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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 computationTue, 14 Dec 2010 12:52:59 +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/14/t1292331214fwrgsjf54b7fw9q.htm/, Retrieved Thu, 02 May 2024 18:54:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109535, Retrieved Thu, 02 May 2024 18:54:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118

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] [] [2010-12-14 12:52:59] [4c4b6062b5416bf30d160a3ba34752af] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3

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'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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109535&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109535&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109535&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
147.333333333333333.4944590623403129
270.666666666666728.2949829582218101
367.083333333333318.613085979948966
476.083333333333319.009367706635163
557.2530.334873420776798
617.41666666666675.4848275573014419

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 47.3333333333333 & 33.4944590623403 & 129 \tabularnewline
2 & 70.6666666666667 & 28.2949829582218 & 101 \tabularnewline
3 & 67.0833333333333 & 18.6130859799489 & 66 \tabularnewline
4 & 76.0833333333333 & 19.0093677066351 & 63 \tabularnewline
5 & 57.25 & 30.3348734207767 & 98 \tabularnewline
6 & 17.4166666666667 & 5.48482755730144 & 19 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109535&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]47.3333333333333[/C][C]33.4944590623403[/C][C]129[/C][/ROW]
[ROW][C]2[/C][C]70.6666666666667[/C][C]28.2949829582218[/C][C]101[/C][/ROW]
[ROW][C]3[/C][C]67.0833333333333[/C][C]18.6130859799489[/C][C]66[/C][/ROW]
[ROW][C]4[/C][C]76.0833333333333[/C][C]19.0093677066351[/C][C]63[/C][/ROW]
[ROW][C]5[/C][C]57.25[/C][C]30.3348734207767[/C][C]98[/C][/ROW]
[ROW][C]6[/C][C]17.4166666666667[/C][C]5.48482755730144[/C][C]19[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109535&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109535&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
147.333333333333333.4944590623403129
270.666666666666728.2949829582218101
367.083333333333318.613085979948966
476.083333333333319.009367706635163
557.2530.334873420776798
617.41666666666675.4848275573014419






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha9.36650762431036
beta0.235332657883956
S.D.0.209485818516902
T-STAT1.12338228692540
p-value0.324137525698743

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.36650762431036 \tabularnewline
beta & 0.235332657883956 \tabularnewline
S.D. & 0.209485818516902 \tabularnewline
T-STAT & 1.12338228692540 \tabularnewline
p-value & 0.324137525698743 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109535&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.36650762431036[/C][/ROW]
[ROW][C]beta[/C][C]0.235332657883956[/C][/ROW]
[ROW][C]S.D.[/C][C]0.209485818516902[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.12338228692540[/C][/ROW]
[ROW][C]p-value[/C][C]0.324137525698743[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109535&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109535&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)
alpha9.36650762431036
beta0.235332657883956
S.D.0.209485818516902
T-STAT1.12338228692540
p-value0.324137525698743






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.843195233190265
beta0.971920456947214
S.D.0.365074564135338
T-STAT2.66225191352118
p-value0.0562581517107556
Lambda0.0280795430527858

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.843195233190265 \tabularnewline
beta & 0.971920456947214 \tabularnewline
S.D. & 0.365074564135338 \tabularnewline
T-STAT & 2.66225191352118 \tabularnewline
p-value & 0.0562581517107556 \tabularnewline
Lambda & 0.0280795430527858 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109535&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.843195233190265[/C][/ROW]
[ROW][C]beta[/C][C]0.971920456947214[/C][/ROW]
[ROW][C]S.D.[/C][C]0.365074564135338[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.66225191352118[/C][/ROW]
[ROW][C]p-value[/C][C]0.0562581517107556[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0280795430527858[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109535&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109535&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-0.843195233190265
beta0.971920456947214
S.D.0.365074564135338
T-STAT2.66225191352118
p-value0.0562581517107556
Lambda0.0280795430527858


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')