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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, 20 Dec 2013 11:03:48 -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/2013/Dec/20/t1387555443dr9z276gzu3o2f1.htm/, Retrieved Wed, 24 Apr 2024 01:43:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232462, Retrieved Wed, 24 Apr 2024 01:43:20 +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] [] [2013-12-20 16:03:48] [9e6a405f514733ea23d87e4507d39d29] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
56
55
54
52
72
71
56
46
47
47
48
50
44
38
33
33
52
54
39
22
31
31
38
42
41
31
36
34
51
47
31
19
30
33
36
40
32
25
28
29
55
55
40
38
44
41
49
59
61
47
43
39
66
68
63
68
67
59
68
78
82
70
62
68
94
102
100
104
103
93
110
114
120
102
95
103
122
139
135
135
137
130
148
148
145
128
131
133
146
163
151
157
152
149
172
167
160
150
160
165
171
179
171
176
170
169
194
196
188
174
186
191
197
206
197
204
201
190
213
213

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'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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232462&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232462&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232462&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
154.58.7230103227560826
238.08333333333339.090037837038332
335.758.389658135845832
441.2511.474279537691734
560.583333333333311.704376285920839
691.833333333333317.324881389248152
7126.16666666666717.973886782235153
8149.514.042144358388444
9171.7513.34932752817746
10196.66666666666711.570600152057339

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 54.5 & 8.72301032275608 & 26 \tabularnewline
2 & 38.0833333333333 & 9.0900378370383 & 32 \tabularnewline
3 & 35.75 & 8.3896581358458 & 32 \tabularnewline
4 & 41.25 & 11.4742795376917 & 34 \tabularnewline
5 & 60.5833333333333 & 11.7043762859208 & 39 \tabularnewline
6 & 91.8333333333333 & 17.3248813892481 & 52 \tabularnewline
7 & 126.166666666667 & 17.9738867822351 & 53 \tabularnewline
8 & 149.5 & 14.0421443583884 & 44 \tabularnewline
9 & 171.75 & 13.349327528177 & 46 \tabularnewline
10 & 196.666666666667 & 11.5706001520573 & 39 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232462&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]54.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]38.0833333333333[/C][C]9.0900378370383[/C][C]32[/C][/ROW]
[ROW][C]3[/C][C]35.75[/C][C]8.3896581358458[/C][C]32[/C][/ROW]
[ROW][C]4[/C][C]41.25[/C][C]11.4742795376917[/C][C]34[/C][/ROW]
[ROW][C]5[/C][C]60.5833333333333[/C][C]11.7043762859208[/C][C]39[/C][/ROW]
[ROW][C]6[/C][C]91.8333333333333[/C][C]17.3248813892481[/C][C]52[/C][/ROW]
[ROW][C]7[/C][C]126.166666666667[/C][C]17.9738867822351[/C][C]53[/C][/ROW]
[ROW][C]8[/C][C]149.5[/C][C]14.0421443583884[/C][C]44[/C][/ROW]
[ROW][C]9[/C][C]171.75[/C][C]13.349327528177[/C][C]46[/C][/ROW]
[ROW][C]10[/C][C]196.666666666667[/C][C]11.5706001520573[/C][C]39[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232462&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232462&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
154.58.7230103227560826
238.08333333333339.090037837038332
335.758.389658135845832
441.2511.474279537691734
560.583333333333311.704376285920839
691.833333333333317.324881389248152
7126.16666666666717.973886782235153
8149.514.042144358388444
9171.7513.34932752817746
10196.66666666666711.570600152057339






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha9.74182879815913
beta0.0271445675988275
S.D.0.0172299521714556
T-STAT1.57542907424881
p-value0.153806214534249

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.74182879815913 \tabularnewline
beta & 0.0271445675988275 \tabularnewline
S.D. & 0.0172299521714556 \tabularnewline
T-STAT & 1.57542907424881 \tabularnewline
p-value & 0.153806214534249 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232462&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.74182879815913[/C][/ROW]
[ROW][C]beta[/C][C]0.0271445675988275[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0172299521714556[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.57542907424881[/C][/ROW]
[ROW][C]p-value[/C][C]0.153806214534249[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232462&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232462&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)
alpha9.74182879815913
beta0.0271445675988275
S.D.0.0172299521714556
T-STAT1.57542907424881
p-value0.153806214534249






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.31102527886591
beta0.267233734869499
S.D.0.109031730977204
T-STAT2.45097213879299
p-value0.0398762263523907
Lambda0.732766265130501

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.31102527886591 \tabularnewline
beta & 0.267233734869499 \tabularnewline
S.D. & 0.109031730977204 \tabularnewline
T-STAT & 2.45097213879299 \tabularnewline
p-value & 0.0398762263523907 \tabularnewline
Lambda & 0.732766265130501 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232462&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.31102527886591[/C][/ROW]
[ROW][C]beta[/C][C]0.267233734869499[/C][/ROW]
[ROW][C]S.D.[/C][C]0.109031730977204[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.45097213879299[/C][/ROW]
[ROW][C]p-value[/C][C]0.0398762263523907[/C][/ROW]
[ROW][C]Lambda[/C][C]0.732766265130501[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232462&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232462&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)
alpha1.31102527886591
beta0.267233734869499
S.D.0.109031730977204
T-STAT2.45097213879299
p-value0.0398762263523907
Lambda0.732766265130501


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')