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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, 13 Dec 2009 09:04:32 -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/13/t12607205871z54ggnusgl5mc5.htm/, Retrieved Sat, 04 May 2024 06:12:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67350, Retrieved Sat, 04 May 2024 06:12:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113

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] [Standard deviatio...] [2008-12-19 15:05:52] [072df11bdb18ed8d65d8164df87f26f2]
-  MPD    [Standard Deviation-Mean Plot] [] [2009-12-13 16:04:32] [66ffaa9e54a90d3ae4874684602d24e9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
17823.2
17872
17420.4
16704.4
15991.2
16583.6
19123.5
17838.7
17209.4
18586.5
16258.1
15141.6
19202.1
17746.5
19090.1
18040.3
17515.5
17751.8
21072.4
17170
19439.5
19795.4
17574.9
16165.4
19464.6
19932.1
19961.2
17343.4
18924.2
18574.1
21350.6
18594.6
19823.1
20844.4
19640.2
17735.4
19813.6
22160
20664.3
17877.4
20906.5
21164.1
21374.4
22952.3
21343.5
23899.3
22392.9
18274.1
22786.7
22321.5
17842.2
16373.5
15993.8
16446.1
17729
16643
16196.7
18252.1
17570.4
15836.8

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67350&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]1 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=67350&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67350&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
117455539.7708649664841167.60000000000
217384.251392.018209890473132.3
316798.91460.950825090753444.9
418519.75734.5494106366611455.6
518377.4251812.464871153833902.4
618243.81693.550001230163630
719175.3251242.301244666532617.8
819360.8751336.149056991772776.5
919510.7751296.766461562503109
1020128.8251787.054064421854282.6
1121599.325922.0556540505932045.8
1221477.452379.271593716595625.2
1319830.9753206.679717272476413.2
1416702.975736.0340226511281735.2
15169641138.163974712492415.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 17455 & 539.770864966484 & 1167.60000000000 \tabularnewline
2 & 17384.25 & 1392.01820989047 & 3132.3 \tabularnewline
3 & 16798.9 & 1460.95082509075 & 3444.9 \tabularnewline
4 & 18519.75 & 734.549410636661 & 1455.6 \tabularnewline
5 & 18377.425 & 1812.46487115383 & 3902.4 \tabularnewline
6 & 18243.8 & 1693.55000123016 & 3630 \tabularnewline
7 & 19175.325 & 1242.30124466653 & 2617.8 \tabularnewline
8 & 19360.875 & 1336.14905699177 & 2776.5 \tabularnewline
9 & 19510.775 & 1296.76646156250 & 3109 \tabularnewline
10 & 20128.825 & 1787.05406442185 & 4282.6 \tabularnewline
11 & 21599.325 & 922.055654050593 & 2045.8 \tabularnewline
12 & 21477.45 & 2379.27159371659 & 5625.2 \tabularnewline
13 & 19830.975 & 3206.67971727247 & 6413.2 \tabularnewline
14 & 16702.975 & 736.034022651128 & 1735.2 \tabularnewline
15 & 16964 & 1138.16397471249 & 2415.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67350&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]17455[/C][C]539.770864966484[/C][C]1167.60000000000[/C][/ROW]
[ROW][C]2[/C][C]17384.25[/C][C]1392.01820989047[/C][C]3132.3[/C][/ROW]
[ROW][C]3[/C][C]16798.9[/C][C]1460.95082509075[/C][C]3444.9[/C][/ROW]
[ROW][C]4[/C][C]18519.75[/C][C]734.549410636661[/C][C]1455.6[/C][/ROW]
[ROW][C]5[/C][C]18377.425[/C][C]1812.46487115383[/C][C]3902.4[/C][/ROW]
[ROW][C]6[/C][C]18243.8[/C][C]1693.55000123016[/C][C]3630[/C][/ROW]
[ROW][C]7[/C][C]19175.325[/C][C]1242.30124466653[/C][C]2617.8[/C][/ROW]
[ROW][C]8[/C][C]19360.875[/C][C]1336.14905699177[/C][C]2776.5[/C][/ROW]
[ROW][C]9[/C][C]19510.775[/C][C]1296.76646156250[/C][C]3109[/C][/ROW]
[ROW][C]10[/C][C]20128.825[/C][C]1787.05406442185[/C][C]4282.6[/C][/ROW]
[ROW][C]11[/C][C]21599.325[/C][C]922.055654050593[/C][C]2045.8[/C][/ROW]
[ROW][C]12[/C][C]21477.45[/C][C]2379.27159371659[/C][C]5625.2[/C][/ROW]
[ROW][C]13[/C][C]19830.975[/C][C]3206.67971727247[/C][C]6413.2[/C][/ROW]
[ROW][C]14[/C][C]16702.975[/C][C]736.034022651128[/C][C]1735.2[/C][/ROW]
[ROW][C]15[/C][C]16964[/C][C]1138.16397471249[/C][C]2415.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67350&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67350&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
117455539.7708649664841167.60000000000
217384.251392.018209890473132.3
316798.91460.950825090753444.9
418519.75734.5494106366611455.6
518377.4251812.464871153833902.4
618243.81693.550001230163630
719175.3251242.301244666532617.8
819360.8751336.149056991772776.5
919510.7751296.766461562503109
1020128.8251787.054064421854282.6
1121599.325922.0556540505932045.8
1221477.452379.271593716595625.2
1319830.9753206.679717272476413.2
1416702.975736.0340226511281735.2
15169641138.163974712492415.3






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1930.17517066029
beta0.179840409466352
S.D.0.109377219035864
T-STAT1.64422181375250
p-value0.124082738349169

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1930.17517066029 \tabularnewline
beta & 0.179840409466352 \tabularnewline
S.D. & 0.109377219035864 \tabularnewline
T-STAT & 1.64422181375250 \tabularnewline
p-value & 0.124082738349169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67350&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1930.17517066029[/C][/ROW]
[ROW][C]beta[/C][C]0.179840409466352[/C][/ROW]
[ROW][C]S.D.[/C][C]0.109377219035864[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.64422181375250[/C][/ROW]
[ROW][C]p-value[/C][C]0.124082738349169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67350&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67350&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-1930.17517066029
beta0.179840409466352
S.D.0.109377219035864
T-STAT1.64422181375250
p-value0.124082738349169






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-15.4521058647511
beta2.30040462801488
S.D.1.41324133826877
T-STAT1.62775073564781
p-value0.127559662730827
Lambda-1.30040462801488

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -15.4521058647511 \tabularnewline
beta & 2.30040462801488 \tabularnewline
S.D. & 1.41324133826877 \tabularnewline
T-STAT & 1.62775073564781 \tabularnewline
p-value & 0.127559662730827 \tabularnewline
Lambda & -1.30040462801488 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67350&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-15.4521058647511[/C][/ROW]
[ROW][C]beta[/C][C]2.30040462801488[/C][/ROW]
[ROW][C]S.D.[/C][C]1.41324133826877[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.62775073564781[/C][/ROW]
[ROW][C]p-value[/C][C]0.127559662730827[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.30040462801488[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67350&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67350&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-15.4521058647511
beta2.30040462801488
S.D.1.41324133826877
T-STAT1.62775073564781
p-value0.127559662730827
Lambda-1.30040462801488


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')