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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 computationTue, 24 Nov 2009 14:20:13 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/24/t1259097768vq6tfsci3ff30nm.htm/, Retrieved Wed, 30 Apr 2025 20:48:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59293, Retrieved Wed, 30 Apr 2025 20:48:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact331

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       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-    D          [Standard Deviation-Mean Plot] [standard deviatio...] [2009-11-24 21:20:13] [f0f26816ac6124f58333f11f6c174000] [Current]
-    D            [Standard Deviation-Mean Plot] [SHw WS8] [2009-11-26 18:11:50] [af2352cd9a951bedd08ebe247d0de1a2]
-    D              [Standard Deviation-Mean Plot] [WS8 - review ] [2009-12-03 16:26:13] [af2352cd9a951bedd08ebe247d0de1a2]
-    D                [Standard Deviation-Mean Plot] [WS8 - review ] [2009-12-03 17:45:49] [af2352cd9a951bedd08ebe247d0de1a2]
- RM                [Variance Reduction Matrix] [] [2009-12-04 20:51:28] [badc6a9acdc45286bea7f74742e15a21]
-                 [Standard Deviation-Mean Plot] [] [2009-11-27 10:02:54] [08fc5c07292c885b941f0cb515ce13f3]
F    D            [Standard Deviation-Mean Plot] [WS8(8)] [2009-11-27 11:40:10] [7d268329e554b8694908ba13e6e6f258]
- RMP               [Box-Cox Normality Plot] [box-cox normality...] [2009-11-27 21:10:48] [cd6314e7e707a6546bd4604c9d1f2b69]
- RMPD              [Variance Reduction Matrix] [WS 9 Estimation o...] [2009-12-05 12:37:10] [101f710c1bf3d900563184d79f7da6e1]
-    D              [Standard Deviation-Mean Plot] [SMP] [2009-12-17 14:47:31] [7d268329e554b8694908ba13e6e6f258]
-                 [Standard Deviation-Mean Plot] [] [2009-12-04 14:24:33] [08fc5c07292c885b941f0cb515ce13f3]
-                 [Standard Deviation-Mean Plot] [paper Fase 2: SDMP] [2010-12-07 16:53:41] [814f53995537cd15c528d8efbf1cf544]
-                 [Standard Deviation-Mean Plot] [paper Fase 2: SDMP 2] [2010-12-07 16:53:41] [814f53995537cd15c528d8efbf1cf544]
- R  D            [Standard Deviation-Mean Plot] [paper Fase 2: SDMP 2] [2010-12-07 16:54:09] [814f53995537cd15c528d8efbf1cf544]
- RMP               [ARIMA Backward Selection] [PAPER timeserie A...] [2010-12-08 15:16:14] [814f53995537cd15c528d8efbf1cf544]
-    D                [ARIMA Backward Selection] [] [2011-12-10 13:42:10] [74be16979710d4c4e7c6647856088456]
- RMP               [ARIMA Forecasting] [Paper ARIMA Forecast] [2010-12-08 15:41:00] [814f53995537cd15c528d8efbf1cf544]
- RMP               [ARIMA Forecasting] [Paper ARIMA Forecast] [2010-12-08 15:46:25] [814f53995537cd15c528d8efbf1cf544]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
153.3
154.5
155.2
156.9
157
157.4
157.2
157.5
158
158.5
159
159.3
160
160.8
161.9
162.5
162.7
162.8
162.9
163
164
164.7
164.8
164.9
165
165.8
166.1
167.2
167.7
168.3
168.6
168.9
169.1
169.5
169.6
169.7
169.8
170.4
170.9
171.9
171.9
172
172
172.4
173
173.7
173.8
173.8
173.9
174.6
175
175.9
176
175.1
175.6
175.9
176.7
176.1
176.1
176.2
176.3
177.8
178.5
179.4
179.5
179.6
179.7
179.7
179.8
179.9
180.2
180.4
180.4
181.3
181.9
182.5
182.7
183.1
183.6
183.7
183.8
183.9
184.1
184.4
184.5
185.9
186.6
187.6
187.8
187.9
188
188.3
188.4
188.5
188.5
188.6
188.6
189.4
190
191.9
192.5
193
193.5
193.9
194.2
194.9
194.9
194.9
194.9
195.5
196
196.2
196.2
196.2
196.2
197
197.7
198
198.2
198.5
198.6
199.5
200
201.3
202.2
202.9
203.5
203.5
204
204.1
204.3
204.5
204.8
205.1
205.7
206.5
206.9
207.1
207.8
208
208.5
208.6
209
209.1
209.7
209.8
209.9
210
210.8
211.4
211.7
212
212.2
212.4
212.9
213.4
213.7
214
214.3
214.8
215
215.9
216.4
216.9
217.2
217.5
217.9
218.1
218.6
218.9
219.3
220.4
220.9
221
221.8
222
222.2
222.5
222.9
223.1
223.4
224
225.1
225.5
225.9
226.3
226.5
227
227.3
227.8
228.1
228.4
228.5
228.8
229
229.1
229.3
229.6
229.9
230
230.2
230.8
231
231.7
231.9
233
235.1
236
236.9
237.1
237.5
238.2
238.9
239.1
240
240.2
240.5
240.7
241.1
241.4
242.2
242.9
243.2
243.9

