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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 computationWed, 22 Dec 2010 19:20:25 +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/22/t1293045622ulnb8l2e32er7jx.htm/, Retrieved Mon, 06 May 2024 10:37:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114520, Retrieved Mon, 06 May 2024 10:37:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact180

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [Unemployment] [2010-11-29 09:29:57] [b98453cac15ba1066b407e146608df68]
-   PD  [Variance Reduction Matrix] [WS9 - Variance Re...] [2010-12-04 11:04:59] [8ef49741e164ec6343c90c7935194465]
-   P     [Variance Reduction Matrix] [WS 9 VRM] [2010-12-05 14:01:21] [8214fe6d084e5ad7598b249a26cc9f06]
- RMPD      [(Partial) Autocorrelation Function] [paper ACF] [2010-12-10 10:47:04] [8214fe6d084e5ad7598b249a26cc9f06]
-   P         [(Partial) Autocorrelation Function] [paper acf met D=1] [2010-12-10 11:19:24] [8214fe6d084e5ad7598b249a26cc9f06]
- RMP           [Spectral Analysis] [paper - cum perio...] [2010-12-10 11:22:34] [8214fe6d084e5ad7598b249a26cc9f06]
-   P             [Spectral Analysis] [paper - cum perio...] [2010-12-10 11:27:22] [8214fe6d084e5ad7598b249a26cc9f06]
-   PD              [Spectral Analysis] [cum periodogram 2 ] [2010-12-20 20:28:39] [8214fe6d084e5ad7598b249a26cc9f06]
-    D                [Spectral Analysis] [cum per 2 paper] [2010-12-22 13:46:56] [8214fe6d084e5ad7598b249a26cc9f06]
-   PD                  [Spectral Analysis] [cum per 1 middeng...] [2010-12-22 19:06:59] [8214fe6d084e5ad7598b249a26cc9f06]
-   P                     [Spectral Analysis] [cum per 2 middeng...] [2010-12-22 19:08:52] [8214fe6d084e5ad7598b249a26cc9f06]
-   PD                      [Spectral Analysis] [cum per 1 hoogges...] [2010-12-22 19:10:38] [8214fe6d084e5ad7598b249a26cc9f06]
-   P                         [Spectral Analysis] [cum per 2 hoogges...] [2010-12-22 19:12:39] [8214fe6d084e5ad7598b249a26cc9f06]
- RMPD                          [Standard Deviation-Mean Plot] [sdmp laaggeschoolden] [2010-12-22 19:15:16] [8214fe6d084e5ad7598b249a26cc9f06]
-    D                            [Standard Deviation-Mean Plot] [sdmp middengescho...] [2010-12-22 19:17:33] [8214fe6d084e5ad7598b249a26cc9f06]
-    D                                [Standard Deviation-Mean Plot] [sdmp hooggeschoolden] [2010-12-22 19:20:25] [b47314d83d48c7bf812ec2bcd743b159] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19246
17549
16428
16209
15235
16186
24971
30776
26416
23157
20155
19790
18849
17573
16597
16158
15507
16433
26325
31144
30535
27596
24064
23854
22407
21125
20226
19547
18933
20372
34331
37329
36761
32737
29321
28883
27436
25101
23776
23782
23027
25606
41328
44751
42855
37628
33544
33275
32009
30813
29143
28121
27007
29112
44067
48481
46581
41166
36824
35936
33633
31630
30434
28546
27660
29830
45599
49303
44417
40386
35544
35019
30400
29602
27701
27937
27283
29372
42821
45386
40170
34371
30077
29251
27202
25714
23784
22968
22243
24255
37282
38794
31828
27949
24605
25695
23338
21941
22034
20637
19418
22454
33261
34995
29132
26171
23828
25743
25204
25679
25281
25136
24794
28278
40062
42590
37885
34061
32412
34647
31750
31288
29331
28768
27780
30113
41240
43271
38108
34382
31551

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=114520&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=114520&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114520&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
120509.83333333334860.530177466315541
222052.91666666675878.6412539314115637
3268317155.8273900621518396
431842.41666666678134.1621176406721724
535771.66666666677626.5274992600521474
636000.08333333337256.5353172575521643
732864.256348.9270263851418103
827693.255470.2368425541116551
9252464911.7830682035315577
1031335.756481.3462423817817796

