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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 computationWed, 08 Dec 2010 07:49:25 +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/08/t1291794563gl0zyjlfo9ibps1.htm/, Retrieved Fri, 03 May 2024 09:11:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106828, Retrieved Fri, 03 May 2024 09:11:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact147

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [] [2010-12-08 07:49:25] [c5046d1373369fc44166204bdcb551c5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
132
131.4
132.7
130.9
126
109.7
68.3
70.6
75.3
74.1
74.9
74
74.2
76
76.2
74.9
74.1
76.5
57.8
59.2
57.3
57.5
60.4
59.9
59.9
60
60.2
65.4
62.4
78.8
65.6
64.4
67.4
65.3
66.7
66.8
69.4
71.7
77.1
81.1
82.1
92.1
77.1
78.2
77.7
77.3
78.5
78.8
78.7
79.8
82.2
84
81.7
77.6
64.3
72.6
73.8
73.8
70.1
70
72.3
72.1
73.3
79.1
77
76.1
66.4
72.7
73.2
70.7
73.6
74.2
72.6
73.6
79.1
79.6
78
85.4
82
91.9
89.4
92.1
93.8
93.6
95.6
99.9
103.7
99.2
93.7
93.5
80.7
91.8
105.8
111.3
110.3
109.4
111.4
111.6
111.8
106.6
104.3
105.5
98.5
108.5
106
101.8
101.3
92.4
88.9
84.9
86.4
90.7
86.8
90.6
88.3
95.4
93.6
91.3
91.3
89.3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time10 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 & 10 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106828&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]10 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=106828&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106828&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 time10 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
199.991666666666729.014587501441264.4
2678.7611746825515319.2
365.24166666666675.0758713239176718.9
478.4255.5583066420693922.7
575.71666666666675.9329332517479919.7
673.39166666666673.2072243262341112.7
784.25833333333337.7929406671951721.2
899.5759.0903670292938530.6
9104.9755.817235363360119.4
1089.79166666666673.0095177304174410.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 99.9916666666667 & 29.0145875014412 & 64.4 \tabularnewline
2 & 67 & 8.76117468255153 & 19.2 \tabularnewline
3 & 65.2416666666667 & 5.07587132391767 & 18.9 \tabularnewline
4 & 78.425 & 5.55830664206939 & 22.7 \tabularnewline
5 & 75.7166666666667 & 5.93293325174799 & 19.7 \tabularnewline
6 & 73.3916666666667 & 3.20722432623411 & 12.7 \tabularnewline
7 & 84.2583333333333 & 7.79294066719517 & 21.2 \tabularnewline
8 & 99.575 & 9.09036702929385 & 30.6 \tabularnewline
9 & 104.975 & 5.8172353633601 & 19.4 \tabularnewline
10 & 89.7916666666667 & 3.00951773041744 & 10.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106828&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]99.9916666666667[/C][C]29.0145875014412[/C][C]64.4[/C][/ROW]
[ROW][C]2[/C][C]67[/C][C]8.76117468255153[/C][C]19.2[/C][/ROW]
[ROW][C]3[/C][C]65.2416666666667[/C][C]5.07587132391767[/C][C]18.9[/C][/ROW]
[ROW][C]4[/C][C]78.425[/C][C]5.55830664206939[/C][C]22.7[/C][/ROW]
[ROW][C]5[/C][C]75.7166666666667[/C][C]5.93293325174799[/C][C]19.7[/C][/ROW]
[ROW][C]6[/C][C]73.3916666666667[/C][C]3.20722432623411[/C][C]12.7[/C][/ROW]
[ROW][C]7[/C][C]84.2583333333333[/C][C]7.79294066719517[/C][C]21.2[/C][/ROW]
[ROW][C]8[/C][C]99.575[/C][C]9.09036702929385[/C][C]30.6[/C][/ROW]
[ROW][C]9[/C][C]104.975[/C][C]5.8172353633601[/C][C]19.4[/C][/ROW]
[ROW][C]10[/C][C]89.7916666666667[/C][C]3.00951773041744[/C][C]10.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106828&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106828&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
199.991666666666729.014587501441264.4
2678.7611746825515319.2
365.24166666666675.0758713239176718.9
478.4255.5583066420693922.7
575.71666666666675.9329332517479919.7
673.39166666666673.2072243262341112.7
784.25833333333337.7929406671951721.2
899.5759.0903670292938530.6
9104.9755.817235363360119.4
1089.79166666666673.0095177304174410.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-10.1587477426315
beta0.220485431129431
S.D.0.170644768598085
T-STAT1.29207260756252
p-value0.232404136248548

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -10.1587477426315 \tabularnewline
beta & 0.220485431129431 \tabularnewline
S.D. & 0.170644768598085 \tabularnewline
T-STAT & 1.29207260756252 \tabularnewline
p-value & 0.232404136248548 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106828&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.1587477426315[/C][/ROW]
[ROW][C]beta[/C][C]0.220485431129431[/C][/ROW]
[ROW][C]S.D.[/C][C]0.170644768598085[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.29207260756252[/C][/ROW]
[ROW][C]p-value[/C][C]0.232404136248548[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106828&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106828&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-10.1587477426315
beta0.220485431129431
S.D.0.170644768598085
T-STAT1.29207260756252
p-value0.232404136248548






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.1573182878326
beta1.37050844964507
S.D.1.23609704668138
T-STAT1.10873855198065
p-value0.299758831310430
Lambda-0.370508449645065

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.1573182878326 \tabularnewline
beta & 1.37050844964507 \tabularnewline
S.D. & 1.23609704668138 \tabularnewline
T-STAT & 1.10873855198065 \tabularnewline
p-value & 0.299758831310430 \tabularnewline
Lambda & -0.370508449645065 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106828&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.1573182878326[/C][/ROW]
[ROW][C]beta[/C][C]1.37050844964507[/C][/ROW]
[ROW][C]S.D.[/C][C]1.23609704668138[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.10873855198065[/C][/ROW]
[ROW][C]p-value[/C][C]0.299758831310430[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.370508449645065[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106828&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106828&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-4.1573182878326
beta1.37050844964507
S.D.1.23609704668138
T-STAT1.10873855198065
p-value0.299758831310430
Lambda-0.370508449645065


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')