FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationMon, 08 Dec 2008 13:09:35 -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/08/t1228767044pedpvshq31jd7fs.htm/, Retrieved Thu, 16 May 2024 18:03:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30915, Retrieved Thu, 16 May 2024 18:03:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact242

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Cross Correlation Function] [Q7 - zonder trans...] [2008-12-01 20:04:13] [299afd6311e4c20059ea2f05c8dd029d]
F RM D    [Variance Reduction Matrix] [Q8] [2008-12-01 20:20:44] [299afd6311e4c20059ea2f05c8dd029d]
F    D      [Variance Reduction Matrix] [Q8 - 2] [2008-12-01 20:25:07] [299afd6311e4c20059ea2f05c8dd029d]
F RM D          [Standard Deviation-Mean Plot] [Deel 2: Step 1] [2008-12-08 20:09:35] [5e2b1e7aa808f9f0d23fd35605d4968f] [Current]
- RM D            [Variance Reduction Matrix] [Deel 2: Step 2 - VRM] [2008-12-08 20:13:17] [299afd6311e4c20059ea2f05c8dd029d]
-                   [Variance Reduction Matrix] [Totale Uitvoer - VRM] [2008-12-17 16:00:59] [299afd6311e4c20059ea2f05c8dd029d]
-  MPD                [Variance Reduction Matrix] [] [2010-12-24 11:50:15] [4dfa50539945b119a90a7606969443b9]
- RM D            [(Partial) Autocorrelation Function] [Deel 2: Step 2 -...] [2008-12-08 20:20:51] [299afd6311e4c20059ea2f05c8dd029d]
- RM D            [(Partial) Autocorrelation Function] [Deel 2: Step 2 - ...] [2008-12-08 20:22:18] [299afd6311e4c20059ea2f05c8dd029d]
-   P               [(Partial) Autocorrelation Function] [Uitvoer vanuit Be...] [2008-12-13 16:33:20] [299afd6311e4c20059ea2f05c8dd029d]
-   P                 [(Partial) Autocorrelation Function] [Uitvoer vanuit Be...] [2008-12-13 16:37:32] [299afd6311e4c20059ea2f05c8dd029d]
-   P                   [(Partial) Autocorrelation Function] [d=0 D=1] [2008-12-14 13:55:01] [299afd6311e4c20059ea2f05c8dd029d]
-   P               [(Partial) Autocorrelation Function] [Totale Uitvoer d=...] [2008-12-17 16:03:30] [299afd6311e4c20059ea2f05c8dd029d]
- RM D            [(Partial) Autocorrelation Function] [Deel 2: Step 2 - ...] [2008-12-08 20:24:54] [299afd6311e4c20059ea2f05c8dd029d]
- RM D            [Spectral Analysis] [Deel 2: Step 2 - ...] [2008-12-08 20:27:07] [299afd6311e4c20059ea2f05c8dd029d]
-   P               [Spectral Analysis] [Totale Uitvoer - ...] [2008-12-17 16:07:59] [299afd6311e4c20059ea2f05c8dd029d]
-  M D                [Spectral Analysis] [Spectral Analysis...] [2010-12-16 10:45:51] [616fb52b46273b7e6805de1e68b3a688]
-  MPD                [Spectral Analysis] [Spectral Analysis...] [2010-12-16 11:12:29] [616fb52b46273b7e6805de1e68b3a688]
-   P                   [Spectral Analysis] [Spectral Analysis...] [2010-12-16 11:14:45] [616fb52b46273b7e6805de1e68b3a688]
-  MPD                [Spectral Analysis] [] [2010-12-24 12:24:57] [4dfa50539945b119a90a7606969443b9]
-  MPD                [Spectral Analysis] [] [2010-12-24 12:35:52] [4dfa50539945b119a90a7606969443b9]
F RM D            [Spectral Analysis] [Deel 2: Step 2 - ...] [2008-12-08 20:29:17] [299afd6311e4c20059ea2f05c8dd029d]
-   P               [Spectral Analysis] [Totale Uitvoer - ...] [2008-12-17 16:10:49] [299afd6311e4c20059ea2f05c8dd029d]
F RM D            [ARIMA Backward Selection] [Deel 2: Step 5] [2008-12-08 20:35:27] [299afd6311e4c20059ea2f05c8dd029d]
-   P               [ARIMA Backward Selection] [Uitvoer vanuit Be...] [2008-12-14 15:42:25] [299afd6311e4c20059ea2f05c8dd029d]
- RMPD                [Multiple Regression] [] [2010-12-21 16:18:28] [1c63f3c303537b65dfa698074d619a3e]
F RMP               [ARIMA Forecasting] [Uitvoer vanuit Be...] [2008-12-14 15:56:40] [299afd6311e4c20059ea2f05c8dd029d]
- RMPD                [ARIMA Forecasting] [Arima Forecasting] [2010-12-28 19:01:32] [74be16979710d4c4e7c6647856088456]
-    D            [Standard Deviation-Mean Plot] [Totale Uitvoer - SMP] [2008-12-17 15:57:12] [299afd6311e4c20059ea2f05c8dd029d]
-  M D              [Standard Deviation-Mean Plot] [Standard Deviatio...] [2010-12-24 13:19:31] [9f313cc7203314d73bf17d2b325aee79]
- RM D              [Variance Reduction Matrix] [Variance Reductio...] [2010-12-24 13:29:11] [9f313cc7203314d73bf17d2b325aee79]
