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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 computationThu, 11 Dec 2008 07:40:37 -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/t1229006867z5u2oyzcy3az2id.htm/, Retrieved Sat, 25 May 2024 20:27:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32277, Retrieved Sat, 25 May 2024 20:27:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153

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] [Standard Deviatio...] [2008-12-11 14:40:37] [6aa66640011d9b98524a5838bcf7301d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
85,0
95,9
108,9
96,2
100,1
105,7
64,5
66,8
110,3
96,1
102,5
97,6
83,6
86,5
96,0
91,1
87,2
84,5
59,2
61,5
98,8
97,9
92,7
84,2
74,5
79,7
86,8
79,8
87,0
91,4
58,7
62,8
87,9
90,4
80,6
73,5
71,4
70,6
78,3
76,0
77,4
80,9
63,4
58,1
88,2
81,2
84,9
76,4
71,5
76,1
82,9
78,0
82,0
84,7
55,7
59,5
83,2
87,6
76,2
76,4
68,3
70,0
76,3
70,9
72,4
80,1
57,4
62,7
82,6
88,9
80,4
72,0
69,4
69,2
77,3
79,4
78,6
76,1
61,8
59,4
78,1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32277&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32277&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32277&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
194.133333333333314.926324112625745.8
285.266666666666712.796756217767439.6
379.42510.506805154063532.7
475.56666666666678.6009865537024130.1
576.159.7897441697467731.9
673.58.7611746825515331.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 94.1333333333333 & 14.9263241126257 & 45.8 \tabularnewline
2 & 85.2666666666667 & 12.7967562177674 & 39.6 \tabularnewline
3 & 79.425 & 10.5068051540635 & 32.7 \tabularnewline
4 & 75.5666666666667 & 8.60098655370241 & 30.1 \tabularnewline
5 & 76.15 & 9.78974416974677 & 31.9 \tabularnewline
6 & 73.5 & 8.76117468255153 & 31.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32277&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]94.1333333333333[/C][C]14.9263241126257[/C][C]45.8[/C][/ROW]
[ROW][C]2[/C][C]85.2666666666667[/C][C]12.7967562177674[/C][C]39.6[/C][/ROW]
[ROW][C]3[/C][C]79.425[/C][C]10.5068051540635[/C][C]32.7[/C][/ROW]
[ROW][C]4[/C][C]75.5666666666667[/C][C]8.60098655370241[/C][C]30.1[/C][/ROW]
[ROW][C]5[/C][C]76.15[/C][C]9.78974416974677[/C][C]31.9[/C][/ROW]
[ROW][C]6[/C][C]73.5[/C][C]8.76117468255153[/C][C]31.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32277&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32277&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
194.133333333333314.926324112625745.8
285.266666666666712.796756217767439.6
379.42510.506805154063532.7
475.56666666666678.6009865537024130.1
576.159.7897441697467731.9
673.58.7611746825515331.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-14.6295986357802
beta0.316417765767696
S.D.0.0263389046381222
T-STAT12.0133228816859
p-value0.000275231854228124

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -14.6295986357802 \tabularnewline
beta & 0.316417765767696 \tabularnewline
S.D. & 0.0263389046381222 \tabularnewline
T-STAT & 12.0133228816859 \tabularnewline
p-value & 0.000275231854228124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32277&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-14.6295986357802[/C][/ROW]
[ROW][C]beta[/C][C]0.316417765767696[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0263389046381222[/C][/ROW]
[ROW][C]T-STAT[/C][C]12.0133228816859[/C][/ROW]
[ROW][C]p-value[/C][C]0.000275231854228124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32277&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32277&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-14.6295986357802
beta0.316417765767696
S.D.0.0263389046381222
T-STAT12.0133228816859
p-value0.000275231854228124






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-7.71230029392368
beta2.29790888941854
S.D.0.239838867293882
T-STAT9.58105296003938
p-value0.000663129420112621
Lambda-1.29790888941854

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -7.71230029392368 \tabularnewline
beta & 2.29790888941854 \tabularnewline
S.D. & 0.239838867293882 \tabularnewline
T-STAT & 9.58105296003938 \tabularnewline
p-value & 0.000663129420112621 \tabularnewline
Lambda & -1.29790888941854 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32277&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.71230029392368[/C][/ROW]
[ROW][C]beta[/C][C]2.29790888941854[/C][/ROW]
[ROW][C]S.D.[/C][C]0.239838867293882[/C][/ROW]
[ROW][C]T-STAT[/C][C]9.58105296003938[/C][/ROW]
[ROW][C]p-value[/C][C]0.000663129420112621[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.29790888941854[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32277&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32277&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-7.71230029392368
beta2.29790888941854
S.D.0.239838867293882
T-STAT9.58105296003938
p-value0.000663129420112621
Lambda-1.29790888941854


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')