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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, 11 Dec 2008 09:24:11 -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/11/t1229012929f2cwj60qtsgfn1o.htm/, Retrieved Fri, 31 May 2024 11:13:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32334, Retrieved Fri, 31 May 2024 11:13:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195

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] [bel20 univariate ...] [2008-12-10 17:19:38] [74be16979710d4c4e7c6647856088456]
- RMPD    [Standard Deviation-Mean Plot] [] [2008-12-11 16:24:11] [759c13c2f2dec2ea2e316204e3fac994] [Current]
-   P       [Standard Deviation-Mean Plot] [] [2008-12-15 20:13:09] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14525.87
14295.79
13830.14
14153.22
15418.03
16666.97
16505.21
17135.96
18033.25
17671
17544.22
17677.9
18470.97
18409.96
18941.6
19685.53
19834.71
19598.93
17039.97
16969.28
16973.38
16329.89
16153.34
15311.7
14760.87
14452.93
13720.95
13266.27
12708.47
13411.84
13975.55
12974.89
12151.11
11576.21
9996.83
10438.9
10511.22
10496.2
10300.79
9981.65
11448.79
11384.49
11717.46
10965.88
10352.27
9751.2
9354.01
8792.5
8721.14
8692.94
8570.73
8538.47
8169.75
7905.84
8145.82
8895.71
9676.31
9884.59
10637.44
10717.13
10205.29
10295.98
10892.76
10631.92
11441.08
11950.95
11037.54
11527.72
11383.89
10989.34
11079.42
11028.93
10973
11068.05
11394.84
11545.71
11809.38
11395.64
11082.38
11402.75
11716.87
12204.98
12986.62
13392.79
14368.05
15650.83
16102.64
16187.64
16311.54
17232.97
16397.83
14990.31
15147.55
15786.78
15934.09
16519.44
16101.07
16775.08
17286.32
17741.23
17128.37
17460.53
17611.14
18001.37
17974.77
16460.95
16235.39
16903.36
15543.76
15532.18
13731.31
13547.84
12602.93
13357.7
13995.33
14084.6
13168.91
12989.35
12123.53
9117.03
8531.45

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=32334&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=32334&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32334&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
114201.255291.173183804187695.730000000001
216431.5425726.6967754331921717.93
317731.5925210.285549253865489.029999999999
418877.015589.0332878256251275.57
518360.72251569.107640271482865.43
616192.0775684.5901494264041661.68
714050.255680.7336966097681494.6
813267.6875553.8663648916891267.08
911040.7625995.256939936452154.28
1010322.465246.601547778328529.57
1111379.155310.979095814065751.58
129562.495657.1941425230961559.77
138630.8289.7328022520195182.67
148279.28427.883072423608989.869999999999
1510228.8675525.7307753578191040.82
1610506.4875316.213587034144687.47
1711489.3225374.614950260041913.41
1811120.395179.489855702209394.549999999999
1911245.4269.674613933162572.709999999999
2011422.5375298.032025837828727
2112575.315755.3173745519171675.92
2215577.29839.8788115357281819.59
2316233.1625926.9224692272462242.66
2415846.965563.5059797671481371.89
2516975.925704.2127481805481640.16
2617550.3525362.053963415676873
2716893.6175772.3233890616461739.38
2814588.77251098.605365099321995.92
2913510.14685.9741407662541481.67
3011849.7051878.082829580924051.88

