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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationTue, 13 Aug 2013 15:32:38 -0400
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/Aug/13/t1376422514czsysnanp0a4fn0.htm/, Retrieved Thu, 02 May 2024 14:54:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211079, Retrieved Thu, 02 May 2024 14:54:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Stap 20/1] [2013-08-13 15:10:40] [9b490dd2ab715f1b5bf65aa31d98df3d]
- RMP     [Standard Deviation-Mean Plot] [stap 26/1] [2013-08-13 19:32:38] [38a0db91cd47487c7649642dcb33e029] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
57
56
55
53
73
72
57
47
48
48
49
51
45
39
34
34
53
55
40
22
31
31
39
43
42
31
37
35
52
48
31
19
30
34
37
41
32
25
28
29
56
56
41
39
45
42
50
60
62
48
44
40
67
69
64
69
68
60
69
79
83
71
63
69
95
103
101
105
104
94
111
116
122
103
96
104
124
141
137
137
139
132
150
150
147
130
133
135
148
165
153
159
154
151
174
169
162
152
162
167
173
181
173
178
172
171
196
199
190
176
188
193
200
209
200
207
204
192
216
216

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=211079&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=211079&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211079&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
155.58.7230103227560826
238.83333333333339.3985814532477933
336.41666666666678.7433957760683433
441.916666666666711.881676751378335
561.583333333333311.704376285920839
692.916666666666717.44319785805253
7127.91666666666718.372203971975754
8151.514.042144358388444
9173.83333333333313.516544295675947
10199.2512.000946932335340

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 55.5 & 8.72301032275608 & 26 \tabularnewline
2 & 38.8333333333333 & 9.39858145324779 & 33 \tabularnewline
3 & 36.4166666666667 & 8.74339577606834 & 33 \tabularnewline
4 & 41.9166666666667 & 11.8816767513783 & 35 \tabularnewline
5 & 61.5833333333333 & 11.7043762859208 & 39 \tabularnewline
6 & 92.9166666666667 & 17.443197858052 & 53 \tabularnewline
7 & 127.916666666667 & 18.3722039719757 & 54 \tabularnewline
8 & 151.5 & 14.0421443583884 & 44 \tabularnewline
9 & 173.833333333333 & 13.5165442956759 & 47 \tabularnewline
10 & 199.25 & 12.0009469323353 & 40 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211079&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]55.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]38.8333333333333[/C][C]9.39858145324779[/C][C]33[/C][/ROW]
[ROW][C]3[/C][C]36.4166666666667[/C][C]8.74339577606834[/C][C]33[/C][/ROW]
[ROW][C]4[/C][C]41.9166666666667[/C][C]11.8816767513783[/C][C]35[/C][/ROW]
[ROW][C]5[/C][C]61.5833333333333[/C][C]11.7043762859208[/C][C]39[/C][/ROW]
[ROW][C]6[/C][C]92.9166666666667[/C][C]17.443197858052[/C][C]53[/C][/ROW]
[ROW][C]7[/C][C]127.916666666667[/C][C]18.3722039719757[/C][C]54[/C][/ROW]
[ROW][C]8[/C][C]151.5[/C][C]14.0421443583884[/C][C]44[/C][/ROW]
[ROW][C]9[/C][C]173.833333333333[/C][C]13.5165442956759[/C][C]47[/C][/ROW]
[ROW][C]10[/C][C]199.25[/C][C]12.0009469323353[/C][C]40[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211079&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211079&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
155.58.7230103227560826
238.83333333333339.3985814532477933
336.41666666666678.7433957760683433
441.916666666666711.881676751378335
561.583333333333311.704376285920839
692.916666666666717.44319785805253
7127.91666666666718.372203971975754
8151.514.042144358388444
9173.83333333333313.516544295675947
10199.2512.000946932335340






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha9.94326996768132
beta0.0269411823705192
S.D.0.0170210969119822
T-STAT1.58281117308918
p-value0.152122280158245

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 9.94326996768132 \tabularnewline
beta & 0.0269411823705192 \tabularnewline
S.D. & 0.0170210969119822 \tabularnewline
T-STAT & 1.58281117308918 \tabularnewline
p-value & 0.152122280158245 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211079&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.94326996768132[/C][/ROW]
[ROW][C]beta[/C][C]0.0269411823705192[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0170210969119822[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.58281117308918[/C][/ROW]
[ROW][C]p-value[/C][C]0.152122280158245[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211079&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211079&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)
alpha9.94326996768132
beta0.0269411823705192
S.D.0.0170210969119822
T-STAT1.58281117308918
p-value0.152122280158245






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.35541137563784
beta0.260473297901083
S.D.0.108061252085398
T-STAT2.41042272668872
p-value0.0424801692877499
Lambda0.739526702098917

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.35541137563784 \tabularnewline
beta & 0.260473297901083 \tabularnewline
S.D. & 0.108061252085398 \tabularnewline
T-STAT & 2.41042272668872 \tabularnewline
p-value & 0.0424801692877499 \tabularnewline
Lambda & 0.739526702098917 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211079&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.35541137563784[/C][/ROW]
[ROW][C]beta[/C][C]0.260473297901083[/C][/ROW]
[ROW][C]S.D.[/C][C]0.108061252085398[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.41042272668872[/C][/ROW]
[ROW][C]p-value[/C][C]0.0424801692877499[/C][/ROW]
[ROW][C]Lambda[/C][C]0.739526702098917[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211079&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211079&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)
alpha1.35541137563784
beta0.260473297901083
S.D.0.108061252085398
T-STAT2.41042272668872
p-value0.0424801692877499
Lambda0.739526702098917


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')