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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, 10 Mar 2015 09:50:16 +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/2015/Mar/10/t1425981054ykvva4956nbjr9w.htm/, Retrieved Fri, 17 May 2024 14:26:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278113, Retrieved Fri, 17 May 2024 14:26:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

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...] [2015-03-10 09:50:16] [cab9dc260884be88f444bea8f40c034b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20
25
15
15
25
25
254
200
165
123
162
145
145
161
155
173
160
47
232
143
161
159
243
192
157
143
221
227
132
41
273
182
188
162
140
186
178
236
202
184
119
16
340
151
240
235
174
309
174
207
209
171
117
10
339
139
186
155
153
222
102
107
188
162
185
24
394
209
248
254
202
258
215
309
240
258
276
48
455
345
311
346
310
297
300
274
292
304
186
14
321
206
160
217
204
246
234
175
364
328
158
40
556
193
221
278
230
253
240
252
228
306
206
48
557
279
399
364
306
471
293
333
316
329
265
61
679
428
394
352
387
590
177
199
203
255
261
115

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=278113&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=278113&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278113&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
197.833333333333386.3437457158445239
2164.2548.9528994405476196
317158.0892729887682232
4198.66666666666785.183580719775324
5173.576.3752696766553329
6194.41666666666793.8920640787585370
7284.16666666666796.3599627658833407
822785.0122985755056307
9252.5126.623637029369516
10304.666666666667132.413493773608509
11368.916666666667155.744813620541618

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 97.8333333333333 & 86.3437457158445 & 239 \tabularnewline
2 & 164.25 & 48.9528994405476 & 196 \tabularnewline
3 & 171 & 58.0892729887682 & 232 \tabularnewline
4 & 198.666666666667 & 85.183580719775 & 324 \tabularnewline
5 & 173.5 & 76.3752696766553 & 329 \tabularnewline
6 & 194.416666666667 & 93.8920640787585 & 370 \tabularnewline
7 & 284.166666666667 & 96.3599627658833 & 407 \tabularnewline
8 & 227 & 85.0122985755056 & 307 \tabularnewline
9 & 252.5 & 126.623637029369 & 516 \tabularnewline
10 & 304.666666666667 & 132.413493773608 & 509 \tabularnewline
11 & 368.916666666667 & 155.744813620541 & 618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278113&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]97.8333333333333[/C][C]86.3437457158445[/C][C]239[/C][/ROW]
[ROW][C]2[/C][C]164.25[/C][C]48.9528994405476[/C][C]196[/C][/ROW]
[ROW][C]3[/C][C]171[/C][C]58.0892729887682[/C][C]232[/C][/ROW]
[ROW][C]4[/C][C]198.666666666667[/C][C]85.183580719775[/C][C]324[/C][/ROW]
[ROW][C]5[/C][C]173.5[/C][C]76.3752696766553[/C][C]329[/C][/ROW]
[ROW][C]6[/C][C]194.416666666667[/C][C]93.8920640787585[/C][C]370[/C][/ROW]
[ROW][C]7[/C][C]284.166666666667[/C][C]96.3599627658833[/C][C]407[/C][/ROW]
[ROW][C]8[/C][C]227[/C][C]85.0122985755056[/C][C]307[/C][/ROW]
[ROW][C]9[/C][C]252.5[/C][C]126.623637029369[/C][C]516[/C][/ROW]
[ROW][C]10[/C][C]304.666666666667[/C][C]132.413493773608[/C][C]509[/C][/ROW]
[ROW][C]11[/C][C]368.916666666667[/C][C]155.744813620541[/C][C]618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278113&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278113&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
197.833333333333386.3437457158445239
2164.2548.9528994405476196
317158.0892729887682232
4198.66666666666785.183580719775324
5173.576.3752696766553329
6194.41666666666793.8920640787585370
7284.16666666666796.3599627658833407
822785.0122985755056307
9252.5126.623637029369516
10304.666666666667132.413493773608509
11368.916666666667155.744813620541618






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha19.7072395255741
beta0.339860371481972
S.D.0.0813088098677476
T-STAT4.17987143133407
p-value0.0023765427538107

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 19.7072395255741 \tabularnewline
beta & 0.339860371481972 \tabularnewline
S.D. & 0.0813088098677476 \tabularnewline
T-STAT & 4.17987143133407 \tabularnewline
p-value & 0.0023765427538107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278113&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]19.7072395255741[/C][/ROW]
[ROW][C]beta[/C][C]0.339860371481972[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0813088098677476[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.17987143133407[/C][/ROW]
[ROW][C]p-value[/C][C]0.0023765427538107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278113&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278113&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)
alpha19.7072395255741
beta0.339860371481972
S.D.0.0813088098677476
T-STAT4.17987143133407
p-value0.0023765427538107






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.12149984740281
beta0.632590117489816
S.D.0.232659192698655
T-STAT2.71895604103277
p-value0.0236481939553198
Lambda0.367409882510184

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.12149984740281 \tabularnewline
beta & 0.632590117489816 \tabularnewline
S.D. & 0.232659192698655 \tabularnewline
T-STAT & 2.71895604103277 \tabularnewline
p-value & 0.0236481939553198 \tabularnewline
Lambda & 0.367409882510184 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278113&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.12149984740281[/C][/ROW]
[ROW][C]beta[/C][C]0.632590117489816[/C][/ROW]
[ROW][C]S.D.[/C][C]0.232659192698655[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.71895604103277[/C][/ROW]
[ROW][C]p-value[/C][C]0.0236481939553198[/C][/ROW]
[ROW][C]Lambda[/C][C]0.367409882510184[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278113&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278113&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)
alpha1.12149984740281
beta0.632590117489816
S.D.0.232659192698655
T-STAT2.71895604103277
p-value0.0236481939553198
Lambda0.367409882510184


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')