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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 computationThu, 22 Dec 2016 18:26:43 +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/2016/Dec/22/t1482427647pwxdmakf13w2oyq.htm/, Retrieved Sun, 28 Apr 2024 22:25:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302589, Retrieved Sun, 28 Apr 2024 22:25:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82

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...] [2016-12-22 17:26:43] [bde5266f17215258f6d7c4cd7e531432] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1549.5
1746.5
1869.5
1784
1795
1942.5
2100
2072.5
2075
2278
2451
2290.5
2388
2574.5
2939.5
2924
3087.5
3259.5
3474.5
3376
3496
3771.5
3743
3474.5
3405
3684.5
3804
3470.5
3453.5
3842
4156.5
4055
4133.5
4552
4588
4423.5
4462.5
4846
4869.5
4637
4841
5114.5
5374.5
5166.5
5236.5
5740.5
5992
5842
5844.5
6384.5
6487
6372
6583.5
6990
6874
6710
6924
7428.5
7415.5
7228.5
6734
7158.5
7192

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302589&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302589&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302589&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11737.375135.414410237611320
21977.5139.716975823746305
32273.625154.075400913535376
42706.5271.085164969732551.5
53299.375166.354227979534387
63621.25157.714140139684297
73591185.497079941078399
83876.75311.116939429533703
94424.25206.292874331616454.5
104703.75191.803067406824407
115124.125219.647966452382533.5
125702.75327.551649871182755.5
136272289.619002599392642.5
146789.375178.975498788708406.5
157249.125235.221659646102504.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1737.375 & 135.414410237611 & 320 \tabularnewline
2 & 1977.5 & 139.716975823746 & 305 \tabularnewline
3 & 2273.625 & 154.075400913535 & 376 \tabularnewline
4 & 2706.5 & 271.085164969732 & 551.5 \tabularnewline
5 & 3299.375 & 166.354227979534 & 387 \tabularnewline
6 & 3621.25 & 157.714140139684 & 297 \tabularnewline
7 & 3591 & 185.497079941078 & 399 \tabularnewline
8 & 3876.75 & 311.116939429533 & 703 \tabularnewline
9 & 4424.25 & 206.292874331616 & 454.5 \tabularnewline
10 & 4703.75 & 191.803067406824 & 407 \tabularnewline
11 & 5124.125 & 219.647966452382 & 533.5 \tabularnewline
12 & 5702.75 & 327.551649871182 & 755.5 \tabularnewline
13 & 6272 & 289.619002599392 & 642.5 \tabularnewline
14 & 6789.375 & 178.975498788708 & 406.5 \tabularnewline
15 & 7249.125 & 235.221659646102 & 504.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302589&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]1737.375[/C][C]135.414410237611[/C][C]320[/C][/ROW]
[ROW][C]2[/C][C]1977.5[/C][C]139.716975823746[/C][C]305[/C][/ROW]
[ROW][C]3[/C][C]2273.625[/C][C]154.075400913535[/C][C]376[/C][/ROW]
[ROW][C]4[/C][C]2706.5[/C][C]271.085164969732[/C][C]551.5[/C][/ROW]
[ROW][C]5[/C][C]3299.375[/C][C]166.354227979534[/C][C]387[/C][/ROW]
[ROW][C]6[/C][C]3621.25[/C][C]157.714140139684[/C][C]297[/C][/ROW]
[ROW][C]7[/C][C]3591[/C][C]185.497079941078[/C][C]399[/C][/ROW]
[ROW][C]8[/C][C]3876.75[/C][C]311.116939429533[/C][C]703[/C][/ROW]
[ROW][C]9[/C][C]4424.25[/C][C]206.292874331616[/C][C]454.5[/C][/ROW]
[ROW][C]10[/C][C]4703.75[/C][C]191.803067406824[/C][C]407[/C][/ROW]
[ROW][C]11[/C][C]5124.125[/C][C]219.647966452382[/C][C]533.5[/C][/ROW]
[ROW][C]12[/C][C]5702.75[/C][C]327.551649871182[/C][C]755.5[/C][/ROW]
[ROW][C]13[/C][C]6272[/C][C]289.619002599392[/C][C]642.5[/C][/ROW]
[ROW][C]14[/C][C]6789.375[/C][C]178.975498788708[/C][C]406.5[/C][/ROW]
[ROW][C]15[/C][C]7249.125[/C][C]235.221659646102[/C][C]504.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302589&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302589&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
11737.375135.414410237611320
21977.5139.716975823746305
32273.625154.075400913535376
42706.5271.085164969732551.5
53299.375166.354227979534387
63621.25157.714140139684297
73591185.497079941078399
83876.75311.116939429533703
94424.25206.292874331616454.5
104703.75191.803067406824407
115124.125219.647966452382533.5
125702.75327.551649871182755.5
136272289.619002599392642.5
146789.375178.975498788708406.5
157249.125235.221659646102504.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha136.922908932187
beta0.0176205911647484
S.D.0.0087287828824643
T-STAT2.01867676192833
p-value0.0646390261604171

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 136.922908932187 \tabularnewline
beta & 0.0176205911647484 \tabularnewline
S.D. & 0.0087287828824643 \tabularnewline
T-STAT & 2.01867676192833 \tabularnewline
p-value & 0.0646390261604171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302589&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]136.922908932187[/C][/ROW]
[ROW][C]beta[/C][C]0.0176205911647484[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0087287828824643[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.01867676192833[/C][/ROW]
[ROW][C]p-value[/C][C]0.0646390261604171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302589&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302589&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)
alpha136.922908932187
beta0.0176205911647484
S.D.0.0087287828824643
T-STAT2.01867676192833
p-value0.0646390261604171






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.12991209412842
beta0.385421285115629
S.D.0.144256275599797
T-STAT2.67178175447205
p-value0.0191990672733072
Lambda0.614578714884371

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.12991209412842 \tabularnewline
beta & 0.385421285115629 \tabularnewline
S.D. & 0.144256275599797 \tabularnewline
T-STAT & 2.67178175447205 \tabularnewline
p-value & 0.0191990672733072 \tabularnewline
Lambda & 0.614578714884371 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302589&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.12991209412842[/C][/ROW]
[ROW][C]beta[/C][C]0.385421285115629[/C][/ROW]
[ROW][C]S.D.[/C][C]0.144256275599797[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.67178175447205[/C][/ROW]
[ROW][C]p-value[/C][C]0.0191990672733072[/C][/ROW]
[ROW][C]Lambda[/C][C]0.614578714884371[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302589&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302589&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)
alpha2.12991209412842
beta0.385421285115629
S.D.0.144256275599797
T-STAT2.67178175447205
p-value0.0191990672733072
Lambda0.614578714884371


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 4 ;
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')