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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 computationThu, 03 Jun 2010 11:43:16 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/03/t1275565564vfrjw20u96fx9pq.htm/, Retrieved Sun, 05 May 2024 21:41:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77355, Retrieved Sun, 05 May 2024 21:41:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact172

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] [] [2010-06-03 11:43:16] [917a4afc20628654d1f716afbd7d9cc1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2953
2635
2404
2413
2136
1565
1451
2037
2477
2785
2994
2681
3098
2708
2517
2445
2087
1801
1216
2173
2286
3121
3458
3511
3524
2767
2744
2603
2527
1846
1066
2327
3066
3048
3806
4042
3583
3438
2957
2885
2744
1837
1447
2504
3248
3098
4318
3561
3316
3379
2717
2354
2445
1542
1606
2590
3588
3202
4704
4005
3810
3488
2781
2944
2817
1960
1937
2903
3357
3552
4581
3905
4581
4037
3345
3175
2808
2050
1719
3143
3756
4776
4540
4309
4563
3506
3665
3361
3094
2440
1633
2935
4159
4159
4894
4921
4577
4155
3851
3429
3370
2726

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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77355&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77355&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77355&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' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12377.58333333333499.1293252588281543
22535.08333333333685.9292911257272295
32780.5823.7738546690852976
42968.33333333333782.4005406827162871
52954932.2906296760783162
63169.58333333333774.9161196053692644
73519.91666666667995.0964739281533057
83610.83333333333997.8855676181543288

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2377.58333333333 & 499.129325258828 & 1543 \tabularnewline
2 & 2535.08333333333 & 685.929291125727 & 2295 \tabularnewline
3 & 2780.5 & 823.773854669085 & 2976 \tabularnewline
4 & 2968.33333333333 & 782.400540682716 & 2871 \tabularnewline
5 & 2954 & 932.290629676078 & 3162 \tabularnewline
6 & 3169.58333333333 & 774.916119605369 & 2644 \tabularnewline
7 & 3519.91666666667 & 995.096473928153 & 3057 \tabularnewline
8 & 3610.83333333333 & 997.885567618154 & 3288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77355&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]2377.58333333333[/C][C]499.129325258828[/C][C]1543[/C][/ROW]
[ROW][C]2[/C][C]2535.08333333333[/C][C]685.929291125727[/C][C]2295[/C][/ROW]
[ROW][C]3[/C][C]2780.5[/C][C]823.773854669085[/C][C]2976[/C][/ROW]
[ROW][C]4[/C][C]2968.33333333333[/C][C]782.400540682716[/C][C]2871[/C][/ROW]
[ROW][C]5[/C][C]2954[/C][C]932.290629676078[/C][C]3162[/C][/ROW]
[ROW][C]6[/C][C]3169.58333333333[/C][C]774.916119605369[/C][C]2644[/C][/ROW]
[ROW][C]7[/C][C]3519.91666666667[/C][C]995.096473928153[/C][C]3057[/C][/ROW]
[ROW][C]8[/C][C]3610.83333333333[/C][C]997.885567618154[/C][C]3288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77355&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77355&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
12377.58333333333499.1293252588281543
22535.08333333333685.9292911257272295
32780.5823.7738546690852976
42968.33333333333782.4005406827162871
52954932.2906296760783162
63169.58333333333774.9161196053692644
73519.91666666667995.0964739281533057
83610.83333333333997.8855676181543288






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-199.763040652068
beta0.338249811956402
S.D.0.0768458025563894
T-STAT4.40166932615734
p-value0.0045601497239967

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -199.763040652068 \tabularnewline
beta & 0.338249811956402 \tabularnewline
S.D. & 0.0768458025563894 \tabularnewline
T-STAT & 4.40166932615734 \tabularnewline
p-value & 0.0045601497239967 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77355&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-199.763040652068[/C][/ROW]
[ROW][C]beta[/C][C]0.338249811956402[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0768458025563894[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.40166932615734[/C][/ROW]
[ROW][C]p-value[/C][C]0.0045601497239967[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77355&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77355&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-199.763040652068
beta0.338249811956402
S.D.0.0768458025563894
T-STAT4.40166932615734
p-value0.0045601497239967






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.21493824049792
beta1.36264029317512
S.D.0.314802949744403
T-STAT4.32854995253852
p-value0.00493647609908891
Lambda-0.362640293175124

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.21493824049792 \tabularnewline
beta & 1.36264029317512 \tabularnewline
S.D. & 0.314802949744403 \tabularnewline
T-STAT & 4.32854995253852 \tabularnewline
p-value & 0.00493647609908891 \tabularnewline
Lambda & -0.362640293175124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77355&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.21493824049792[/C][/ROW]
[ROW][C]beta[/C][C]1.36264029317512[/C][/ROW]
[ROW][C]S.D.[/C][C]0.314802949744403[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.32854995253852[/C][/ROW]
[ROW][C]p-value[/C][C]0.00493647609908891[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.362640293175124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77355&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77355&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-4.21493824049792
beta1.36264029317512
S.D.0.314802949744403
T-STAT4.32854995253852
p-value0.00493647609908891
Lambda-0.362640293175124


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')