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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 computationThu, 27 May 2010 14:28:21 +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/May/27/t1274970520cc8xcnidcek9o0s.htm/, Retrieved Thu, 02 May 2024 05:46:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76607, Retrieved Thu, 02 May 2024 05:46:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact175

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] [Spreidings- en ge...] [2010-05-17 14:46:44] [05bbf10299dcd1da03eee55b39d86f8c]
-   P     [Standard Deviation-Mean Plot] [Spreidings- en ge...] [2010-05-27 14:28:21] [d4eb12efc488666eba544481d350541e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.1591
1.1203
1.0886
1.0701
1.0630
1.0377
1.0370
1.0605
1.0497
1.0706
1.0328
1.0110
1.0131
0.9834
0.9643
0.9449
0.9059
0.9505
0.9386
0.9045
0.8695
0.8525
0.8552
0.8983
0.9376
0.9205
0.9083
0.8925
0.8753
0.8530
0.8615
0.9014
0.9114
0.9050
0.8883
0.8912
0.8832
0.8707
0.8766
0.8860
0.9170
0.9561
0.9935
0.9781
0.9806
0.9812
1.0013
1.0194
1.0622
1.0785
1.0797
1.0862
1.1556
1.1674
1.1365
1.1155
1.1267
1.1714
1.1710
1.2298
1.2638
1.2640
1.2261
1.1989
1.2000
1.2146
1.2266
1.2191
1.2224
1.2507
1.2997
1.3406
1.3123
1.3013
1.3185
1.2943
1.2697
1.2155
1.2041
1.2295
1.2234
1.2022
1.1789
1.1861
1.2126
1.1940
1.2028
1.2273
1.2767
1.2661
1.2681
1.2810
1.2722
1.2617
1.2888
1.3205
1.2993
1.3080
1.3246
1.3513
1.3518
1.3421
1.3726
1.3626
1.3910
1.4233
1.4683
1.4559
1.4728
1.4759
1.5520
1.5754
1.5554
1.5562
1.5759
1.4955
1.4342
1.3266
1.2744
1.3511
1.3244
1.2797
1.3050
1.3199
1.3646
1.4014
1.4092
1.4266
1.4575
1.4821
1.4908
1.4579

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76607&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76607&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76607&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11.06670.04071298653657420.1481
20.9233916666666670.05101098737853770.1606
30.89550.02409967936414390.0846
40.9453083333333330.05488506102977770.1487
51.131708333333330.04984987386385670.1676
61.2438750.04244237001779320.1417
71.244650.05139903607161240.1396
81.255983333333330.03839320094480110.1265
91.37090.05455470982084280.169
101.470450.103880967720490.3015
111.393258333333330.07309650480803790.2111

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.0667 & 0.0407129865365742 & 0.1481 \tabularnewline
2 & 0.923391666666667 & 0.0510109873785377 & 0.1606 \tabularnewline
3 & 0.8955 & 0.0240996793641439 & 0.0846 \tabularnewline
4 & 0.945308333333333 & 0.0548850610297777 & 0.1487 \tabularnewline
5 & 1.13170833333333 & 0.0498498738638567 & 0.1676 \tabularnewline
6 & 1.243875 & 0.0424423700177932 & 0.1417 \tabularnewline
7 & 1.24465 & 0.0513990360716124 & 0.1396 \tabularnewline
8 & 1.25598333333333 & 0.0383932009448011 & 0.1265 \tabularnewline
9 & 1.3709 & 0.0545547098208428 & 0.169 \tabularnewline
10 & 1.47045 & 0.10388096772049 & 0.3015 \tabularnewline
11 & 1.39325833333333 & 0.0730965048080379 & 0.2111 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76607&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]1.0667[/C][C]0.0407129865365742[/C][C]0.1481[/C][/ROW]
[ROW][C]2[/C][C]0.923391666666667[/C][C]0.0510109873785377[/C][C]0.1606[/C][/ROW]
[ROW][C]3[/C][C]0.8955[/C][C]0.0240996793641439[/C][C]0.0846[/C][/ROW]
[ROW][C]4[/C][C]0.945308333333333[/C][C]0.0548850610297777[/C][C]0.1487[/C][/ROW]
[ROW][C]5[/C][C]1.13170833333333[/C][C]0.0498498738638567[/C][C]0.1676[/C][/ROW]
[ROW][C]6[/C][C]1.243875[/C][C]0.0424423700177932[/C][C]0.1417[/C][/ROW]
[ROW][C]7[/C][C]1.24465[/C][C]0.0513990360716124[/C][C]0.1396[/C][/ROW]
[ROW][C]8[/C][C]1.25598333333333[/C][C]0.0383932009448011[/C][C]0.1265[/C][/ROW]
[ROW][C]9[/C][C]1.3709[/C][C]0.0545547098208428[/C][C]0.169[/C][/ROW]
[ROW][C]10[/C][C]1.47045[/C][C]0.10388096772049[/C][C]0.3015[/C][/ROW]
[ROW][C]11[/C][C]1.39325833333333[/C][C]0.0730965048080379[/C][C]0.2111[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76607&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76607&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
11.06670.04071298653657420.1481
20.9233916666666670.05101098737853770.1606
30.89550.02409967936414390.0846
40.9453083333333330.05488506102977770.1487
51.131708333333330.04984987386385670.1676
61.2438750.04244237001779320.1417
71.244650.05139903607161240.1396
81.255983333333330.03839320094480110.1265
91.37090.05455470982084280.169
101.470450.103880967720490.3015
111.393258333333330.07309650480803790.2111






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.0277749608848275
beta0.0687582178797317
S.D.0.0261683288978133
T-STAT2.62753568056374
p-value0.0274694178555294

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0277749608848275 \tabularnewline
beta & 0.0687582178797317 \tabularnewline
S.D. & 0.0261683288978133 \tabularnewline
T-STAT & 2.62753568056374 \tabularnewline
p-value & 0.0274694178555294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76607&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0277749608848275[/C][/ROW]
[ROW][C]beta[/C][C]0.0687582178797317[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0261683288978133[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.62753568056374[/C][/ROW]
[ROW][C]p-value[/C][C]0.0274694178555294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76607&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76607&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-0.0277749608848275
beta0.0687582178797317
S.D.0.0261683288978133
T-STAT2.62753568056374
p-value0.0274694178555294






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.20011739635839
beta1.35448684317884
S.D.0.546540771798907
T-STAT2.47829057422492
p-value0.0350897173789072
Lambda-0.354486843178842

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.20011739635839 \tabularnewline
beta & 1.35448684317884 \tabularnewline
S.D. & 0.546540771798907 \tabularnewline
T-STAT & 2.47829057422492 \tabularnewline
p-value & 0.0350897173789072 \tabularnewline
Lambda & -0.354486843178842 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76607&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.20011739635839[/C][/ROW]
[ROW][C]beta[/C][C]1.35448684317884[/C][/ROW]
[ROW][C]S.D.[/C][C]0.546540771798907[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.47829057422492[/C][/ROW]
[ROW][C]p-value[/C][C]0.0350897173789072[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.354486843178842[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76607&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76607&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-3.20011739635839
beta1.35448684317884
S.D.0.546540771798907
T-STAT2.47829057422492
p-value0.0350897173789072
Lambda-0.354486843178842


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')