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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 computationMon, 12 May 2014 15:26:35 -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/2014/May/12/t1399922880ek61ir3jngppfu5.htm/, Retrieved Wed, 15 May 2024 13:46:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234848, Retrieved Wed, 15 May 2024 13:46:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114

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] [] [2014-05-12 19:26:35] [3faf596b3f292f8d9ff7bbf57fa10dd3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
812
100
113
213
149
134
228
138
162
291
182
2081
2752
125
144
274
257
186
327
209
213
375
400
1054
3377
101
120
221
222
167
297
185
189
298
237
1011
3013
110
109
215
176
134
202
139
169
262
214
1238
3748
127
160
138
134
163
172
163
193
226
344
1294
3524
141
186
135
161
131
170
146
160
151
151
1365

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234848&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234848&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234848&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1383.583333333333567.9022736565181981
2526.333333333333742.7702854649592627
3535.416666666667926.3781339008913276
4498.416666666667850.2431158560512904
5571.8333333333331051.671036825193621
6535.0833333333331003.776184608843393

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 383.583333333333 & 567.902273656518 & 1981 \tabularnewline
2 & 526.333333333333 & 742.770285464959 & 2627 \tabularnewline
3 & 535.416666666667 & 926.378133900891 & 3276 \tabularnewline
4 & 498.416666666667 & 850.243115856051 & 2904 \tabularnewline
5 & 571.833333333333 & 1051.67103682519 & 3621 \tabularnewline
6 & 535.083333333333 & 1003.77618460884 & 3393 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234848&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]383.583333333333[/C][C]567.902273656518[/C][C]1981[/C][/ROW]
[ROW][C]2[/C][C]526.333333333333[/C][C]742.770285464959[/C][C]2627[/C][/ROW]
[ROW][C]3[/C][C]535.416666666667[/C][C]926.378133900891[/C][C]3276[/C][/ROW]
[ROW][C]4[/C][C]498.416666666667[/C][C]850.243115856051[/C][C]2904[/C][/ROW]
[ROW][C]5[/C][C]571.833333333333[/C][C]1051.67103682519[/C][C]3621[/C][/ROW]
[ROW][C]6[/C][C]535.083333333333[/C][C]1003.77618460884[/C][C]3393[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234848&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234848&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
1383.583333333333567.9022736565181981
2526.333333333333742.7702854649592627
3535.416666666667926.3781339008913276
4498.416666666667850.2431158560512904
5571.8333333333331051.671036825193621
6535.0833333333331003.776184608843393






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-380.287926349682
beta2.43372003553667
S.D.0.627233645276989
T-STAT3.88008528219485
p-value0.0178399852927786

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -380.287926349682 \tabularnewline
beta & 2.43372003553667 \tabularnewline
S.D. & 0.627233645276989 \tabularnewline
T-STAT & 3.88008528219485 \tabularnewline
p-value & 0.0178399852927786 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234848&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-380.287926349682[/C][/ROW]
[ROW][C]beta[/C][C]2.43372003553667[/C][/ROW]
[ROW][C]S.D.[/C][C]0.627233645276989[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.88008528219485[/C][/ROW]
[ROW][C]p-value[/C][C]0.0178399852927786[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234848&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234848&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-380.287926349682
beta2.43372003553667
S.D.0.627233645276989
T-STAT3.88008528219485
p-value0.0178399852927786






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.40135469748369
beta1.46773176935882
S.D.0.337763179799952
T-STAT4.34544632789199
p-value0.012200621445347
Lambda-0.467731769358822

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.40135469748369 \tabularnewline
beta & 1.46773176935882 \tabularnewline
S.D. & 0.337763179799952 \tabularnewline
T-STAT & 4.34544632789199 \tabularnewline
p-value & 0.012200621445347 \tabularnewline
Lambda & -0.467731769358822 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234848&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.40135469748369[/C][/ROW]
[ROW][C]beta[/C][C]1.46773176935882[/C][/ROW]
[ROW][C]S.D.[/C][C]0.337763179799952[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.34544632789199[/C][/ROW]
[ROW][C]p-value[/C][C]0.012200621445347[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.467731769358822[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234848&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234848&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-2.40135469748369
beta1.46773176935882
S.D.0.337763179799952
T-STAT4.34544632789199
p-value0.012200621445347
Lambda-0.467731769358822


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')