666666670.0169364297157090.0482
90.017050.01078201364225710.0313
100.03415833333333330.002549316604801210.0089






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.00905348805406278
beta-0.106575713817301
S.D.0.141133674835354
T-STAT-0.755140216830829
p-value0.471809015036529

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.00905348805406278 \tabularnewline
beta & -0.106575713817301 \tabularnewline
S.D. & 0.141133674835354 \tabularnewline
T-STAT & -0.755140216830829 \tabularnewline
p-value & 0.471809015036529 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160153&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.00905348805406278[/C][/ROW]
[ROW][C]beta[/C][C]-0.106575713817301[/C][/ROW]
[ROW][C]S.D.[/C][C]0.141133674835354[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.755140216830829[/C][/ROW]
[ROW][C]p-value[/C][C]0.471809015036529[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160153&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160153&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)
alpha0.00905348805406278
beta-0.106575713817301
S.D.0.141133674835354
T-STAT-0.755140216830829
p-value0.471809015036529






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-6.93292674716461
beta-0.435731216159984
S.D.0.336978144149701
T-STAT-1.29305482781225
p-value0.232080578301237
Lambda1.43573121615998

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -6.93292674716461 \tabularnewline
beta & -0.435731216159984 \tabularnewline
S.D. & 0.336978144149701 \tabularnewline
T-STAT & -1.29305482781225 \tabularnewline
p-value & 0.232080578301237 \tabularnewline
Lambda & 1.43573121615998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160153&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-6.93292674716461[/C][/ROW]
[ROW][C]beta[/C][C]-0.435731216159984[/C][/ROW]
[ROW][C]S.D.[/C][C]0.336978144149701[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.29305482781225[/C][/ROW]
[ROW][C]p-value[/C][C]0.232080578301237[/C][/ROW]
[ROW][C]Lambda[/C][C]1.43573121615998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160153&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160153&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-6.93292674716461
beta-0.435731216159984
S.D.0.336978144149701
T-STAT-1.29305482781225
p-value0.232080578301237
Lambda1.43573121615998


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = multiplicative ; par2 = 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')