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 20509.8333333333 & 4860.5301774663 & 15541 \tabularnewline
2 & 22052.9166666667 & 5878.64125393141 & 15637 \tabularnewline
3 & 26831 & 7155.82739006215 & 18396 \tabularnewline
4 & 31842.4166666667 & 8134.16211764067 & 21724 \tabularnewline
5 & 35771.6666666667 & 7626.52749926005 & 21474 \tabularnewline
6 & 36000.0833333333 & 7256.53531725755 & 21643 \tabularnewline
7 & 32864.25 & 6348.92702638514 & 18103 \tabularnewline
8 & 27693.25 & 5470.23684255411 & 16551 \tabularnewline
9 & 25246 & 4911.78306820353 & 15577 \tabularnewline
10 & 31335.75 & 6481.34624238178 & 17796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114520&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]20509.8333333333[/C][C]4860.5301774663[/C][C]15541[/C][/ROW]
[ROW][C]2[/C][C]22052.9166666667[/C][C]5878.64125393141[/C][C]15637[/C][/ROW]
[ROW][C]3[/C][C]26831[/C][C]7155.82739006215[/C][C]18396[/C][/ROW]
[ROW][C]4[/C][C]31842.4166666667[/C][C]8134.16211764067[/C][C]21724[/C][/ROW]
[ROW][C]5[/C][C]35771.6666666667[/C][C]7626.52749926005[/C][C]21474[/C][/ROW]
[ROW][C]6[/C][C]36000.0833333333[/C][C]7256.53531725755[/C][C]21643[/C][/ROW]
[ROW][C]7[/C][C]32864.25[/C][C]6348.92702638514[/C][C]18103[/C][/ROW]
[ROW][C]8[/C][C]27693.25[/C][C]5470.23684255411[/C][C]16551[/C][/ROW]
[ROW][C]9[/C][C]25246[/C][C]4911.78306820353[/C][C]15577[/C][/ROW]
[ROW][C]10[/C][C]31335.75[/C][C]6481.34624238178[/C][C]17796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114520&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114520&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
120509.83333333334860.530177466315541
222052.91666666675878.6412539314115637
3268317155.8273900621518396
431842.41666666678134.1621176406721724
535771.66666666677626.5274992600521474
636000.08333333337256.5353172575521643
732864.256348.9270263851418103
827693.255470.2368425541116551
9252464911.7830682035315577
1031335.756481.3462423817817796






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1900.9456669112
beta0.155490266489008
S.D.0.049404786197481
T-STAT3.14727131633526
p-value0.0136545696037264

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1900.9456669112 \tabularnewline
beta & 0.155490266489008 \tabularnewline
S.D. & 0.049404786197481 \tabularnewline
T-STAT & 3.14727131633526 \tabularnewline
p-value & 0.0136545696037264 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114520&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1900.9456669112[/C][/ROW]
[ROW][C]beta[/C][C]0.155490266489008[/C][/ROW]
[ROW][C]S.D.[/C][C]0.049404786197481[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.14727131633526[/C][/ROW]
[ROW][C]p-value[/C][C]0.0136545696037264[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114520&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114520&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)
alpha1900.9456669112
beta0.155490266489008
S.D.0.049404786197481
T-STAT3.14727131633526
p-value0.0136545696037264






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.58554213477413
beta0.69851209382945
S.D.0.215248563749495
T-STAT3.24514171737923
p-value0.0117865058988477
Lambda0.30148790617055

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.58554213477413 \tabularnewline
beta & 0.69851209382945 \tabularnewline
S.D. & 0.215248563749495 \tabularnewline
T-STAT & 3.24514171737923 \tabularnewline
p-value & 0.0117865058988477 \tabularnewline
Lambda & 0.30148790617055 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114520&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.58554213477413[/C][/ROW]
[ROW][C]beta[/C][C]0.69851209382945[/C][/ROW]
[ROW][C]S.D.[/C][C]0.215248563749495[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.24514171737923[/C][/ROW]
[ROW][C]p-value[/C][C]0.0117865058988477[/C][/ROW]
[ROW][C]Lambda[/C][C]0.30148790617055[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114520&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114520&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)
alpha1.58554213477413
beta0.69851209382945
S.D.0.215248563749495
T-STAT3.24514171737923
p-value0.0117865058988477
Lambda0.30148790617055


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')