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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, 14 Dec 2008 11:07:34 -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/2008/Dec/14/t1229278132ns82v73gnkdnfwd.htm/, Retrieved Thu, 16 May 2024 00:11:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33516, Retrieved Thu, 16 May 2024 00:11:52 +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)
-     [Univariate Data Series] [Industriele produ...] [2008-12-14 16:49:51] [b82ef11dce0545f3fd4676ec3ebed828]
- RMP   [Central Tendency] [Central Tendency ...] [2008-12-14 17:03:16] [b82ef11dce0545f3fd4676ec3ebed828]
- RM      [Percentiles] [Percentiles - - ...] [2008-12-14 17:08:17] [b82ef11dce0545f3fd4676ec3ebed828]
- RM        [Tukey lambda PPCC Plot] [Tukey lambda PPCC...] [2008-12-14 17:26:43] [b82ef11dce0545f3fd4676ec3ebed828]
- RMP         [Blocked Bootstrap Plot - Central Tendency] [Blocked bootstrap...] [2008-12-14 17:29:20] [b82ef11dce0545f3fd4676ec3ebed828]
- RMP           [Harrell-Davis Quantiles] [Harrell-Davis Qua...] [2008-12-14 17:35:42] [b82ef11dce0545f3fd4676ec3ebed828]
- RMP             [Univariate Explorative Data Analysis] [Univariate EDA -...] [2008-12-14 17:39:39] [b82ef11dce0545f3fd4676ec3ebed828]
- RMP               [Mean Plot] [Mean plot - Indus...] [2008-12-14 17:56:47] [b82ef11dce0545f3fd4676ec3ebed828]
- RM                  [Variance Reduction Matrix] [VRM - Industriele...] [2008-12-14 18:03:27] [b82ef11dce0545f3fd4676ec3ebed828]
- RM                      [Standard Deviation-Mean Plot] [SDMP - Industriel...] [2008-12-14 18:07:34] [4b953869c7238aca4b6e0cfb0c5cddd6] [Current]
- RM                        [(Partial) Autocorrelation Function] [(Partial) ACF - ...] [2008-12-14 18:14:08] [b82ef11dce0545f3fd4676ec3ebed828]
- RM                          [Spectral Analysis] [Spectrum - Indust...] [2008-12-14 18:16:42] [b82ef11dce0545f3fd4676ec3ebed828]
- RM                            [ARIMA Backward Selection] [ARIMA Backward Se...] [2008-12-14 18:25:02] [b82ef11dce0545f3fd4676ec3ebed828]
- RM                              [ARIMA Forecasting] [ARIMA Forecasting...] [2008-12-14 18:33:23] [b82ef11dce0545f3fd4676ec3ebed828]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97.4
97
105.4
102.7
98.1
104.5
87.4
89.9
109.8
111.7
98.6
96.9
95.1
97
112.7
102.9
97.4
111.4
87.4
96.8
114.1
110.3
103.9
101.6
94.6
95.9
104.7
102.8
98.1
113.9
80.9
95.7
113.2
105.9
108.8
102.3
99
100.7
115.5
100.7
109.9
114.6
85.4
100.5
114.8
116.5
112.9
102
106
105.3
118.8
106.1
109.3
117.2
92.5
104.2
112.5
122.4
113.3
100
110.7
112.8
109.8
117.3
109.1
115.9
96
99.8
117

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=33516&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=33516&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33516&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
199.957.2695504425214424.3
2102.558.2741107734250926.7
3101.49.1665399440276633
4106.0416666666679.4891764498806631.1
5108.9666666666678.4264015109797929.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 99.95 & 7.26955044252144 & 24.3 \tabularnewline
2 & 102.55 & 8.27411077342509 & 26.7 \tabularnewline
3 & 101.4 & 9.16653994402766 & 33 \tabularnewline
4 & 106.041666666667 & 9.48917644988066 & 31.1 \tabularnewline
5 & 108.966666666667 & 8.42640151097979 & 29.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33516&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]99.95[/C][C]7.26955044252144[/C][C]24.3[/C][/ROW]
[ROW][C]2[/C][C]102.55[/C][C]8.27411077342509[/C][C]26.7[/C][/ROW]
[ROW][C]3[/C][C]101.4[/C][C]9.16653994402766[/C][C]33[/C][/ROW]
[ROW][C]4[/C][C]106.041666666667[/C][C]9.48917644988066[/C][C]31.1[/C][/ROW]
[ROW][C]5[/C][C]108.966666666667[/C][C]8.42640151097979[/C][C]29.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33516&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33516&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
199.957.2695504425214424.3
2102.558.2741107734250926.7
3101.49.1665399440276633
4106.0416666666679.4891764498806631.1
5108.9666666666678.4264015109797929.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.60843366685685
beta0.097643348931479
S.D.0.123797838387940
T-STAT0.788732260619112
p-value0.487853165292207

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.60843366685685 \tabularnewline
beta & 0.097643348931479 \tabularnewline
S.D. & 0.123797838387940 \tabularnewline
T-STAT & 0.788732260619112 \tabularnewline
p-value & 0.487853165292207 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33516&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.60843366685685[/C][/ROW]
[ROW][C]beta[/C][C]0.097643348931479[/C][/ROW]
[ROW][C]S.D.[/C][C]0.123797838387940[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.788732260619112[/C][/ROW]
[ROW][C]p-value[/C][C]0.487853165292207[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33516&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33516&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-1.60843366685685
beta0.097643348931479
S.D.0.123797838387940
T-STAT0.788732260619112
p-value0.487853165292207






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.87535127649888
beta1.29564848100560
S.D.1.53240951828272
T-STAT0.845497541973999
p-value0.459934249914382
Lambda-0.295648481005603

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.87535127649888 \tabularnewline
beta & 1.29564848100560 \tabularnewline
S.D. & 1.53240951828272 \tabularnewline
T-STAT & 0.845497541973999 \tabularnewline
p-value & 0.459934249914382 \tabularnewline
Lambda & -0.295648481005603 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33516&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.87535127649888[/C][/ROW]
[ROW][C]beta[/C][C]1.29564848100560[/C][/ROW]
[ROW][C]S.D.[/C][C]1.53240951828272[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.845497541973999[/C][/ROW]
[ROW][C]p-value[/C][C]0.459934249914382[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.295648481005603[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33516&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33516&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-3.87535127649888
beta1.29564848100560
S.D.1.53240951828272
T-STAT0.845497541973999
p-value0.459934249914382
Lambda-0.295648481005603


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')