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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 computationFri, 23 Dec 2011 14:01:42 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t13246669623gtpac11but8ehw.htm/, Retrieved Mon, 29 Apr 2024 18:19:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160659, Retrieved Mon, 29 Apr 2024 18:19:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Spectral Analysis] [] [2011-12-23 18:50:40] [2ba7ee2cbaa966a49160c7cfb7436069]
- RMP     [Standard Deviation-Mean Plot] [] [2011-12-23 19:01:42] [393d554610c677f923bed472882d0fdb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
302
262
218
175
100
77
43
47
49
69
152
205
246
294
242
181
107
56
49
47
47
71
151
244
280
230
185
148
98
61
46
45
55
48
115
185
276
220
181
151
83
55
49
42
46
74
103
200
237
247
215
182
80
46
65
40
44
63
85
185
247
231
167
117
79
45
40
38
41
69
152
232
282
255
161
107
53
40
39
34
35
56
97
210
260
257
210
125
80
42
35
31
32
50
92
189
256
250
198
136
73
39
32
30
31
45

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160659&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160659&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160659&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1141.58333333333390.3150630075659259
2144.58333333333393.5204968620961247
3124.66666666666780.4378171275329235
4123.33333333333379.7066591644106234
5124.08333333333381.7217655811288207
6121.581.7318231112638209
7114.08333333333390.8019406413895248
8116.91666666666789.1367267774965229

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 141.583333333333 & 90.3150630075659 & 259 \tabularnewline
2 & 144.583333333333 & 93.5204968620961 & 247 \tabularnewline
3 & 124.666666666667 & 80.4378171275329 & 235 \tabularnewline
4 & 123.333333333333 & 79.7066591644106 & 234 \tabularnewline
5 & 124.083333333333 & 81.7217655811288 & 207 \tabularnewline
6 & 121.5 & 81.7318231112638 & 209 \tabularnewline
7 & 114.083333333333 & 90.8019406413895 & 248 \tabularnewline
8 & 116.916666666667 & 89.1367267774965 & 229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160659&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]141.583333333333[/C][C]90.3150630075659[/C][C]259[/C][/ROW]
[ROW][C]2[/C][C]144.583333333333[/C][C]93.5204968620961[/C][C]247[/C][/ROW]
[ROW][C]3[/C][C]124.666666666667[/C][C]80.4378171275329[/C][C]235[/C][/ROW]
[ROW][C]4[/C][C]123.333333333333[/C][C]79.7066591644106[/C][C]234[/C][/ROW]
[ROW][C]5[/C][C]124.083333333333[/C][C]81.7217655811288[/C][C]207[/C][/ROW]
[ROW][C]6[/C][C]121.5[/C][C]81.7318231112638[/C][C]209[/C][/ROW]
[ROW][C]7[/C][C]114.083333333333[/C][C]90.8019406413895[/C][C]248[/C][/ROW]
[ROW][C]8[/C][C]116.916666666667[/C][C]89.1367267774965[/C][C]229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160659&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160659&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
1141.58333333333390.3150630075659259
2144.58333333333393.5204968620961247
3124.66666666666780.4378171275329235
4123.33333333333379.7066591644106234
5124.08333333333381.7217655811288207
6121.581.7318231112638209
7114.08333333333390.8019406413895248
8116.91666666666789.1367267774965229






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha60.0255892449363
beta0.204964213023392
S.D.0.188267107499844
T-STAT1.08868838399486
p-value0.318075734160631

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 60.0255892449363 \tabularnewline
beta & 0.204964213023392 \tabularnewline
S.D. & 0.188267107499844 \tabularnewline
T-STAT & 1.08868838399486 \tabularnewline
p-value & 0.318075734160631 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160659&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]60.0255892449363[/C][/ROW]
[ROW][C]beta[/C][C]0.204964213023392[/C][/ROW]
[ROW][C]S.D.[/C][C]0.188267107499844[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.08868838399486[/C][/ROW]
[ROW][C]p-value[/C][C]0.318075734160631[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160659&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160659&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)
alpha60.0255892449363
beta0.204964213023392
S.D.0.188267107499844
T-STAT1.08868838399486
p-value0.318075734160631






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.08888448512441
beta0.281799905981569
S.D.0.28868455426982
T-STAT0.976151656933415
p-value0.366688019353974
Lambda0.718200094018431

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.08888448512441 \tabularnewline
beta & 0.281799905981569 \tabularnewline
S.D. & 0.28868455426982 \tabularnewline
T-STAT & 0.976151656933415 \tabularnewline
p-value & 0.366688019353974 \tabularnewline
Lambda & 0.718200094018431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160659&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.08888448512441[/C][/ROW]
[ROW][C]beta[/C][C]0.281799905981569[/C][/ROW]
[ROW][C]S.D.[/C][C]0.28868455426982[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.976151656933415[/C][/ROW]
[ROW][C]p-value[/C][C]0.366688019353974[/C][/ROW]
[ROW][C]Lambda[/C][C]0.718200094018431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160659&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160659&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)
alpha3.08888448512441
beta0.281799905981569
S.D.0.28868455426982
T-STAT0.976151656933415
p-value0.366688019353974
Lambda0.718200094018431


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')