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59293&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59293&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59293&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1156.9833333333331.813501551912186
2162.9166666666671.540267587928884.90000000000001
3167.9583333333331.604798675186014.69999999999999
4172.1333333333331.312411613185534
5175.5916666666670.7925314256268052.79999999999998
6179.2333333333331.164890422730694.09999999999999
7182.951.230299298397084
8187.551.261672771291424.09999999999999
9192.6416666666672.227292826130716.30000000000001
10196.7166666666671.145610859945143.59999999999999
11202.3666666666672.044653041620045.9
12207.2583333333331.491465620445104.29999999999998
13211.351.290877080268933.70000000000002
14215.9751.575450873415434.40000000000001
15221.1333333333331.554075775228324.5
16226.2751.577181029558755
17229.8250.9705902608956313.19999999999999
18236.9916666666672.621400851499528.29999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 156.983333333333 & 1.81350155191218 & 6 \tabularnewline
2 & 162.916666666667 & 1.54026758792888 & 4.90000000000001 \tabularnewline
3 & 167.958333333333 & 1.60479867518601 & 4.69999999999999 \tabularnewline
4 & 172.133333333333 & 1.31241161318553 & 4 \tabularnewline
5 & 175.591666666667 & 0.792531425626805 & 2.79999999999998 \tabularnewline
6 & 179.233333333333 & 1.16489042273069 & 4.09999999999999 \tabularnewline
7 & 182.95 & 1.23029929839708 & 4 \tabularnewline
8 & 187.55 & 1.26167277129142 & 4.09999999999999 \tabularnewline
9 & 192.641666666667 & 2.22729282613071 & 6.30000000000001 \tabularnewline
10 & 196.716666666667 & 1.14561085994514 & 3.59999999999999 \tabularnewline
11 & 202.366666666667 & 2.04465304162004 & 5.9 \tabularnewline
12 & 207.258333333333 & 1.49146562044510 & 4.29999999999998 \tabularnewline
13 & 211.35 & 1.29087708026893 & 3.70000000000002 \tabularnewline
14 & 215.975 & 1.57545087341543 & 4.40000000000001 \tabularnewline
15 & 221.133333333333 & 1.55407577522832 & 4.5 \tabularnewline
16 & 226.275 & 1.57718102955875 & 5 \tabularnewline
17 & 229.825 & 0.970590260895631 & 3.19999999999999 \tabularnewline
18 & 236.991666666667 & 2.62140085149952 & 8.29999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59293&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]156.983333333333[/C][C]1.81350155191218[/C][C]6[/C][/ROW]
[ROW][C]2[/C][C]162.916666666667[/C][C]1.54026758792888[/C][C]4.90000000000001[/C][/ROW]
[ROW][C]3[/C][C]167.958333333333[/C][C]1.60479867518601[/C][C]4.69999999999999[/C][/ROW]
[ROW][C]4[/C][C]172.133333333333[/C][C]1.31241161318553[/C][C]4[/C][/ROW]
[ROW][C]5[/C][C]175.591666666667[/C][C]0.792531425626805[/C][C]2.79999999999998[/C][/ROW]
[ROW][C]6[/C][C]179.233333333333[/C][C]1.16489042273069[/C][C]4.09999999999999[/C][/ROW]
[ROW][C]7[/C][C]182.95[/C][C]1.23029929839708[/C][C]4[/C][/ROW]
[ROW][C]8[/C][C]187.55[/C][C]1.26167277129142[/C][C]4.09999999999999[/C][/ROW]
[ROW][C]9[/C][C]192.641666666667[/C][C]2.22729282613071[/C][C]6.30000000000001[/C][/ROW]
[ROW][C]10[/C][C]196.716666666667[/C][C]1.14561085994514[/C][C]3.59999999999999[/C][/ROW]
[ROW][C]11[/C][C]202.366666666667[/C][C]2.04465304162004[/C][C]5.9[/C][/ROW]
[ROW][C]12[/C][C]207.258333333333[/C][C]1.49146562044510[/C][C]4.29999999999998[/C][/ROW]
[ROW][C]13[/C][C]211.35[/C][C]1.29087708026893[/C][C]3.70000000000002[/C][/ROW]
[ROW][C]14[/C][C]215.975[/C][C]1.57545087341543[/C][C]4.40000000000001[/C][/ROW]
[ROW][C]15[/C][C]221.133333333333[/C][C]1.55407577522832[/C][C]4.5[/C][/ROW]
[ROW][C]16[/C][C]226.275[/C][C]1.57718102955875[/C][C]5[/C][/ROW]
[ROW][C]17[/C][C]229.825[/C][C]0.970590260895631[/C][C]3.19999999999999[/C][/ROW]
[ROW][C]18[/C][C]236.991666666667[/C][C]2.62140085149952[/C][C]8.29999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59293&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59293&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
1156.9833333333331.813501551912186
2162.9166666666671.540267587928884.90000000000001
3167.9583333333331.604798675186014.69999999999999
4172.1333333333331.312411613185534
5175.5916666666670.7925314256268052.79999999999998
6179.2333333333331.164890422730694.09999999999999
7182.951.230299298397084
8187.551.261672771291424.09999999999999
9192.6416666666672.227292826130716.30000000000001
10196.7166666666671.145610859945143.59999999999999
11202.3666666666672.044653041620045.9
12207.2583333333331.491465620445104.29999999999998
13211.351.290877080268933.70000000000002
14215.9751.575450873415434.40000000000001
15221.1333333333331.554075775228324.5
16226.2751.577181029558755
17229.8250.9705902608956313.19999999999999
18236.9916666666672.621400851499528.29999999999998






