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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 15:09:12 +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/t129337600672nwmrexhwl0q6v.htm/, Retrieved Mon, 06 May 2024 18:18:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115646, Retrieved Mon, 06 May 2024 18:18:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102

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]
-   P           [Standard Deviation-Mean Plot] [WS6 - Stationarity] [2010-12-14 19:01:47] [8ed0bd3560b9ca2814a2ed0a29182575]
-    D              [Standard Deviation-Mean Plot] [Stationarity Euro...] [2010-12-26 15:09:12] [c9d5faca36bd2ada281161976df30bf1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.4271
7.7662
7.6289
7.5281
7.3831
7.2355
7.0617
7.1237
7.4533
7.5411
7.4978
7.3525
7.3862
7.311
7.2013
7.249
7.3321
7.59
7.9082
8.2123
8.0929
8.118
8.1206
8.2883
8.4281
8.7917
8.9168
8.9446
8.9786
9.5862
9.6533
9.4125
9.2195
9.2882
9.6774
9.6857
10.1688
10.4399
10.4675
10.149
9.9163
9.9268
10.0529
10.1622
10.083
10.1134
10.3423
10.7536
11.0967
10.8588
10.7719
10.9262
10.708
10.5062
10.0683
9.8954
9.9589
9.9177
9.7189
9.5273
9.5746
9.763
9.6117
9.6581
9.8361
10.2353
10.1285
10.1347
10.2141
10.0971
9.9651
10.1286
10.3356
10.1238
10.1326
10.2467
10.44
10.3689
10.2415
10.3899
10.3162
10.4533
10.6741
10.8957
10.7404
10.6568
10.5682
10.9833
11.0237
10.8462
10.7287
10.7809
10.2609
9.8252
9.1071
8.695
9.2205
9.0496
8.7406
8.921
9.011
9.3157
9.5786
9.6246
9.7485
9.9431
10.1152
10.1827
9.9777
9.7436
9.3462
9.2623
9.1505
8.5794
8.3245
8.6538
8.752
8.8104
9.2665
9.0895

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=115646&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=115646&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115646&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
17.416583333333330.2029436143515250.7045
27.734158333333330.4256799084637391.087
39.215216666666670.4074278091846081.2576
410.21464166666670.2442450612074730.8373
510.3295250.5372452599308641.5694
69.9455750.2447950018986200.6607
710.38485833333330.2197499217430130.7719
810.35136666666670.7562797706637082.3287
99.454258333333330.4829109619763981.4421
109.07970.483684989524081.6532

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7.41658333333333 & 0.202943614351525 & 0.7045 \tabularnewline
2 & 7.73415833333333 & 0.425679908463739 & 1.087 \tabularnewline
3 & 9.21521666666667 & 0.407427809184608 & 1.2576 \tabularnewline
4 & 10.2146416666667 & 0.244245061207473 & 0.8373 \tabularnewline
5 & 10.329525 & 0.537245259930864 & 1.5694 \tabularnewline
6 & 9.945575 & 0.244795001898620 & 0.6607 \tabularnewline
7 & 10.3848583333333 & 0.219749921743013 & 0.7719 \tabularnewline
8 & 10.3513666666667 & 0.756279770663708 & 2.3287 \tabularnewline
9 & 9.45425833333333 & 0.482910961976398 & 1.4421 \tabularnewline
10 & 9.0797 & 0.48368498952408 & 1.6532 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115646&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]7.41658333333333[/C][C]0.202943614351525[/C][C]0.7045[/C][/ROW]
[ROW][C]2[/C][C]7.73415833333333[/C][C]0.425679908463739[/C][C]1.087[/C][/ROW]
[ROW][C]3[/C][C]9.21521666666667[/C][C]0.407427809184608[/C][C]1.2576[/C][/ROW]
[ROW][C]4[/C][C]10.2146416666667[/C][C]0.244245061207473[/C][C]0.8373[/C][/ROW]
[ROW][C]5[/C][C]10.329525[/C][C]0.537245259930864[/C][C]1.5694[/C][/ROW]
[ROW][C]6[/C][C]9.945575[/C][C]0.244795001898620[/C][C]0.6607[/C][/ROW]
[ROW][C]7[/C][C]10.3848583333333[/C][C]0.219749921743013[/C][C]0.7719[/C][/ROW]
[ROW][C]8[/C][C]10.3513666666667[/C][C]0.756279770663708[/C][C]2.3287[/C][/ROW]
[ROW][C]9[/C][C]9.45425833333333[/C][C]0.482910961976398[/C][C]1.4421[/C][/ROW]
[ROW][C]10[/C][C]9.0797[/C][C]0.48368498952408[/C][C]1.6532[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115646&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115646&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
17.416583333333330.2029436143515250.7045
27.734158333333330.4256799084637391.087
39.215216666666670.4074278091846081.2576
410.21464166666670.2442450612074730.8373
510.3295250.5372452599308641.5694
69.9455750.2447950018986200.6607
710.38485833333330.2197499217430130.7719
810.35136666666670.7562797706637082.3287
99.454258333333330.4829109619763981.4421
109.07970.483684989524081.6532






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0419540655479845
beta0.0380917715350084
S.D.0.0560119336888773
T-STAT0.680065282991158
p-value0.515656688890863

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0419540655479845 \tabularnewline
beta & 0.0380917715350084 \tabularnewline
S.D. & 0.0560119336888773 \tabularnewline
T-STAT & 0.680065282991158 \tabularnewline
p-value & 0.515656688890863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115646&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0419540655479845[/C][/ROW]
[ROW][C]beta[/C][C]0.0380917715350084[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0560119336888773[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.680065282991158[/C][/ROW]
[ROW][C]p-value[/C][C]0.515656688890863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115646&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115646&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)
alpha0.0419540655479845
beta0.0380917715350084
S.D.0.0560119336888773
T-STAT0.680065282991158
p-value0.515656688890863






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.66111055190509
beta0.741507238871507
S.D.1.26868181092333
T-STAT0.584470615474377
p-value0.575011461643373
Lambda0.258492761128493

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.66111055190509 \tabularnewline
beta & 0.741507238871507 \tabularnewline
S.D. & 1.26868181092333 \tabularnewline
T-STAT & 0.584470615474377 \tabularnewline
p-value & 0.575011461643373 \tabularnewline
Lambda & 0.258492761128493 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115646&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.66111055190509[/C][/ROW]
[ROW][C]beta[/C][C]0.741507238871507[/C][/ROW]
[ROW][C]S.D.[/C][C]1.26868181092333[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.584470615474377[/C][/ROW]
[ROW][C]p-value[/C][C]0.575011461643373[/C][/ROW]
[ROW][C]Lambda[/C][C]0.258492761128493[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115646&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115646&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-2.66111055190509
beta0.741507238871507
S.D.1.26868181092333
T-STAT0.584470615474377
p-value0.575011461643373
Lambda0.258492761128493


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')