- RMPD              [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2010-12-24 13:35:08] [9f313cc7203314d73bf17d2b325aee79]
- RMPD              [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2010-12-24 13:37:51] [9f313cc7203314d73bf17d2b325aee79]
- RMPD              [Spectral Analysis] [Spectral Analysis] [2010-12-24 13:45:16] [9f313cc7203314d73bf17d2b325aee79]
- RMPD              [Spectral Analysis] [Spectral Analysis] [2010-12-24 13:47:24] [9f313cc7203314d73bf17d2b325aee79]
- RMPD              [Spectral Analysis] [Spectral Analysis] [2010-12-24 13:51:23] [9f313cc7203314d73bf17d2b325aee79]
- RMPD              [ARIMA Backward Selection] [ARIMA Backward Se...] [2010-12-24 14:04:47] [9f313cc7203314d73bf17d2b325aee79]
- RMPD              [ARIMA Forecasting] [ARIMA Forecasting] [2010-12-24 14:15:31] [9f313cc7203314d73bf17d2b325aee79]
- RMPD                [Standard Deviation-Mean Plot] [Standard Deviatio...] [2010-12-27 09:50:14] [9f313cc7203314d73bf17d2b325aee79]
- RMPD                [Variance Reduction Matrix] [Variance Reductio...] [2010-12-27 09:53:20] [9f313cc7203314d73bf17d2b325aee79]
- RMPD                [Spectral Analysis] [Spectral Analysis] [2010-12-27 10:01:30] [9f313cc7203314d73bf17d2b325aee79]
- RMPD                [Spectral Analysis] [Spectral Analysis] [2010-12-27 10:03:10] [9f313cc7203314d73bf17d2b325aee79]
- RMPD                [Classical Decomposition] [Classical Decompo...] [2010-12-27 10:06:19] [9f313cc7203314d73bf17d2b325aee79]
- RMPD                [Decomposition by Loess] [Decomposition by ...] [2010-12-27 10:08:53] [9f313cc7203314d73bf17d2b325aee79]
- RMPD                [ARIMA Backward Selection] [ARIMA Backward Se...] [2010-12-27 10:15:12] [9f313cc7203314d73bf17d2b325aee79]
-   PD                [ARIMA Forecasting] [ARIMA Forecasting] [2010-12-27 10:20:40] [9f313cc7203314d73bf17d2b325aee79]
Feedback Forum
2008-12-14 22:27:44 [Niels Herremans] [reply] 
Ik denk dat je hier best ook kijkt naar de p-waarde (0.07) in de eerste tabel.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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
22160
20664,3
17877,4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30915&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]4 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=30915&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30915&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
114896.71666666671233.528074510694860
215077.91240.852211550235022.8
316421.8751409.654893372524037.4
417567.63333333331347.030088975774060.5
518598.851511.140765057374907
619666.8251391.760931093484424.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14896.7166666667 & 1233.52807451069 & 4860 \tabularnewline
2 & 15077.9 & 1240.85221155023 & 5022.8 \tabularnewline
3 & 16421.875 & 1409.65489337252 & 4037.4 \tabularnewline
4 & 17567.6333333333 & 1347.03008897577 & 4060.5 \tabularnewline
5 & 18598.85 & 1511.14076505737 & 4907 \tabularnewline
6 & 19666.825 & 1391.76093109348 & 4424.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30915&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]14896.7166666667[/C][C]1233.52807451069[/C][C]4860[/C][/ROW]
[ROW][C]2[/C][C]15077.9[/C][C]1240.85221155023[/C][C]5022.8[/C][/ROW]
[ROW][C]3[/C][C]16421.875[/C][C]1409.65489337252[/C][C]4037.4[/C][/ROW]
[ROW][C]4[/C][C]17567.6333333333[/C][C]1347.03008897577[/C][C]4060.5[/C][/ROW]
[ROW][C]5[/C][C]18598.85[/C][C]1511.14076505737[/C][C]4907[/C][/ROW]
[ROW][C]6[/C][C]19666.825[/C][C]1391.76093109348[/C][C]4424.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30915&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30915&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
114896.71666666671233.528074510694860
215077.91240.852211550235022.8
316421.8751409.654893372524037.4
417567.63333333331347.030088975774060.5
518598.851511.140765057374907
619666.8251391.760931093484424.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha628.901064815833
beta0.0426544958090993
S.D.0.0176709629321909
T-STAT2.41381841910812
p-value0.0732513270899405