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14201.255 & 291.173183804187 & 695.730000000001 \tabularnewline
2 & 16431.5425 & 726.696775433192 & 1717.93 \tabularnewline
3 & 17731.5925 & 210.285549253865 & 489.029999999999 \tabularnewline
4 & 18877.015 & 589.033287825625 & 1275.57 \tabularnewline
5 & 18360.7225 & 1569.10764027148 & 2865.43 \tabularnewline
6 & 16192.0775 & 684.590149426404 & 1661.68 \tabularnewline
7 & 14050.255 & 680.733696609768 & 1494.6 \tabularnewline
8 & 13267.6875 & 553.866364891689 & 1267.08 \tabularnewline
9 & 11040.7625 & 995.25693993645 & 2154.28 \tabularnewline
10 & 10322.465 & 246.601547778328 & 529.57 \tabularnewline
11 & 11379.155 & 310.979095814065 & 751.58 \tabularnewline
12 & 9562.495 & 657.194142523096 & 1559.77 \tabularnewline
13 & 8630.82 & 89.7328022520195 & 182.67 \tabularnewline
14 & 8279.28 & 427.883072423608 & 989.869999999999 \tabularnewline
15 & 10228.8675 & 525.730775357819 & 1040.82 \tabularnewline
16 & 10506.4875 & 316.213587034144 & 687.47 \tabularnewline
17 & 11489.3225 & 374.614950260041 & 913.41 \tabularnewline
18 & 11120.395 & 179.489855702209 & 394.549999999999 \tabularnewline
19 & 11245.4 & 269.674613933162 & 572.709999999999 \tabularnewline
20 & 11422.5375 & 298.032025837828 & 727 \tabularnewline
21 & 12575.315 & 755.317374551917 & 1675.92 \tabularnewline
22 & 15577.29 & 839.878811535728 & 1819.59 \tabularnewline
23 & 16233.1625 & 926.922469227246 & 2242.66 \tabularnewline
24 & 15846.965 & 563.505979767148 & 1371.89 \tabularnewline
25 & 16975.925 & 704.212748180548 & 1640.16 \tabularnewline
26 & 17550.3525 & 362.053963415676 & 873 \tabularnewline
27 & 16893.6175 & 772.323389061646 & 1739.38 \tabularnewline
28 & 14588.7725 & 1098.60536509932 & 1995.92 \tabularnewline
29 & 13510.14 & 685.974140766254 & 1481.67 \tabularnewline
30 & 11849.705 & 1878.08282958092 & 4051.88 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32334&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]14201.255[/C][C]291.173183804187[/C][C]695.730000000001[/C][/ROW]
[ROW][C]2[/C][C]16431.5425[/C][C]726.696775433192[/C][C]1717.93[/C][/ROW]
[ROW][C]3[/C][C]17731.5925[/C][C]210.285549253865[/C][C]489.029999999999[/C][/ROW]
[ROW][C]4[/C][C]18877.015[/C][C]589.033287825625[/C][C]1275.57[/C][/ROW]
[ROW][C]5[/C][C]18360.7225[/C][C]1569.10764027148[/C][C]2865.43[/C][/ROW]
[ROW][C]6[/C][C]16192.0775[/C][C]684.590149426404[/C][C]1661.68[/C][/ROW]
[ROW][C]7[/C][C]14050.255[/C][C]680.733696609768[/C][C]1494.6[/C][/ROW]
[ROW][C]8[/C][C]13267.6875[/C][C]553.866364891689[/C][C]1267.08[/C][/ROW]
[ROW][C]9[/C][C]11040.7625[/C][C]995.25693993645[/C][C]2154.28[/C][/ROW]
[ROW][C]10[/C][C]10322.465[/C][C]246.601547778328[/C][C]529.57[/C][/ROW]
[ROW][C]11[/C][C]11379.155[/C][C]310.979095814065[/C][C]751.58[/C][/ROW]
[ROW][C]12[/C][C]9562.495[/C][C]657.194142523096[/C][C]1559.77[/C][/ROW]
[ROW][C]13[/C][C]8630.82[/C][C]89.7328022520195[/C][C]182.67[/C][/ROW]
[ROW][C]14[/C][C]8279.28[/C][C]427.883072423608[/C][C]989.869999999999[/C][/ROW]
[ROW][C]15[/C][C]10228.8675[/C][C]525.730775357819[/C][C]1040.82[/C][/ROW]
[ROW][C]16[/C][C]10506.4875[/C][C]316.213587034144[/C][C]687.47[/C][/ROW]
[ROW][C]17[/C][C]11489.3225[/C][C]374.614950260041[/C][C]913.41[/C][/ROW]
[ROW][C]18[/C][C]11120.395[/C][C]179.489855702209[/C][C]394.549999999999[/C][/ROW]
[ROW][C]19[/C][C]11245.4[/C][C]269.674613933162[/C][C]572.709999999999[/C][/ROW]
[ROW][C]20[/C][C]11422.5375[/C][C]298.032025837828[/C][C]727[/C][/ROW]
[ROW][C]21[/C][C]12575.315[/C][C]755.317374551917[/C][C]1675.92[/C][/ROW]
[ROW][C]22[/C][C]15577.29[/C][C]839.878811535728[/C][C]1819.59[/C][/ROW]
[ROW][C]23[/C][C]16233.1625[/C][C]926.922469227246[/C][C]2242.66[/C][/ROW]
[ROW][C]24[/C][C]15846.965[/C][C]563.505979767148[/C][C]1371.89[/C][/ROW]
[ROW][C]25[/C][C]16975.925[/C][C]704.212748180548[/C][C]1640.16[/C][/ROW]
[ROW][C]26[/C][C]17550.3525[/C][C]362.053963415676[/C][C]873[/C][/ROW]
[ROW][C]27[/C][C]16893.6175[/C][C]772.323389061646[/C][C]1739.38[/C][/ROW]
[ROW][C]28[/C][C]14588.7725[/C][C]1098.60536509932[/C][C]1995.92[/C][/ROW]
[ROW][C]29[/C][C]13510.14[/C][C]685.974140766254[/C][C]1481.67[/C][/ROW]
[ROW][C]30[/C][C]11849.705[/C][C]1878.08282958092[/C][C]4051.88[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32334&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32334&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
114201.255291.173183804187695.730000000001
216431.5425726.6967754331921717.93
317731.5925210.285549253865489.029999999999
418877.015589.0332878256251275.57
518360.72251569.107640271482865.43
616192.0775684.5901494264041661.68
714050.255680.7336966097681494.6
813267.6875553.8663648916891267.08
911040.7625995.256939936452154.28
1010322.465246.601547778328529.57
1111379.155310.979095814065751.58
129562.495657.1941425230961559.77
138630.8289.7328022520195182.67
148279.28427.883072423608989.869999999999
1510228.8675525.7307753578191040.82
1610506.4875316.213587034144687.47
1711489.3225374.614950260041913.41
1811120.395179.489855702209394.549999999999
1911245.4269.674613933162572.709999999999
2011422.5375298.032025837828727
2112575.315755.3173745519171675.92
2215577.29839.8788115357281819.59
2316233.1625926.9224692272462242.66
2415846.965563.5059797671481371.89
2516975.925704.2127481805481640.16
2617550.3525362.053963415676873
2716893.6175772.3233890616461739.38
2814588.77251098.605365099321995.92
2913510.14685.9741407662541481.67
3011849.7051878.082829580924051.88






