FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationFri, 23 Nov 2007 08:36:17 -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/2007/Nov/23/t1195831677o2ltqnke28euidg.htm/, Retrieved Mon, 29 Apr 2024 03:21:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6195, Retrieved Mon, 29 Apr 2024 03:21:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact168

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] [Workshop7-q1b] [2007-11-23 15:36:17] [129742d52914620af0bad7eb53591257] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
102,86
102,12
100,74
100,96
101,01
100,41
100,35
99,33
98,66
98,69
98,61
96,41
96,3
96,12
97,32
101,78
102,28
101,12
104,55
107,4
108,41
109,43
110,34
115,06
113,13
116,56
121,39
119,12
123,31
128,57
127,71
125,68
133,8
130,97
129,99
124
118,63
121,86
119,97
125,03
130,09
126,65
121,7
119,24
122,63
116,66
114,12
113,11
112,61
113,4
115,18
121,01
119,44
116,68
117,07
117,41
119,58
120,92
117,09
116,77
119,39
122,49
124,08
118,29
112,94
113,79
114,43
118,7
120,36
118,27
118,34
117,82
117,65
118,18
121,02
124,78
131,16
130,14
131,75
134,73
135,35
140,32
136,35
131,6
128,9
133,89
138,25
146,23
144,76
149,3
156,8
159,08
165,12
163,14
153,43
151,01

Tables (Output of Computation)





Summary of compuational 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 compuational 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=6195&T=0

[TABLE]
[ROW][C]Summary of compuational 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=6195&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6195&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 compuational 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
1100.01251.764107423032966.56
2104.1758333333336.068785198693318.94
3124.5191666666676.1743685114472736.48
4120.80754.9765890564083829.13
5117.2633333333332.6816763187953720
6118.2416666666673.3138136046043123.67
7129.4191666666677.39092374388239.97
8149.15916666666711.358723086311965.79

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100.0125 & 1.76410742303296 & 6.56 \tabularnewline
2 & 104.175833333333 & 6.0687851986933 & 18.94 \tabularnewline
3 & 124.519166666667 & 6.17436851144727 & 36.48 \tabularnewline
4 & 120.8075 & 4.97658905640838 & 29.13 \tabularnewline
5 & 117.263333333333 & 2.68167631879537 & 20 \tabularnewline
6 & 118.241666666667 & 3.31381360460431 & 23.67 \tabularnewline
7 & 129.419166666667 & 7.390923743882 & 39.97 \tabularnewline
8 & 149.159166666667 & 11.3587230863119 & 65.79 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6195&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]100.0125[/C][C]1.76410742303296[/C][C]6.56[/C][/ROW]
[ROW][C]2[/C][C]104.175833333333[/C][C]6.0687851986933[/C][C]18.94[/C][/ROW]
[ROW][C]3[/C][C]124.519166666667[/C][C]6.17436851144727[/C][C]36.48[/C][/ROW]
[ROW][C]4[/C][C]120.8075[/C][C]4.97658905640838[/C][C]29.13[/C][/ROW]
[ROW][C]5[/C][C]117.263333333333[/C][C]2.68167631879537[/C][C]20[/C][/ROW]
[ROW][C]6[/C][C]118.241666666667[/C][C]3.31381360460431[/C][C]23.67[/C][/ROW]
[ROW][C]7[/C][C]129.419166666667[/C][C]7.390923743882[/C][C]39.97[/C][/ROW]
[ROW][C]8[/C][C]149.159166666667[/C][C]11.3587230863119[/C][C]65.79[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6195&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6195&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
1100.01251.764107423032966.56
2104.1758333333336.068785198693318.94
3124.5191666666676.1743685114472736.48
4120.80754.9765890564083829.13
5117.2633333333332.6816763187953720
6118.2416666666673.3138136046043123.67
7129.4191666666677.39092374388239.97
8149.15916666666711.358723086311965.79






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-14.5196168615559
beta0.165925901181809
S.D.0.0465535077285862
T-STAT3.56419761426318
p-value0.0118669103034895

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -14.5196168615559 \tabularnewline
beta & 0.165925901181809 \tabularnewline
S.D. & 0.0465535077285862 \tabularnewline
T-STAT & 3.56419761426318 \tabularnewline
p-value & 0.0118669103034895 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6195&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-14.5196168615559[/C][/ROW]
[ROW][C]beta[/C][C]0.165925901181809[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0465535077285862[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.56419761426318[/C][/ROW]
[ROW][C]p-value[/C][C]0.0118669103034895[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6195&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6195&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-14.5196168615559
beta0.165925901181809
S.D.0.0465535077285862
T-STAT3.56419761426318
p-value0.0118669103034895






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-15.9958202498409
beta3.66757299484052
S.D.1.28135812241849
T-STAT2.86225445538847
p-value0.0287167769530344
Lambda-2.66757299484052

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -15.9958202498409 \tabularnewline
beta & 3.66757299484052 \tabularnewline
S.D. & 1.28135812241849 \tabularnewline
T-STAT & 2.86225445538847 \tabularnewline
p-value & 0.0287167769530344 \tabularnewline
Lambda & -2.66757299484052 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6195&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-15.9958202498409[/C][/ROW]
[ROW][C]beta[/C][C]3.66757299484052[/C][/ROW]
[ROW][C]S.D.[/C][C]1.28135812241849[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.86225445538847[/C][/ROW]
[ROW][C]p-value[/C][C]0.0287167769530344[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.66757299484052[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6195&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6195&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-15.9958202498409
beta3.66757299484052
S.D.1.28135812241849
T-STAT2.86225445538847
p-value0.0287167769530344
Lambda-2.66757299484052


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')