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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, 13 Dec 2012 16:16:29 -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/2012/Dec/13/t1355433449l62t2hfx9sqnnys.htm/, Retrieved Sun, 28 Apr 2024 23:13:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=199426, Retrieved Sun, 28 Apr 2024 23:13:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2012-11-21 08:39:17] [d2c1a12335a0e7c18f8727e39be21dbc]
- R PD  [(Partial) Autocorrelation Function] [Paper Autocorrela...] [2012-12-13 20:09:47] [86dcce9422b96d4554cb918e531c1d5d]
- RMP       [Standard Deviation-Mean Plot] [Paper Standard De...] [2012-12-13 21:16:29] [c63d55528b56cf8bb48e0b5d1a959d8e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
68.897
38.683
44.720
39.525
45.315
50.380
40.600
36.279
42.438
38.064
31.879
11.379
70.249
39.253
47.060
41.697
38.708
49.267
39.018
32.228
40.870
39.383
34.571
12.066
70.938
34.077
45.409
40.809
37.013
44.953
37.848
32.745
43.412
34.931
33.008
8.620
68.906
39.556
50.669
36.432
40.891
48.428
36.222
33.425
39.401
37.967
34.801
12.657
69.116
41.519
51.321
38.529
41.547
52.073
38.401
40.898
40.439
41.888
37.898
8.771
68.184
50.530
47.221
41.756
45.633
48.138
39.486
39.341
41.117
41.629
29.722
7.054
56.676
34.870
35.117
30.169
30.936
35.699
33.228
27.733
33.666
35.429
27.438
8.170
63.410
38.040
45.389
37.353
37.024
50.957
37.994
36.454
46.080
43.373
37.395
10.963
76.058
50.179
57.452
47.568
50.050
50.856
41.992
39.284
44.521
43.832
41.153
17.100

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'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199426&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199426&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199426&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'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
140.679916666666713.138186435372557.518
240.364166666666713.234001860451158.183
338.646916666666714.018925509716162.318
439.9462513.041080554261156.249
541.866666666666713.729544184536960.345
641.650916666666714.210663611005361.13
732.427583333333310.72702833931348.506
840.369333333333312.17325027436952.447
946.670416666666713.537502995606758.958

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 40.6799166666667 & 13.1381864353725 & 57.518 \tabularnewline
2 & 40.3641666666667 & 13.2340018604511 & 58.183 \tabularnewline
3 & 38.6469166666667 & 14.0189255097161 & 62.318 \tabularnewline
4 & 39.94625 & 13.0410805542611 & 56.249 \tabularnewline
5 & 41.8666666666667 & 13.7295441845369 & 60.345 \tabularnewline
6 & 41.6509166666667 & 14.2106636110053 & 61.13 \tabularnewline
7 & 32.4275833333333 & 10.727028339313 & 48.506 \tabularnewline
8 & 40.3693333333333 & 12.173250274369 & 52.447 \tabularnewline
9 & 46.6704166666667 & 13.5375029956067 & 58.958 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199426&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]40.6799166666667[/C][C]13.1381864353725[/C][C]57.518[/C][/ROW]
[ROW][C]2[/C][C]40.3641666666667[/C][C]13.2340018604511[/C][C]58.183[/C][/ROW]
[ROW][C]3[/C][C]38.6469166666667[/C][C]14.0189255097161[/C][C]62.318[/C][/ROW]
[ROW][C]4[/C][C]39.94625[/C][C]13.0410805542611[/C][C]56.249[/C][/ROW]
[ROW][C]5[/C][C]41.8666666666667[/C][C]13.7295441845369[/C][C]60.345[/C][/ROW]
[ROW][C]6[/C][C]41.6509166666667[/C][C]14.2106636110053[/C][C]61.13[/C][/ROW]
[ROW][C]7[/C][C]32.4275833333333[/C][C]10.727028339313[/C][C]48.506[/C][/ROW]
[ROW][C]8[/C][C]40.3693333333333[/C][C]12.173250274369[/C][C]52.447[/C][/ROW]
[ROW][C]9[/C][C]46.6704166666667[/C][C]13.5375029956067[/C][C]58.958[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199426&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199426&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
140.679916666666713.138186435372557.518
240.364166666666713.234001860451158.183
338.646916666666714.018925509716162.318
439.9462513.041080554261156.249
541.866666666666713.729544184536960.345
641.650916666666714.210663611005361.13
732.427583333333310.72702833931348.506
840.369333333333312.17325027436952.447
946.670416666666713.537502995606758.958






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4.86843152298638
beta0.20405343870159
S.D.0.0773775324148469
T-STAT2.63711483596545
p-value0.0335638466527127

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4.86843152298638 \tabularnewline
beta & 0.20405343870159 \tabularnewline
S.D. & 0.0773775324148469 \tabularnewline
T-STAT & 2.63711483596545 \tabularnewline
p-value & 0.0335638466527127 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199426&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.86843152298638[/C][/ROW]
[ROW][C]beta[/C][C]0.20405343870159[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0773775324148469[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.63711483596545[/C][/ROW]
[ROW][C]p-value[/C][C]0.0335638466527127[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199426&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199426&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)
alpha4.86843152298638
beta0.20405343870159
S.D.0.0773775324148469
T-STAT2.63711483596545
p-value0.0335638466527127






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.0579927725964226
beta0.67999157632445
S.D.0.225517654969878
T-STAT3.01524763733143
p-value0.0195168804511093
Lambda0.32000842367555

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.0579927725964226 \tabularnewline
beta & 0.67999157632445 \tabularnewline
S.D. & 0.225517654969878 \tabularnewline
T-STAT & 3.01524763733143 \tabularnewline
p-value & 0.0195168804511093 \tabularnewline
Lambda & 0.32000842367555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199426&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0579927725964226[/C][/ROW]
[ROW][C]beta[/C][C]0.67999157632445[/C][/ROW]
[ROW][C]S.D.[/C][C]0.225517654969878[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.01524763733143[/C][/ROW]
[ROW][C]p-value[/C][C]0.0195168804511093[/C][/ROW]
[ROW][C]Lambda[/C][C]0.32000842367555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199426&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199426&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)
alpha0.0579927725964226
beta0.67999157632445
S.D.0.225517654969878
T-STAT3.01524763733143
p-value0.0195168804511093
Lambda0.32000842367555


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 2 ; par4 = 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')