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha86.0428819163148
beta0.0394206687430238
S.D.0.0231522226594582
T-STAT1.7026731870566
p-value0.0997073613325273

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 86.0428819163148 \tabularnewline
beta & 0.0394206687430238 \tabularnewline
S.D. & 0.0231522226594582 \tabularnewline
T-STAT & 1.7026731870566 \tabularnewline
p-value & 0.0997073613325273 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32334&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]86.0428819163148[/C][/ROW]
[ROW][C]beta[/C][C]0.0394206687430238[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0231522226594582[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.7026731870566[/C][/ROW]
[ROW][C]p-value[/C][C]0.0997073613325273[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32334&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32334&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)
alpha86.0428819163148
beta0.0394206687430238
S.D.0.0231522226594582
T-STAT1.7026731870566
p-value0.0997073613325273






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.04390279114832
beta1.18885266258656
S.D.0.484721077497703
T-STAT2.45265311903461
p-value0.0206713470853176
Lambda-0.188852662586557

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.04390279114832 \tabularnewline
beta & 1.18885266258656 \tabularnewline
S.D. & 0.484721077497703 \tabularnewline
T-STAT & 2.45265311903461 \tabularnewline
p-value & 0.0206713470853176 \tabularnewline
Lambda & -0.188852662586557 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32334&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.04390279114832[/C][/ROW]
[ROW][C]beta[/C][C]1.18885266258656[/C][/ROW]
[ROW][C]S.D.[/C][C]0.484721077497703[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.45265311903461[/C][/ROW]
[ROW][C]p-value[/C][C]0.0206713470853176[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.188852662586557[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32334&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32334&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-5.04390279114832
beta1.18885266258656
S.D.0.484721077497703
T-STAT2.45265311903461
p-value0.0206713470853176
Lambda-0.188852662586557


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')