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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 computationSun, 18 Dec 2016 10:51:30 +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/18/t14820548213re0vr7nc0fop96.htm/, Retrieved Wed, 08 May 2024 19:54:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300988, Retrieved Wed, 08 May 2024 19:54:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94

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] [st dev mean plot ...] [2016-12-18 09:51:30] [afe7f6443461a2cd6ee0b843643e84a9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2119.9
2108.7
2092
2104.2
2110.1
2114
2138.8
2165.5
2155.1
2135.2
2163.1
2175.2
2183.3
2201.5
2212.3
2223.8
2241.9
2269.2
2261.4
2273.4
2299.3
2315.5
2338.7
2333
2311
2303.6
2310.5
2295.8
2265.5
2271.1
2231.9
2245
2249.7
2300.5
2280.4
2290.7
2261.5
2259.1
2249.8
2271.2
2259
2259.4
2250.2
2243.3
2234.3
2216.5
2197.6
2211.7
2206.7
2214.6
2229.8
2219.5
2213.8
2214.1
2224.1
2229.6
2251.7
2262.9
2268.9
2293.7
2312.4
2342
2327.4
2366.2
2371.8
2364.4
2370.5
2412.8
2447.3
2443.5
2459.3
2480.7
2504.4
2505.5
2534
2538.7
2538.1
2522
2566.4
2572.8
2557.3
2541
2540.7
2508.5
2567.1
2553.6
2522.4
2520.6
2499.4
2470.8
2479.3
2481.8
2470.3
2491
2479.1
2456.6
2456.1
2482.2
2444.7
2425.3
2389.3
2367.7
2339.3
2342.4
2343.6
2346.3
2363.5
2338.7
2369.4
2356
2348.6
2349.7
2371.9
2364.9
2394.1
2399.2
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA

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=300988&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=300988&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300988&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
12131.8166666666727.652283592477383.1999999999998
22262.77551.821075477419155.4
32279.6416666666726.929823222365979.0999999999999
42242.823.037795033379473.5999999999999
52235.7833333333327.242007446166187
62391.52555.4684697496121168.3
72535.7833333333322.714386043504168.4000000000001
82499.3333333333334.6309722997238110.5
92386.5916666666751.9610423706301143.5
102369.22518.991257387094150.5999999999999
11NaNNA-Inf
12NaNNA-Inf

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2131.81666666667 & 27.6522835924773 & 83.1999999999998 \tabularnewline
2 & 2262.775 & 51.821075477419 & 155.4 \tabularnewline
3 & 2279.64166666667 & 26.9298232223659 & 79.0999999999999 \tabularnewline
4 & 2242.8 & 23.0377950333794 & 73.5999999999999 \tabularnewline
5 & 2235.78333333333 & 27.2420074461661 & 87 \tabularnewline
6 & 2391.525 & 55.4684697496121 & 168.3 \tabularnewline
7 & 2535.78333333333 & 22.7143860435041 & 68.4000000000001 \tabularnewline
8 & 2499.33333333333 & 34.6309722997238 & 110.5 \tabularnewline
9 & 2386.59166666667 & 51.9610423706301 & 143.5 \tabularnewline
10 & 2369.225 & 18.9912573870941 & 50.5999999999999 \tabularnewline
11 & NaN & NA & -Inf \tabularnewline
12 & NaN & NA & -Inf \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300988&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]2131.81666666667[/C][C]27.6522835924773[/C][C]83.1999999999998[/C][/ROW]
[ROW][C]2[/C][C]2262.775[/C][C]51.821075477419[/C][C]155.4[/C][/ROW]
[ROW][C]3[/C][C]2279.64166666667[/C][C]26.9298232223659[/C][C]79.0999999999999[/C][/ROW]
[ROW][C]4[/C][C]2242.8[/C][C]23.0377950333794[/C][C]73.5999999999999[/C][/ROW]
[ROW][C]5[/C][C]2235.78333333333[/C][C]27.2420074461661[/C][C]87[/C][/ROW]
[ROW][C]6[/C][C]2391.525[/C][C]55.4684697496121[/C][C]168.3[/C][/ROW]
[ROW][C]7[/C][C]2535.78333333333[/C][C]22.7143860435041[/C][C]68.4000000000001[/C][/ROW]
[ROW][C]8[/C][C]2499.33333333333[/C][C]34.6309722997238[/C][C]110.5[/C][/ROW]
[ROW][C]9[/C][C]2386.59166666667[/C][C]51.9610423706301[/C][C]143.5[/C][/ROW]
[ROW][C]10[/C][C]2369.225[/C][C]18.9912573870941[/C][C]50.5999999999999[/C][/ROW]
[ROW][C]11[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[ROW][C]12[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300988&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300988&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
12131.8166666666727.652283592477383.1999999999998
22262.77551.821075477419155.4
32279.6416666666726.929823222365979.0999999999999
42242.823.037795033379473.5999999999999
52235.7833333333327.242007446166187
62391.52555.4684697496121168.3
72535.7833333333322.714386043504168.4000000000001
82499.3333333333334.6309722997238110.5
92386.5916666666751.9610423706301143.5
102369.22518.991257387094150.5999999999999
11NaNNA-Inf
12NaNNA-Inf






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha8.77789288851649
beta0.0108278211307648
S.D.0.0385788099689007
T-STAT0.280667577343452
p-value0.786087066831435

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 8.77789288851649 \tabularnewline
beta & 0.0108278211307648 \tabularnewline
S.D. & 0.0385788099689007 \tabularnewline
T-STAT & 0.280667577343452 \tabularnewline
p-value & 0.786087066831435 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300988&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.77789288851649[/C][/ROW]
[ROW][C]beta[/C][C]0.0108278211307648[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0385788099689007[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.280667577343452[/C][/ROW]
[ROW][C]p-value[/C][C]0.786087066831435[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300988&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300988&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)
alpha8.77789288851649
beta0.0108278211307648
S.D.0.0385788099689007
T-STAT0.280667577343452
p-value0.786087066831435






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.19981653912245
beta0.600720045810547
S.D.2.53836073506416
T-STAT0.236656688512542
p-value0.818870248943773
Lambda0.399279954189453

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.19981653912245 \tabularnewline
beta & 0.600720045810547 \tabularnewline
S.D. & 2.53836073506416 \tabularnewline
T-STAT & 0.236656688512542 \tabularnewline
p-value & 0.818870248943773 \tabularnewline
Lambda & 0.399279954189453 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300988&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.19981653912245[/C][/ROW]
[ROW][C]beta[/C][C]0.600720045810547[/C][/ROW]
[ROW][C]S.D.[/C][C]2.53836073506416[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.236656688512542[/C][/ROW]
[ROW][C]p-value[/C][C]0.818870248943773[/C][/ROW]
[ROW][C]Lambda[/C][C]0.399279954189453[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300988&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300988&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-1.19981653912245
beta0.600720045810547
S.D.2.53836073506416
T-STAT0.236656688512542
p-value0.818870248943773
Lambda0.399279954189453


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = n1862 ; 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')