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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 computationMon, 28 Dec 2009 12:01:56 -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/Dec/28/t12620273637nsegvcsx3fhcph.htm/, Retrieved Sat, 04 May 2024 21:49:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71037, Retrieved Sat, 04 May 2024 21:49:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136

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] [VRM Olie] [2008-12-19 13:50:37] [7458e879e85b911182071700fff19fbd]
- RM D  [Variance Reduction Matrix] [] [2009-12-28 18:04:03] [a171cf7519360d15de770637ace99f7a]
- RM        [Standard Deviation-Mean Plot] [] [2009-12-28 19:01:56] [8dc3430f82ac55eb052bda9ec3452bd3] [Current]
-    D        [Standard Deviation-Mean Plot] [] [2009-12-31 08:27:55] [74be16979710d4c4e7c6647856088456]
-    D        [Standard Deviation-Mean Plot] [] [2009-12-31 08:30:19] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
40.22
44.23
45.85
53.38
53.26
51.8
55.3
57.81
63.96
63.77
59.15
56.12
57.42
63.52
61.71
63.01
68.18
72.03
69.75
74.41
74.33
64.24
60.03
59.44
62.5
55.04
58.34
61.92
67.65
67.68
70.3
75.26
71.44
76.36
81.71
92.6
90.6
92.23
94.09
102.79
109.65
124.05
132.69
135.81
116.07
101.42
75.73
55.48
43.8
45.29
44.01
47.48
51.07
57.84
69.04
65.61
72.87
68.41
73.25
77.43

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' @ 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71037&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71037&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71037&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' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
145.925.5076492263033613.16
254.54252.608733728586866.01
360.753.804444768951187.84
461.4152.770204565250256.1
571.09252.718435518210186.22999999999999
664.516.8867166826192814.89
759.453.468121489605967.46
870.22253.580711056014817.61
980.52759.0755032000067821.16
1094.92755.4321289564957912.19
11125.5511.709073404842926.16
1287.17526.915931465707660.59
1345.1451.690216948599603.68
1460.898.0505859000033917.97
1572.993.686552138064339.02000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 45.92 & 5.50764922630336 & 13.16 \tabularnewline
2 & 54.5425 & 2.60873372858686 & 6.01 \tabularnewline
3 & 60.75 & 3.80444476895118 & 7.84 \tabularnewline
4 & 61.415 & 2.77020456525025 & 6.1 \tabularnewline
5 & 71.0925 & 2.71843551821018 & 6.22999999999999 \tabularnewline
6 & 64.51 & 6.88671668261928 & 14.89 \tabularnewline
7 & 59.45 & 3.46812148960596 & 7.46 \tabularnewline
8 & 70.2225 & 3.58071105601481 & 7.61 \tabularnewline
9 & 80.5275 & 9.07550320000678 & 21.16 \tabularnewline
10 & 94.9275 & 5.43212895649579 & 12.19 \tabularnewline
11 & 125.55 & 11.7090734048429 & 26.16 \tabularnewline
12 & 87.175 & 26.9159314657076 & 60.59 \tabularnewline
13 & 45.145 & 1.69021694859960 & 3.68 \tabularnewline
14 & 60.89 & 8.05058590000339 & 17.97 \tabularnewline
15 & 72.99 & 3.68655213806433 & 9.02000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71037&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]45.92[/C][C]5.50764922630336[/C][C]13.16[/C][/ROW]
[ROW][C]2[/C][C]54.5425[/C][C]2.60873372858686[/C][C]6.01[/C][/ROW]
[ROW][C]3[/C][C]60.75[/C][C]3.80444476895118[/C][C]7.84[/C][/ROW]
[ROW][C]4[/C][C]61.415[/C][C]2.77020456525025[/C][C]6.1[/C][/ROW]
[ROW][C]5[/C][C]71.0925[/C][C]2.71843551821018[/C][C]6.22999999999999[/C][/ROW]
[ROW][C]6[/C][C]64.51[/C][C]6.88671668261928[/C][C]14.89[/C][/ROW]
[ROW][C]7[/C][C]59.45[/C][C]3.46812148960596[/C][C]7.46[/C][/ROW]
[ROW][C]8[/C][C]70.2225[/C][C]3.58071105601481[/C][C]7.61[/C][/ROW]
[ROW][C]9[/C][C]80.5275[/C][C]9.07550320000678[/C][C]21.16[/C][/ROW]
[ROW][C]10[/C][C]94.9275[/C][C]5.43212895649579[/C][C]12.19[/C][/ROW]
[ROW][C]11[/C][C]125.55[/C][C]11.7090734048429[/C][C]26.16[/C][/ROW]
[ROW][C]12[/C][C]87.175[/C][C]26.9159314657076[/C][C]60.59[/C][/ROW]
[ROW][C]13[/C][C]45.145[/C][C]1.69021694859960[/C][C]3.68[/C][/ROW]
[ROW][C]14[/C][C]60.89[/C][C]8.05058590000339[/C][C]17.97[/C][/ROW]
[ROW][C]15[/C][C]72.99[/C][C]3.68655213806433[/C][C]9.02000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71037&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71037&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
145.925.5076492263033613.16
254.54252.608733728586866.01
360.753.804444768951187.84
461.4152.770204565250256.1
571.09252.718435518210186.22999999999999
664.516.8867166826192814.89
759.453.468121489605967.46
870.22253.580711056014817.61
980.52759.0755032000067821.16
1094.92755.4321289564957912.19
11125.5511.709073404842926.16
1287.17526.915931465707660.59
1345.1451.690216948599603.68
1460.898.0505859000033917.97
1572.993.686552138064339.02000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.16852342187864
beta0.152053568359093
S.D.0.0734978731877608
T-STAT2.06881589581035
p-value0.0590559887484758

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.16852342187864 \tabularnewline
beta & 0.152053568359093 \tabularnewline
S.D. & 0.0734978731877608 \tabularnewline
T-STAT & 2.06881589581035 \tabularnewline
p-value & 0.0590559887484758 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71037&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.16852342187864[/C][/ROW]
[ROW][C]beta[/C][C]0.152053568359093[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0734978731877608[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.06881589581035[/C][/ROW]
[ROW][C]p-value[/C][C]0.0590559887484758[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71037&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71037&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-4.16852342187864
beta0.152053568359093
S.D.0.0734978731877608
T-STAT2.06881589581035
p-value0.0590559887484758






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.18632250285239
beta1.60946461098981
S.D.0.576131480071302
T-STAT2.79357172218853
p-value0.0152157759795984
Lambda-0.609464610989813

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.18632250285239 \tabularnewline
beta & 1.60946461098981 \tabularnewline
S.D. & 0.576131480071302 \tabularnewline
T-STAT & 2.79357172218853 \tabularnewline
p-value & 0.0152157759795984 \tabularnewline
Lambda & -0.609464610989813 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71037&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.18632250285239[/C][/ROW]
[ROW][C]beta[/C][C]1.60946461098981[/C][/ROW]
[ROW][C]S.D.[/C][C]0.576131480071302[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.79357172218853[/C][/ROW]
[ROW][C]p-value[/C][C]0.0152157759795984[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.609464610989813[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71037&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71037&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-5.18632250285239
beta1.60946461098981
S.D.0.576131480071302
T-STAT2.79357172218853
p-value0.0152157759795984
Lambda-0.609464610989813


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
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')