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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 computationMon, 06 Dec 2010 20:16:01 +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/Dec/06/t1291666451tfrme2xbhyflu5i.htm/, Retrieved Mon, 29 Apr 2024 01:24:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105859, Retrieved Mon, 29 Apr 2024 01:24:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177

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] [WS9: SMP] [2010-12-03 10:37:40] [1fd136673b2a4fecb5c545b9b4a05d64]
F   P     [Standard Deviation-Mean Plot] [WS9: stationary v...] [2010-12-06 20:16:01] [380f6bceef280be3d93cc6fafd18141e] [Current]
- R PD      [Standard Deviation-Mean Plot] [] [2011-12-06 23:10:28] [74be16979710d4c4e7c6647856088456]
Feedback Forum
2010-12-13 18:29:30 [Stefanie Van Esbroeck] [reply] 
Je maakt hier een correcte berekening maar je interpretatie vind ik aan de korte kant. Je zegt wel dat we hier nu een nieuwe waarde te zien krijgen: de lambda waarde en hoeveel deze waarde juist is en daar stopt het dan. Je had hier nog aan kunnen toevoegen dat die lambdawaarde (als je die afrond op 0 decimalen) dat die dan gelijk is aan 1 en dat je hierdoor weet dat je geen transformatie moet doorvoeren.
2010-12-13 18:29:49 [00c625c7d009d84797af914265b614f9] [reply] 
Er is hier duidelijk geen verband tussen gemiddelde en variantie, we mogen zeggen dat de slope (beta) gelijk is aan 0. De kans dat we ons vergissen bij het verwerpen van de nulhypothese ( beta = 0 ) is zeer groot namelijk 73%. Er moet hier dus geen box-cox transformatie gebeuren.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
46
62
66
59
58
61
41
27
58
70
49
59
44
36
72
45
56
54
53
35
61
52
47
51
52
63
74
45
51
64
36
30
55
64
39
40
63
45
59
55
40
64
27
28
45
57
45
69
60
56
58
50
51
53
37
22
55
70
62
58
39
49
58
47
42
62
39
40
72
70
54
65

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105859&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105859&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105859&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
154.666666666666711.972189997378643
250.510.264679067736937
351.083333333333313.466850433789744
449.7513.712137954116742
552.666666666666712.470571418950848
653.083333333333312.191340692425433

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 54.6666666666667 & 11.9721899973786 & 43 \tabularnewline
2 & 50.5 & 10.2646790677369 & 37 \tabularnewline
3 & 51.0833333333333 & 13.4668504337897 & 44 \tabularnewline
4 & 49.75 & 13.7121379541167 & 42 \tabularnewline
5 & 52.6666666666667 & 12.4705714189508 & 48 \tabularnewline
6 & 53.0833333333333 & 12.1913406924254 & 33 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105859&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]54.6666666666667[/C][C]11.9721899973786[/C][C]43[/C][/ROW]
[ROW][C]2[/C][C]50.5[/C][C]10.2646790677369[/C][C]37[/C][/ROW]
[ROW][C]3[/C][C]51.0833333333333[/C][C]13.4668504337897[/C][C]44[/C][/ROW]
[ROW][C]4[/C][C]49.75[/C][C]13.7121379541167[/C][C]42[/C][/ROW]
[ROW][C]5[/C][C]52.6666666666667[/C][C]12.4705714189508[/C][C]48[/C][/ROW]
[ROW][C]6[/C][C]53.0833333333333[/C][C]12.1913406924254[/C][C]33[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105859&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105859&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
154.666666666666711.972189997378643
250.510.264679067736937
351.083333333333313.466850433789744
449.7513.712137954116742
552.666666666666712.470571418950848
653.083333333333312.191340692425433






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha18.6919922134069
beta-0.122130501093963
S.D.0.330735930979881
T-STAT-0.36926892319236
p-value0.730644321403997

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 18.6919922134069 \tabularnewline
beta & -0.122130501093963 \tabularnewline
S.D. & 0.330735930979881 \tabularnewline
T-STAT & -0.36926892319236 \tabularnewline
p-value & 0.730644321403997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105859&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]18.6919922134069[/C][/ROW]
[ROW][C]beta[/C][C]-0.122130501093963[/C][/ROW]
[ROW][C]S.D.[/C][C]0.330735930979881[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.36926892319236[/C][/ROW]
[ROW][C]p-value[/C][C]0.730644321403997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105859&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105859&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)
alpha18.6919922134069
beta-0.122130501093963
S.D.0.330735930979881
T-STAT-0.36926892319236
p-value0.730644321403997






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha4.09200505081255
beta-0.400772512903985
S.D.1.45747244856086
T-STAT-0.274977762564031
p-value0.796952199848244
Lambda1.40077251290398

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.09200505081255 \tabularnewline
beta & -0.400772512903985 \tabularnewline
S.D. & 1.45747244856086 \tabularnewline
T-STAT & -0.274977762564031 \tabularnewline
p-value & 0.796952199848244 \tabularnewline
Lambda & 1.40077251290398 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105859&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.09200505081255[/C][/ROW]
[ROW][C]beta[/C][C]-0.400772512903985[/C][/ROW]
[ROW][C]S.D.[/C][C]1.45747244856086[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.274977762564031[/C][/ROW]
[ROW][C]p-value[/C][C]0.796952199848244[/C][/ROW]
[ROW][C]Lambda[/C][C]1.40077251290398[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105859&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105859&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)
alpha4.09200505081255
beta-0.400772512903985
S.D.1.45747244856086
T-STAT-0.274977762564031
p-value0.796952199848244
Lambda1.40077251290398


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = pearson ;
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')