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 628.901064815833 \tabularnewline
beta & 0.0426544958090993 \tabularnewline
S.D. & 0.0176709629321909 \tabularnewline
T-STAT & 2.41381841910812 \tabularnewline
p-value & 0.0732513270899405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30915&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]628.901064815833[/C][/ROW]
[ROW][C]beta[/C][C]0.0426544958090993[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0176709629321909[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.41381841910812[/C][/ROW]
[ROW][C]p-value[/C][C]0.0732513270899405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30915&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30915&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)
alpha628.901064815833
beta0.0426544958090993
S.D.0.0176709629321909
T-STAT2.41381841910812
p-value0.0732513270899405






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.82098853610487
beta0.553350721768427
S.D.0.211554993822869
T-STAT2.61563535688378
p-value0.0590693296517506
Lambda0.446649278231573

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.82098853610487 \tabularnewline
beta & 0.553350721768427 \tabularnewline
S.D. & 0.211554993822869 \tabularnewline
T-STAT & 2.61563535688378 \tabularnewline
p-value & 0.0590693296517506 \tabularnewline
Lambda & 0.446649278231573 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30915&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.82098853610487[/C][/ROW]
[ROW][C]beta[/C][C]0.553350721768427[/C][/ROW]
[ROW][C]S.D.[/C][C]0.211554993822869[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.61563535688378[/C][/ROW]
[ROW][C]p-value[/C][C]0.0590693296517506[/C][/ROW]
[ROW][C]Lambda[/C][C]0.446649278231573[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30915&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30915&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)
alpha1.82098853610487
beta0.553350721768427
S.D.0.211554993822869
T-STAT2.61563535688378
p-value0.0590693296517506
Lambda0.446649278231573


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')