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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 04 May 2011 15:07:18 +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/2011/May/04/t130452140202o4k8q86uyf72j.htm/, Retrieved Mon, 13 May 2024 07:24:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=120964, Retrieved Mon, 13 May 2024 07:24:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact77

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] [] [2011-05-04 15:07:18] [70ebd814bf1379a9657d768a4ecd0382] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
70938
34077
45409
40809
37013
44953
19848
32745
43412
34931
33008
8620
68906
39556
50669
36432
40891
48428
36222
33425
39401
37967
34801
12657
69116
41519
51321
38529
41547
52073
38401
40898
40439
41888
37898
8771
68184
50530
47221
41756
45633
48138
39486
39341
41117
41629
29722
7054
56676
34870
35117
30169
30936
35699
33228
27733
33666
35429
27438
8170
63410
38040
45389
37353
37024
50957
37994
36454
46080
43373
37395
10963
75001

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' @ www.wessa.org

\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' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120964&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' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120964&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120964&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' @ www.wessa.org






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
137146.916666666715038.115201400962318
239946.2513041.080554261156249
341866.666666666713729.544184536960345
441650.916666666714210.663611005361130
532427.583333333310727.02833931348506
640369.333333333312173.25027436952447

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 37146.9166666667 & 15038.1152014009 & 62318 \tabularnewline
2 & 39946.25 & 13041.0805542611 & 56249 \tabularnewline
3 & 41866.6666666667 & 13729.5441845369 & 60345 \tabularnewline
4 & 41650.9166666667 & 14210.6636110053 & 61130 \tabularnewline
5 & 32427.5833333333 & 10727.028339313 & 48506 \tabularnewline
6 & 40369.3333333333 & 12173.250274369 & 52447 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120964&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]37146.9166666667[/C][C]15038.1152014009[/C][C]62318[/C][/ROW]
[ROW][C]2[/C][C]39946.25[/C][C]13041.0805542611[/C][C]56249[/C][/ROW]
[ROW][C]3[/C][C]41866.6666666667[/C][C]13729.5441845369[/C][C]60345[/C][/ROW]
[ROW][C]4[/C][C]41650.9166666667[/C][C]14210.6636110053[/C][C]61130[/C][/ROW]
[ROW][C]5[/C][C]32427.5833333333[/C][C]10727.028339313[/C][C]48506[/C][/ROW]
[ROW][C]6[/C][C]40369.3333333333[/C][C]12173.250274369[/C][C]52447[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120964&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120964&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
137146.916666666715038.115201400962318
239946.2513041.080554261156249
341866.666666666713729.544184536960345
441650.916666666714210.663611005361130
532427.583333333310727.02833931348506
640369.333333333312173.25027436952447






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3841.44583796332
beta0.239370916709847
S.D.0.177740245397018
T-STAT1.34674573096917
p-value0.249307537365594

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3841.44583796332 \tabularnewline
beta & 0.239370916709847 \tabularnewline
S.D. & 0.177740245397018 \tabularnewline
T-STAT & 1.34674573096917 \tabularnewline
p-value & 0.249307537365594 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120964&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3841.44583796332[/C][/ROW]
[ROW][C]beta[/C][C]0.239370916709847[/C][/ROW]
[ROW][C]S.D.[/C][C]0.177740245397018[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.34674573096917[/C][/ROW]
[ROW][C]p-value[/C][C]0.249307537365594[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120964&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120964&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)
alpha3841.44583796332
beta0.239370916709847
S.D.0.177740245397018
T-STAT1.34674573096917
p-value0.249307537365594






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.40915051877591
beta0.763779666196239
S.D.0.49080725798675
T-STAT1.55617027614709
p-value0.194652040806554
Lambda0.236220333803761

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.40915051877591 \tabularnewline
beta & 0.763779666196239 \tabularnewline
S.D. & 0.49080725798675 \tabularnewline
T-STAT & 1.55617027614709 \tabularnewline
p-value & 0.194652040806554 \tabularnewline
Lambda & 0.236220333803761 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120964&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.40915051877591[/C][/ROW]
[ROW][C]beta[/C][C]0.763779666196239[/C][/ROW]
[ROW][C]S.D.[/C][C]0.49080725798675[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.55617027614709[/C][/ROW]
[ROW][C]p-value[/C][C]0.194652040806554[/C][/ROW]
[ROW][C]Lambda[/C][C]0.236220333803761[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120964&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120964&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)
alpha1.40915051877591
beta0.763779666196239
S.D.0.49080725798675
T-STAT1.55617027614709
p-value0.194652040806554
Lambda0.236220333803761


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')