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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, 26 May 2015 21:43:38 +0100
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/May/26/t1432673042kmzqilbzhg0km5w.htm/, Retrieved Tue, 30 Apr 2024 13:43:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279436, Retrieved Tue, 30 Apr 2024 13:43:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74

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] [] [2015-05-26 20:43:38] [f898ec974b62c60a8bec4044c4c271e3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
507
233
346
159
225
146
253
169
246
129
318
378
580
336
468
229
189
181
210
270
229
319
377
275
365
269
377
194
337
212
278
197
305
343
588
382
266
305
345
249
253
167
149
286
260
375
339
322
396
421
254
279
347
264
324
243
324
420
295
731
576
391
229
347
262
317
249
211
303
337
383
588
456
375
507
405
363
394
166
217
299
549
395
730

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=279436&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=279436&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279436&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
1259.083333333333111.40463376468378
2305.25120.630257775191399
3320.583333333333108.298794027814394
4276.33333333333368.231335554239226
5358.166666666667132.769679817298488
6349.416666666667122.796548910148377
7404.666666666667149.529767990028564

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 259.083333333333 & 111.40463376468 & 378 \tabularnewline
2 & 305.25 & 120.630257775191 & 399 \tabularnewline
3 & 320.583333333333 & 108.298794027814 & 394 \tabularnewline
4 & 276.333333333333 & 68.231335554239 & 226 \tabularnewline
5 & 358.166666666667 & 132.769679817298 & 488 \tabularnewline
6 & 349.416666666667 & 122.796548910148 & 377 \tabularnewline
7 & 404.666666666667 & 149.529767990028 & 564 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279436&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]259.083333333333[/C][C]111.40463376468[/C][C]378[/C][/ROW]
[ROW][C]2[/C][C]305.25[/C][C]120.630257775191[/C][C]399[/C][/ROW]
[ROW][C]3[/C][C]320.583333333333[/C][C]108.298794027814[/C][C]394[/C][/ROW]
[ROW][C]4[/C][C]276.333333333333[/C][C]68.231335554239[/C][C]226[/C][/ROW]
[ROW][C]5[/C][C]358.166666666667[/C][C]132.769679817298[/C][C]488[/C][/ROW]
[ROW][C]6[/C][C]349.416666666667[/C][C]122.796548910148[/C][C]377[/C][/ROW]
[ROW][C]7[/C][C]404.666666666667[/C][C]149.529767990028[/C][C]564[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279436&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279436&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
1259.083333333333111.40463376468378
2305.25120.630257775191399
3320.583333333333108.298794027814394
4276.33333333333368.231335554239226
5358.166666666667132.769679817298488
6349.416666666667122.796548910148377
7404.666666666667149.529767990028564






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-11.4851242649922
beta0.393251325134965
S.D.0.140160975776632
T-STAT2.80571195338759
p-value0.0377385050240232

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -11.4851242649922 \tabularnewline
beta & 0.393251325134965 \tabularnewline
S.D. & 0.140160975776632 \tabularnewline
T-STAT & 2.80571195338759 \tabularnewline
p-value & 0.0377385050240232 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279436&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.4851242649922[/C][/ROW]
[ROW][C]beta[/C][C]0.393251325134965[/C][/ROW]
[ROW][C]S.D.[/C][C]0.140160975776632[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.80571195338759[/C][/ROW]
[ROW][C]p-value[/C][C]0.0377385050240232[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279436&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279436&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)
alpha-11.4851242649922
beta0.393251325134965
S.D.0.140160975776632
T-STAT2.80571195338759
p-value0.0377385050240232






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.89374686049371
beta1.14764054067502
S.D.0.504228190855477
T-STAT2.27603406847984
p-value0.0718938601421343
Lambda-0.14764054067502

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.89374686049371 \tabularnewline
beta & 1.14764054067502 \tabularnewline
S.D. & 0.504228190855477 \tabularnewline
T-STAT & 2.27603406847984 \tabularnewline
p-value & 0.0718938601421343 \tabularnewline
Lambda & -0.14764054067502 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279436&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.89374686049371[/C][/ROW]
[ROW][C]beta[/C][C]1.14764054067502[/C][/ROW]
[ROW][C]S.D.[/C][C]0.504228190855477[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.27603406847984[/C][/ROW]
[ROW][C]p-value[/C][C]0.0718938601421343[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.14764054067502[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279436&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279436&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-1.89374686049371
beta1.14764054067502
S.D.0.504228190855477
T-STAT2.27603406847984
p-value0.0718938601421343
Lambda-0.14764054067502


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')