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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, 09 Aug 2016 22:21:29 +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/Aug/09/t1470777789orcr8qftogiv7nh.htm/, Retrieved Sat, 18 May 2024 16:45:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296154, Retrieved Sat, 18 May 2024 16:45:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108

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] [] [2016-08-09 21:21:29] [50e1ac7d003038f762f5217b1e15faa4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14724.00
14404.00
14058.00
13427.00
19946.00
19631.00
14724.00
11462.00
11778.00
11778.00
12093.00
12760.00
13742.00
13427.00
11462.00
11778.00
20929.00
22893.00
17666.00
14724.00
15387.00
15707.00
17351.00
18964.00
19315.00
16022.00
16369.00
12093.00
24222.00
27800.00
19631.00
17004.00
18649.00
20613.00
23555.00
27164.00
27164.00
24853.00
23871.00
17982.00
27800.00
32391.00
28462.00
24222.00
24853.00
27164.00
30426.00
34355.00
31724.00
30111.00
30111.00
24853.00
32391.00
37297.00
33373.00
29129.00
30426.00
35653.00
37964.00
41222.00
38595.00
34355.00
33373.00
25520.00
30742.00
36315.00
30111.00
26502.00
30111.00
33689.00
35653.00
40906.00
38280.00
31724.00
32391.00
26186.00
31409.00
36000.00
30742.00
27164.00
30426.00
34355.00
33689.00
41542.00
40244.00
35017.00
35333.00
28462.00
32706.00
39262.00
34355.00
31409.00
36315.00
39262.00
36982.00
47431.00
44835.00
38946.00
37297.00
29764.00
34035.00
37964.00
33053.00
33053.00
38595.00
41542.00
39924.00
51355.00
48413.00
42871.00
40560.00
32391.00
35333.00
40560.00
36631.00
35653.00
40244.00
44168.00
39924.00
50057.00

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296154&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296154&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296154&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
114232.08333333332851.638235959798484
216169.16666666673530.1113769020611431
320203.08333333334723.6634176593615707
426961.91666666674324.9979602377416373
532854.54515.6868902647716369
632989.33333333334614.7058870790915386
732825.66666666674354.0375689140715356
836398.16666666674880.2762372139518969
938363.58333333335830.7761912479821591
1040567.08333333335259.575967324817666

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14232.0833333333 & 2851.63823595979 & 8484 \tabularnewline
2 & 16169.1666666667 & 3530.11137690206 & 11431 \tabularnewline
3 & 20203.0833333333 & 4723.66341765936 & 15707 \tabularnewline
4 & 26961.9166666667 & 4324.99796023774 & 16373 \tabularnewline
5 & 32854.5 & 4515.68689026477 & 16369 \tabularnewline
6 & 32989.3333333333 & 4614.70588707909 & 15386 \tabularnewline
7 & 32825.6666666667 & 4354.03756891407 & 15356 \tabularnewline
8 & 36398.1666666667 & 4880.27623721395 & 18969 \tabularnewline
9 & 38363.5833333333 & 5830.77619124798 & 21591 \tabularnewline
10 & 40567.0833333333 & 5259.5759673248 & 17666 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296154&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]14232.0833333333[/C][C]2851.63823595979[/C][C]8484[/C][/ROW]
[ROW][C]2[/C][C]16169.1666666667[/C][C]3530.11137690206[/C][C]11431[/C][/ROW]
[ROW][C]3[/C][C]20203.0833333333[/C][C]4723.66341765936[/C][C]15707[/C][/ROW]
[ROW][C]4[/C][C]26961.9166666667[/C][C]4324.99796023774[/C][C]16373[/C][/ROW]
[ROW][C]5[/C][C]32854.5[/C][C]4515.68689026477[/C][C]16369[/C][/ROW]
[ROW][C]6[/C][C]32989.3333333333[/C][C]4614.70588707909[/C][C]15386[/C][/ROW]
[ROW][C]7[/C][C]32825.6666666667[/C][C]4354.03756891407[/C][C]15356[/C][/ROW]
[ROW][C]8[/C][C]36398.1666666667[/C][C]4880.27623721395[/C][C]18969[/C][/ROW]
[ROW][C]9[/C][C]38363.5833333333[/C][C]5830.77619124798[/C][C]21591[/C][/ROW]
[ROW][C]10[/C][C]40567.0833333333[/C][C]5259.5759673248[/C][C]17666[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296154&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296154&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
114232.08333333332851.638235959798484
216169.16666666673530.1113769020611431
320203.08333333334723.6634176593615707
426961.91666666674324.9979602377416373
532854.54515.6868902647716369
632989.33333333334614.7058870790915386
732825.66666666674354.0375689140715356
836398.16666666674880.2762372139518969
938363.58333333335830.7761912479821591
1040567.08333333335259.575967324817666






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2290.97655623932
beta0.0753716515194388
S.D.0.0169291902138179
T-STAT4.45217110608866
p-value0.00213313507645316

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2290.97655623932 \tabularnewline
beta & 0.0753716515194388 \tabularnewline
S.D. & 0.0169291902138179 \tabularnewline
T-STAT & 4.45217110608866 \tabularnewline
p-value & 0.00213313507645316 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296154&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2290.97655623932[/C][/ROW]
[ROW][C]beta[/C][C]0.0753716515194388[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0169291902138179[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.45217110608866[/C][/ROW]
[ROW][C]p-value[/C][C]0.00213313507645316[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296154&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296154&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)
alpha2290.97655623932
beta0.0753716515194388
S.D.0.0169291902138179
T-STAT4.45217110608866
p-value0.00213313507645316






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.60251228253677
beta0.468453961525005
S.D.0.0964665506847866
T-STAT4.85612845281181
p-value0.00126199092221759
Lambda0.531546038474995

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.60251228253677 \tabularnewline
beta & 0.468453961525005 \tabularnewline
S.D. & 0.0964665506847866 \tabularnewline
T-STAT & 4.85612845281181 \tabularnewline
p-value & 0.00126199092221759 \tabularnewline
Lambda & 0.531546038474995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296154&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.60251228253677[/C][/ROW]
[ROW][C]beta[/C][C]0.468453961525005[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0964665506847866[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.85612845281181[/C][/ROW]
[ROW][C]p-value[/C][C]0.00126199092221759[/C][/ROW]
[ROW][C]Lambda[/C][C]0.531546038474995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296154&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296154&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)
alpha3.60251228253677
beta0.468453961525005
S.D.0.0964665506847866
T-STAT4.85612845281181
p-value0.00126199092221759
Lambda0.531546038474995


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')