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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 computationWed, 09 Dec 2009 07:29:45 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/09/t1260370027f504vz2vnwtoph9.htm/, Retrieved Mon, 29 Apr 2024 13:21:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64976, Retrieved Mon, 29 Apr 2024 13:21:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
- R  D        [Standard Deviation-Mean Plot] [WS08 - Heteroskel...] [2009-11-25 22:14:53] [df6326eec97a6ca984a853b142930499]
-    D            [Standard Deviation-Mean Plot] [WS10 - Heteroskel...] [2009-12-09 14:29:45] [0cc924834281808eda7297686c82928f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
286.1
307
358.1
341.8
378.8
375.2
295.6
362.7
409.6
336.8
389.1
389.3
355.9
542
648.4
452
582.4
506.5
555.5
530.4
609.4
543.9
616.2
634.6
541.7
549.8
627.6
797.4
689.8
1576.6
1572.1
1626.4
1972.4
1509.6
1584.9
1880
1324
1777.7
2172.4
1780.3
2134.9
1838.4
1557
1755.2
1702
1577.5
1485.9
2179.1
1740.9
1724.5
2328.1
1774.1
2224.2
1536.3
1521.2
2051.8
2483.1
1929.8
1808.6
2584.9
1997.9
1639.9
2379.1
1715
2750.9
1865.4
1647.4
2180.4
2593
2057.2
2635.8
2315.4
1863.6
2038
2235.8
2222.1
2636.9
2076.8
1935.5
2086.3
2470.9
1854.6
2041.3
2170.8
1905.5
2130.2
2791.2
2539.7
2661.3
1764.9
2176.9
2458.5
2179
2242.5
2089.6
2661.6
2112
2367.3
2543
2603.9
3146.7
1789.2
2114.8
2236.3
2288.1
2173.2
1877.7
2807.4
2357.4
2107.7
2856.8
2510.8
2875
2229.7
2055.1
2545.4
2775.1
2252.2
2091.7
2433

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64976&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64976&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64976&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1352.50833333333339.7427971366187123.5
2548.182.8161380847521292.5
31244.025551.6914439414321430.7
41773.7275.353878094750855.1
51975.625357.8795407421581063.7
62148.11666666667391.8295311932881111
72136.05233.506447253798782.3
82300.075320.9802149807541026.3
92338.3386.3419328663521357.5
102424.15833333333294.587605300986819.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 352.508333333333 & 39.7427971366187 & 123.5 \tabularnewline
2 & 548.1 & 82.8161380847521 & 292.5 \tabularnewline
3 & 1244.025 & 551.691443941432 & 1430.7 \tabularnewline
4 & 1773.7 & 275.353878094750 & 855.1 \tabularnewline
5 & 1975.625 & 357.879540742158 & 1063.7 \tabularnewline
6 & 2148.11666666667 & 391.829531193288 & 1111 \tabularnewline
7 & 2136.05 & 233.506447253798 & 782.3 \tabularnewline
8 & 2300.075 & 320.980214980754 & 1026.3 \tabularnewline
9 & 2338.3 & 386.341932866352 & 1357.5 \tabularnewline
10 & 2424.15833333333 & 294.587605300986 & 819.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64976&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]352.508333333333[/C][C]39.7427971366187[/C][C]123.5[/C][/ROW]
[ROW][C]2[/C][C]548.1[/C][C]82.8161380847521[/C][C]292.5[/C][/ROW]
[ROW][C]3[/C][C]1244.025[/C][C]551.691443941432[/C][C]1430.7[/C][/ROW]
[ROW][C]4[/C][C]1773.7[/C][C]275.353878094750[/C][C]855.1[/C][/ROW]
[ROW][C]5[/C][C]1975.625[/C][C]357.879540742158[/C][C]1063.7[/C][/ROW]
[ROW][C]6[/C][C]2148.11666666667[/C][C]391.829531193288[/C][C]1111[/C][/ROW]
[ROW][C]7[/C][C]2136.05[/C][C]233.506447253798[/C][C]782.3[/C][/ROW]
[ROW][C]8[/C][C]2300.075[/C][C]320.980214980754[/C][C]1026.3[/C][/ROW]
[ROW][C]9[/C][C]2338.3[/C][C]386.341932866352[/C][C]1357.5[/C][/ROW]
[ROW][C]10[/C][C]2424.15833333333[/C][C]294.587605300986[/C][C]819.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64976&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64976&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
1352.50833333333339.7427971366187123.5
2548.182.8161380847521292.5
31244.025551.6914439414321430.7
41773.7275.353878094750855.1
51975.625357.8795407421581063.7
62148.11666666667391.8295311932881111
72136.05233.506447253798782.3
82300.075320.9802149807541026.3
92338.3386.3419328663521357.5
102424.15833333333294.587605300986819.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha98.5077133328543
beta0.113084567803125
S.D.0.0579437007728248
T-STAT1.95162832706331
p-value0.0867735879710064

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 98.5077133328543 \tabularnewline
beta & 0.113084567803125 \tabularnewline
S.D. & 0.0579437007728248 \tabularnewline
T-STAT & 1.95162832706331 \tabularnewline
p-value & 0.0867735879710064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64976&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]98.5077133328543[/C][/ROW]
[ROW][C]beta[/C][C]0.113084567803125[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0579437007728248[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.95162832706331[/C][/ROW]
[ROW][C]p-value[/C][C]0.0867735879710064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64976&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64976&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)
alpha98.5077133328543
beta0.113084567803125
S.D.0.0579437007728248
T-STAT1.95162832706331
p-value0.0867735879710064






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.07376600668275
beta1.03408881014465
S.D.0.208769016359639
T-STAT4.95326762647224
p-value0.00111629266457383
Lambda-0.0340888101446539

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.07376600668275 \tabularnewline
beta & 1.03408881014465 \tabularnewline
S.D. & 0.208769016359639 \tabularnewline
T-STAT & 4.95326762647224 \tabularnewline
p-value & 0.00111629266457383 \tabularnewline
Lambda & -0.0340888101446539 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64976&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.07376600668275[/C][/ROW]
[ROW][C]beta[/C][C]1.03408881014465[/C][/ROW]
[ROW][C]S.D.[/C][C]0.208769016359639[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.95326762647224[/C][/ROW]
[ROW][C]p-value[/C][C]0.00111629266457383[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0340888101446539[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64976&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64976&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-2.07376600668275
beta1.03408881014465
S.D.0.208769016359639
T-STAT4.95326762647224
p-value0.00111629266457383
Lambda-0.0340888101446539


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')