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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 computationFri, 09 Dec 2016 19:36:20 +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/09/t1481308703ziehka1om8x41n2.htm/, Retrieved Fri, 17 May 2024 18:47:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298603, Retrieved Fri, 17 May 2024 18:47:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72

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] [standardd deviati...] [2016-12-09 18:36:20] [e6dc02234f5305f92311fb16bc25f73e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13663
11635
9606
8784.5
9415.5
10418
11344.5
11271
11895
12152.5
12731
12951
10692
8563.5
6217
5562
6294.5
7422
9254.5
10607
11268
12041
12962.5
12200.5
10400.5
8765
7000
6677
7318
7999
8762
9696
10373
10682.5
10935.5
10815.5
8669
7079.5
5640
5238.5
5777.5
6479
7290
7343
7810.5
8171.5
8532
8719
7281.5
5923.5
4837
4675.5
4585.5
5083
5766
6201
6778
7393.5
7849.5
8282.5
7610
6192.5
4693.5
4869
5149
5648.5
6230.5
7032
7727
8087.5
8443
9002
7717.5
6374.5
4995.5
4655
5198
5501
6119.5
6922
7390
7466.5
7773
7865
6567
5132.5
3656.5
3623
4045.5
4617
5374
6022.5
6464.5
7058
7484.5
7955
6801
5499
4179.5
4305.5
3304
5773.5
6419.5
6938
7760
8224
8381
8667
7304.5
5565.5
4023
3932.5
4508.5
5491
6284

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298603&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]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298603&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298603&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 time0 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
111322.251509.781990583714878.5
29423.708333333332580.647015930957400.5
39118.666666666671577.520887822144258.5
47229.1251221.526171434733480.5
56221.3751289.161815871073697
66723.708333333331465.250838878224308.5
76498.1251182.893411877693210
85666.666666666671488.405619405814332
96354.333333333331777.968597397985363

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 11322.25 & 1509.78199058371 & 4878.5 \tabularnewline
2 & 9423.70833333333 & 2580.64701593095 & 7400.5 \tabularnewline
3 & 9118.66666666667 & 1577.52088782214 & 4258.5 \tabularnewline
4 & 7229.125 & 1221.52617143473 & 3480.5 \tabularnewline
5 & 6221.375 & 1289.16181587107 & 3697 \tabularnewline
6 & 6723.70833333333 & 1465.25083887822 & 4308.5 \tabularnewline
7 & 6498.125 & 1182.89341187769 & 3210 \tabularnewline
8 & 5666.66666666667 & 1488.40561940581 & 4332 \tabularnewline
9 & 6354.33333333333 & 1777.96859739798 & 5363 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298603&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]11322.25[/C][C]1509.78199058371[/C][C]4878.5[/C][/ROW]
[ROW][C]2[/C][C]9423.70833333333[/C][C]2580.64701593095[/C][C]7400.5[/C][/ROW]
[ROW][C]3[/C][C]9118.66666666667[/C][C]1577.52088782214[/C][C]4258.5[/C][/ROW]
[ROW][C]4[/C][C]7229.125[/C][C]1221.52617143473[/C][C]3480.5[/C][/ROW]
[ROW][C]5[/C][C]6221.375[/C][C]1289.16181587107[/C][C]3697[/C][/ROW]
[ROW][C]6[/C][C]6723.70833333333[/C][C]1465.25083887822[/C][C]4308.5[/C][/ROW]
[ROW][C]7[/C][C]6498.125[/C][C]1182.89341187769[/C][C]3210[/C][/ROW]
[ROW][C]8[/C][C]5666.66666666667[/C][C]1488.40561940581[/C][C]4332[/C][/ROW]
[ROW][C]9[/C][C]6354.33333333333[/C][C]1777.96859739798[/C][C]5363[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298603&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298603&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
111322.251509.781990583714878.5
29423.708333333332580.647015930957400.5
39118.666666666671577.520887822144258.5
47229.1251221.526171434733480.5
56221.3751289.161815871073697
66723.708333333331465.250838878224308.5
76498.1251182.893411877693210
85666.666666666671488.405619405814332
96354.333333333331777.968597397985363






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha887.470226491874
beta0.0890622250022094
S.D.0.0774025853104822
T-STAT1.15063630814084
p-value0.287666646591776

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 887.470226491874 \tabularnewline
beta & 0.0890622250022094 \tabularnewline
S.D. & 0.0774025853104822 \tabularnewline
T-STAT & 1.15063630814084 \tabularnewline
p-value & 0.287666646591776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298603&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]887.470226491874[/C][/ROW]
[ROW][C]beta[/C][C]0.0890622250022094[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0774025853104822[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.15063630814084[/C][/ROW]
[ROW][C]p-value[/C][C]0.287666646591776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298603&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298603&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)
alpha887.470226491874
beta0.0890622250022094
S.D.0.0774025853104822
T-STAT1.15063630814084
p-value0.287666646591776






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.54442693766424
beta0.424635977724107
S.D.0.347801295630908
T-STAT1.22091545678064
p-value0.261641926954288
Lambda0.575364022275893

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.54442693766424 \tabularnewline
beta & 0.424635977724107 \tabularnewline
S.D. & 0.347801295630908 \tabularnewline
T-STAT & 1.22091545678064 \tabularnewline
p-value & 0.261641926954288 \tabularnewline
Lambda & 0.575364022275893 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298603&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.54442693766424[/C][/ROW]
[ROW][C]beta[/C][C]0.424635977724107[/C][/ROW]
[ROW][C]S.D.[/C][C]0.347801295630908[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.22091545678064[/C][/ROW]
[ROW][C]p-value[/C][C]0.261641926954288[/C][/ROW]
[ROW][C]Lambda[/C][C]0.575364022275893[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298603&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298603&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)
alpha3.54442693766424
beta0.424635977724107
S.D.0.347801295630908
T-STAT1.22091545678064
p-value0.261641926954288
Lambda0.575364022275893


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 1 ; par3 = 2 ; par4 = 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')