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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 computationSat, 18 Dec 2010 16:48:24 +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/18/t12926907612161favq19m92fj.htm/, Retrieved Tue, 30 Apr 2024 06:56:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112096, Retrieved Tue, 30 Apr 2024 06:56:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [] [] [1970-01-01 00:00:00] [ed939ef6f97e5f2afb6796311d9e7a5f]
- RMPD  [Standard Deviation-Mean Plot] [] [2010-12-17 17:32:20] [ed939ef6f97e5f2afb6796311d9e7a5f]
-           [Standard Deviation-Mean Plot] [Paper] [2010-12-18 16:48:24] [476d588d86fe88306e0383abd6004235] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
31.514
27.071
29.462
26.105
22.397
23.843
21.705
18.089
20.764
25.316
17.704
15.548
28.029
29.383
36.438
32.034
22.679
24.319
18.004
17.537
20.366
22.782
19.169
13.807
29.743
25.591
29.096
26.482
22.405
27.044
17.970
18.730
19.684
19.785
18.479
10.698
31.956
29.506
34.506
27.165
26.736
23.691
18.157
17.328
18.205
20.995
17.382
9.367
31.124
26.551
30.651
25.859
25.100
25.778
20.418
18.688
20.424
24.776
19.814
12.738
31.566
30.111
30.019
31.934
25.826
26.835
20.205
17.789
20.520
22.518
15.572
11.509
25.447
24.090
27.786
26.195
20.516
22.759
19.028
16.971
20.036
22.485
18.730
14.538

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112096&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112096&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112096&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
123.29316666666674.8639772508688515.966
223.712256.6398206865848422.631
322.142255.6083585043786519.045
422.91616666666677.3030689045251725.139
523.49341666666675.2659772719589218.386
623.70033333333336.7312083790671820.425
721.54841666666673.9571273662120413.248

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 23.2931666666667 & 4.86397725086885 & 15.966 \tabularnewline
2 & 23.71225 & 6.63982068658484 & 22.631 \tabularnewline
3 & 22.14225 & 5.60835850437865 & 19.045 \tabularnewline
4 & 22.9161666666667 & 7.30306890452517 & 25.139 \tabularnewline
5 & 23.4934166666667 & 5.26597727195892 & 18.386 \tabularnewline
6 & 23.7003333333333 & 6.73120837906718 & 20.425 \tabularnewline
7 & 21.5484166666667 & 3.95712736621204 & 13.248 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112096&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]23.2931666666667[/C][C]4.86397725086885[/C][C]15.966[/C][/ROW]
[ROW][C]2[/C][C]23.71225[/C][C]6.63982068658484[/C][C]22.631[/C][/ROW]
[ROW][C]3[/C][C]22.14225[/C][C]5.60835850437865[/C][C]19.045[/C][/ROW]
[ROW][C]4[/C][C]22.9161666666667[/C][C]7.30306890452517[/C][C]25.139[/C][/ROW]
[ROW][C]5[/C][C]23.4934166666667[/C][C]5.26597727195892[/C][C]18.386[/C][/ROW]
[ROW][C]6[/C][C]23.7003333333333[/C][C]6.73120837906718[/C][C]20.425[/C][/ROW]
[ROW][C]7[/C][C]21.5484166666667[/C][C]3.95712736621204[/C][C]13.248[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112096&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112096&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
123.29316666666674.8639772508688515.966
223.712256.6398206865848422.631
322.142255.6083585043786519.045
422.91616666666677.3030689045251725.139
523.49341666666675.2659772719589218.386
623.70033333333336.7312083790671820.425
721.54841666666673.9571273662120413.248






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-13.0631764482304
beta0.819694373973662
S.D.0.518859884659224
T-STAT1.57979909067748
p-value0.17498944695869

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -13.0631764482304 \tabularnewline
beta & 0.819694373973662 \tabularnewline
S.D. & 0.518859884659224 \tabularnewline
T-STAT & 1.57979909067748 \tabularnewline
p-value & 0.17498944695869 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112096&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-13.0631764482304[/C][/ROW]
[ROW][C]beta[/C][C]0.819694373973662[/C][/ROW]
[ROW][C]S.D.[/C][C]0.518859884659224[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.57979909067748[/C][/ROW]
[ROW][C]p-value[/C][C]0.17498944695869[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112096&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112096&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-13.0631764482304
beta0.819694373973662
S.D.0.518859884659224
T-STAT1.57979909067748
p-value0.17498944695869






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-9.58961765650983
beta3.61316467316827
S.D.2.0500452030062
T-STAT1.76248048963501
p-value0.138280699420952
Lambda-2.61316467316827

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -9.58961765650983 \tabularnewline
beta & 3.61316467316827 \tabularnewline
S.D. & 2.0500452030062 \tabularnewline
T-STAT & 1.76248048963501 \tabularnewline
p-value & 0.138280699420952 \tabularnewline
Lambda & -2.61316467316827 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112096&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-9.58961765650983[/C][/ROW]
[ROW][C]beta[/C][C]3.61316467316827[/C][/ROW]
[ROW][C]S.D.[/C][C]2.0500452030062[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.76248048963501[/C][/ROW]
[ROW][C]p-value[/C][C]0.138280699420952[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.61316467316827[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112096&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112096&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-9.58961765650983
beta3.61316467316827
S.D.2.0500452030062
T-STAT1.76248048963501
p-value0.138280699420952
Lambda-2.61316467316827


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')