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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, 07 Dec 2008 07:07:45 -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/2008/Dec/07/t1228658920fph1a0vz324jup3.htm/, Retrieved Sun, 19 May 2024 10:10:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29995, Retrieved Sun, 19 May 2024 10:10:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact212

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP   [Standard Deviation-Mean Plot] [Q1: SMP] [2008-12-07 13:37:37] [1ce0d16c8f4225c977b42c8fa93bc163]
F    D      [Standard Deviation-Mean Plot] [Q1: SMP eigen tij...] [2008-12-07 14:07:45] [8758b22b4a10c08c31202f233362e983] [Current]
Feedback Forum
2008-12-14 13:31:40 [Matthieu Blondeau] [reply] 
Dit is correct. De Beta is positief dus er is een stijgende lijn in de grafiek. De p-waarde bedraagt 0,001 dus de kans dat ons resultaat aan het toeval te wijten is, is klein.
2008-12-14 20:30:17 [Michaël De Kuyer] [reply] 
De beta-coëfficiënt is slechts heel beperkt niet significant verschillend van nul, in principe zouden we niet meer naar de volgende tabel moeten kijken. Op de standard deviation mean plot kunnen we echter een verband opmerken tussen het gemiddelde en de standaardafwijking. Naar mijn mening moet er een transformatie plaatsvinden en dit met een waarde van 0,30.
2008-12-15 19:10:29 [be464a3cae54f8118e26892c61355e0b] [reply] 
5.54261828820849e-05 is de wetenschappelijke notatie voor een zeer klein getal, niet een zeer groot. De relevante p-waarde moet trouwens teruggevonden worden in de eerste tabel, niet in de tweede.
2008-12-15 22:31:48 [Niels Herremans] [reply] 
de Beta waarde is net niet significant verschillend van 0. Maar we nemen toch een transformatie met lambda waarde 0.3. De p-waarde is enorm klein en niet hoog zoals jij besluit in je document. De kans op toeval is dus ook enorm klein.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9568,3
9920,3
11353,5
9247,5
10114,2
10763,1
8456,1
8071,6
10328
10551,4
10186,1
8821,6
9841,3
10233,6
10794,6
10289,3
10513,4
10607,6
9707,4
8103,5
10982,6
11836,9
10517,5
9810,5
10374,8
10855,3
11671,3
11901,2
10846,4
11917,5
11362,8
9314,5
12605,9
12815,1
11254,5
11111,8
11282,9
11554,5
12935,6
12146,3
11615,3
13214,8
11735,5
9522,3
12694,8
12317,6
11450
11380,9
10604,6
10972,2
13331,5
11733,1
11284,7
13295,8
11881,4
10374,2
13828
13490,5
13092,2
13184,4
12398,4
13882,3
15861,5
13286,1
15634,9
14211
13646,8
12224,6
15916,4
16535,9
15796
14418,6
15044,5
14944,2
16754,8
14254
15454,9
15644,8
14568,3
12520,2
14803
15873,2
14755,3
12875,1
14291,1
14205,3
15859,4
15258,9
15498,6
15106,5
15023,6
12083
15761,3
16943
15070,3
13659,6
14768,9
14725,1
15998,1
15370,6
14956,9
15469,7
15101,8
11703,7
16283,6
16726,5
14968,9
14861
14583,3
15305,8
17903,9
16379,4
15420,3
17870,5
15912,8
13866,5
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
22238,5
20682,2
17818,6
21872,1
22117
21865,9
23451,3
20953,7
22497,3