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.652474068308027
beta0.00438885327955577
S.D.0.00447711574728643
T-STAT0.980285864223154
p-value0.341536197888881

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.652474068308027 \tabularnewline
beta & 0.00438885327955577 \tabularnewline
S.D. & 0.00447711574728643 \tabularnewline
T-STAT & 0.980285864223154 \tabularnewline
p-value & 0.341536197888881 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59293&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.652474068308027[/C][/ROW]
[ROW][C]beta[/C][C]0.00438885327955577[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00447711574728643[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.980285864223154[/C][/ROW]
[ROW][C]p-value[/C][C]0.341536197888881[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59293&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59293&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)
alpha0.652474068308027
beta0.00438885327955577
S.D.0.00447711574728643
T-STAT0.980285864223154
p-value0.341536197888881






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.86097976704424
beta0.423996886114892
S.D.0.571125813735332
T-STAT0.742387887078377
p-value0.468612008528257
Lambda0.576003113885108

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.86097976704424 \tabularnewline
beta & 0.423996886114892 \tabularnewline
S.D. & 0.571125813735332 \tabularnewline
T-STAT & 0.742387887078377 \tabularnewline
p-value & 0.468612008528257 \tabularnewline
Lambda & 0.576003113885108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59293&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.86097976704424[/C][/ROW]
[ROW][C]beta[/C][C]0.423996886114892[/C][/ROW]
[ROW][C]S.D.[/C][C]0.571125813735332[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.742387887078377[/C][/ROW]
[ROW][C]p-value[/C][C]0.468612008528257[/C][/ROW]
[ROW][C]Lambda[/C][C]0.576003113885108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59293&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59293&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-1.86097976704424
beta0.423996886114892
S.D.0.571125813735332
T-STAT0.742387887078377
p-value0.468612008528257
Lambda0.576003113885108


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')