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=29995&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=29995&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29995&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
19781.80833333333979.4361545467543281.9
210269.85898.459045962993733.4
311335.925958.653250540953500.6
411820.875968.9036354420023692.5
512256.051245.640558471463453.8
614484.3751453.422786594084311.3
714791.0251185.201388429984234.6
814896.71666666671233.528074510694860
915077.91240.852211550235022.8
1016421.8751409.654893372524037.4
1117567.63333333331347.030088975774060.5
1218598.851511.140765057374907
1319669.95833333331412.746523271304503.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9781.80833333333 & 979.436154546754 & 3281.9 \tabularnewline
2 & 10269.85 & 898.45904596299 & 3733.4 \tabularnewline
3 & 11335.925 & 958.65325054095 & 3500.6 \tabularnewline
4 & 11820.875 & 968.903635442002 & 3692.5 \tabularnewline
5 & 12256.05 & 1245.64055847146 & 3453.8 \tabularnewline
6 & 14484.375 & 1453.42278659408 & 4311.3 \tabularnewline
7 & 14791.025 & 1185.20138842998 & 4234.6 \tabularnewline
8 & 14896.7166666667 & 1233.52807451069 & 4860 \tabularnewline
9 & 15077.9 & 1240.85221155023 & 5022.8 \tabularnewline
10 & 16421.875 & 1409.65489337252 & 4037.4 \tabularnewline
11 & 17567.6333333333 & 1347.03008897577 & 4060.5 \tabularnewline
12 & 18598.85 & 1511.14076505737 & 4907 \tabularnewline
13 & 19669.9583333333 & 1412.74652327130 & 4503.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29995&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]9781.80833333333[/C][C]979.436154546754[/C][C]3281.9[/C][/ROW]
[ROW][C]2[/C][C]10269.85[/C][C]898.45904596299[/C][C]3733.4[/C][/ROW]
[ROW][C]3[/C][C]11335.925[/C][C]958.65325054095[/C][C]3500.6[/C][/ROW]
[ROW][C]4[/C][C]11820.875[/C][C]968.903635442002[/C][C]3692.5[/C][/ROW]
[ROW][C]5[/C][C]12256.05[/C][C]1245.64055847146[/C][C]3453.8[/C][/ROW]
[ROW][C]6[/C][C]14484.375[/C][C]1453.42278659408[/C][C]4311.3[/C][/ROW]
[ROW][C]7[/C][C]14791.025[/C][C]1185.20138842998[/C][C]4234.6[/C][/ROW]
[ROW][C]8[/C][C]14896.7166666667[/C][C]1233.52807451069[/C][C]4860[/C][/ROW]
[ROW][C]9[/C][C]15077.9[/C][C]1240.85221155023[/C][C]5022.8[/C][/ROW]
[ROW][C]10[/C][C]16421.875[/C][C]1409.65489337252[/C][C]4037.4[/C][/ROW]
[ROW][C]11[/C][C]17567.6333333333[/C][C]1347.03008897577[/C][C]4060.5[/C][/ROW]
[ROW][C]12[/C][C]18598.85[/C][C]1511.14076505737[/C][C]4907[/C][/ROW]
[ROW][C]13[/C][C]19669.9583333333[/C][C]1412.74652327130[/C][C]4503.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29995&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29995&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
19781.80833333333979.4361545467543281.9
210269.85898.459045962993733.4
311335.925958.653250540953500.6
411820.875968.9036354420023692.5
512256.051245.640558471463453.8
614484.3751453.422786594084311.3
714791.0251185.201388429984234.6
814896.71666666671233.528074510694860
915077.91240.852211550235022.8
1016421.8751409.654893372524037.4
1117567.63333333331347.030088975774060.5
1218598.851511.140765057374907
1319669.95833333331412.746523271304503.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha389.767914790725
beta0.0576430586836833
S.D.0.00982600060410413
T-STAT5.86638053529194
p-value0.000108277031872625

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 389.767914790725 \tabularnewline
beta & 0.0576430586836833 \tabularnewline
S.D. & 0.00982600060410413 \tabularnewline
T-STAT & 5.86638053529194 \tabularnewline
p-value & 0.000108277031872625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29995&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]389.767914790725[/C][/ROW]
[ROW][C]beta[/C][C]0.0576430586836833[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00982600060410413[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.86638053529194[/C][/ROW]
[ROW][C]p-value[/C][C]0.000108277031872625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29995&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29995&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)
alpha389.767914790725
beta0.0576430586836833
S.D.0.00982600060410413
T-STAT5.86638053529194
p-value0.000108277031872625






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.365100396759141
beta0.704250321112686
S.D.0.111129476383701
T-STAT6.33720542946764
p-value5.54261828820849e-05
Lambda0.295749678887314

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.365100396759141 \tabularnewline
beta & 0.704250321112686 \tabularnewline
S.D. & 0.111129476383701 \tabularnewline
T-STAT & 6.33720542946764 \tabularnewline
p-value & 5.54261828820849e-05 \tabularnewline
Lambda & 0.295749678887314 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29995&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.365100396759141[/C][/ROW]
[ROW][C]beta[/C][C]0.704250321112686[/C][/ROW]
[ROW][C]S.D.[/C][C]0.111129476383701[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.33720542946764[/C][/ROW]
[ROW][C]p-value[/C][C]5.54261828820849e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]0.295749678887314[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29995&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29995&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)
alpha0.365100396759141
beta0.704250321112686
S.D.0.111129476383701
T-STAT6.33720542946764
p-value5.54261828820849e-05
Lambda0.295749678887314


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')