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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 computationSat, 17 May 2008 04:59:31 -0600
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/May/17/t1211022091dr0oaus4ydm1p38.htm/, Retrieved Mon, 13 May 2024 20:56:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12639, Retrieved Mon, 13 May 2024 20:56:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact229

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] [standaard deviati...] [2008-05-17 10:59:31] [9eefa1691b07b95ff73d963c22019b45] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.1591
1.1203
1.0886
1.0701
1.0630
1.0377
1.0370
1.0606
1.0497
1.0706
1.0328
1.0110
1.0131
0.9834
0.9643
0.9449
0.9059
0.9505
0.9386
0.9045
0.8695
0.8525
0.8552
0.8983
0.9376
0.9205
0.9083
0.8925
0.8753
0.8530
0.8615
0.9014
0.9114
0.9050
0.8883
0.8912
0.8832
0.8706
0.8766
0.8860
0.9170
0.9561
0.9935
0.9781
0.9806
0.9812
1.0013
1.0194
1.0622
1.0785
1.0805
1.0862
1.1556
1.1674
1.1365
1.1155
1.1266
1.1714
1.1710
1.2298
1.2638
1.2640
1.2261
1.1989
1.2000
1.2146
1.2266
1.2191
1.2224
1.2507
1.2997
1.3406

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=12639&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=12639&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12639&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
11.1095250.03901267956276100.089
21.0495750.01415306209506150.026
31.0410250.02529220894531230.0596000000000001
40.9764250.02906628917950600.0681999999999999
50.9248750.02323938825930380.046
60.8688750.02098703965149280.0458000000000000
70.9147250.01907745178651140.0451
80.87280.02116553802765240.0484
90.8989750.01103158344632960.0231
100.87910.006902173570694940.0154000000000000
110.9611750.03320917292957880.0765
120.9956250.01854083331460590.0388000000000001
131.076850.01029708696671050.024
141.143750.02273301563805380.0519000000000001
151.17470.04232493354985920.1032
161.23820.03168543303580790.0651
171.2150750.01120278983110900.0266000000000000
181.278350.052363505102950.1182

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.109525 & 0.0390126795627610 & 0.089 \tabularnewline
2 & 1.049575 & 0.0141530620950615 & 0.026 \tabularnewline
3 & 1.041025 & 0.0252922089453123 & 0.0596000000000001 \tabularnewline
4 & 0.976425 & 0.0290662891795060 & 0.0681999999999999 \tabularnewline
5 & 0.924875 & 0.0232393882593038 & 0.046 \tabularnewline
6 & 0.868875 & 0.0209870396514928 & 0.0458000000000000 \tabularnewline
7 & 0.914725 & 0.0190774517865114 & 0.0451 \tabularnewline
8 & 0.8728 & 0.0211655380276524 & 0.0484 \tabularnewline
9 & 0.898975 & 0.0110315834463296 & 0.0231 \tabularnewline
10 & 0.8791 & 0.00690217357069494 & 0.0154000000000000 \tabularnewline
11 & 0.961175 & 0.0332091729295788 & 0.0765 \tabularnewline
12 & 0.995625 & 0.0185408333146059 & 0.0388000000000001 \tabularnewline
13 & 1.07685 & 0.0102970869667105 & 0.024 \tabularnewline
14 & 1.14375 & 0.0227330156380538 & 0.0519000000000001 \tabularnewline
15 & 1.1747 & 0.0423249335498592 & 0.1032 \tabularnewline
16 & 1.2382 & 0.0316854330358079 & 0.0651 \tabularnewline
17 & 1.215075 & 0.0112027898311090 & 0.0266000000000000 \tabularnewline
18 & 1.27835 & 0.05236350510295 & 0.1182 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12639&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]1.109525[/C][C]0.0390126795627610[/C][C]0.089[/C][/ROW]
[ROW][C]2[/C][C]1.049575[/C][C]0.0141530620950615[/C][C]0.026[/C][/ROW]
[ROW][C]3[/C][C]1.041025[/C][C]0.0252922089453123[/C][C]0.0596000000000001[/C][/ROW]
[ROW][C]4[/C][C]0.976425[/C][C]0.0290662891795060[/C][C]0.0681999999999999[/C][/ROW]
[ROW][C]5[/C][C]0.924875[/C][C]0.0232393882593038[/C][C]0.046[/C][/ROW]
[ROW][C]6[/C][C]0.868875[/C][C]0.0209870396514928[/C][C]0.0458000000000000[/C][/ROW]
[ROW][C]7[/C][C]0.914725[/C][C]0.0190774517865114[/C][C]0.0451[/C][/ROW]
[ROW][C]8[/C][C]0.8728[/C][C]0.0211655380276524[/C][C]0.0484[/C][/ROW]
[ROW][C]9[/C][C]0.898975[/C][C]0.0110315834463296[/C][C]0.0231[/C][/ROW]
[ROW][C]10[/C][C]0.8791[/C][C]0.00690217357069494[/C][C]0.0154000000000000[/C][/ROW]
[ROW][C]11[/C][C]0.961175[/C][C]0.0332091729295788[/C][C]0.0765[/C][/ROW]
[ROW][C]12[/C][C]0.995625[/C][C]0.0185408333146059[/C][C]0.0388000000000001[/C][/ROW]
[ROW][C]13[/C][C]1.07685[/C][C]0.0102970869667105[/C][C]0.024[/C][/ROW]
[ROW][C]14[/C][C]1.14375[/C][C]0.0227330156380538[/C][C]0.0519000000000001[/C][/ROW]
[ROW][C]15[/C][C]1.1747[/C][C]0.0423249335498592[/C][C]0.1032[/C][/ROW]
[ROW][C]16[/C][C]1.2382[/C][C]0.0316854330358079[/C][C]0.0651[/C][/ROW]
[ROW][C]17[/C][C]1.215075[/C][C]0.0112027898311090[/C][C]0.0266000000000000[/C][/ROW]
[ROW][C]18[/C][C]1.27835[/C][C]0.05236350510295[/C][C]0.1182[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12639&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12639&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
11.1095250.03901267956276100.089
21.0495750.01415306209506150.026
31.0410250.02529220894531230.0596000000000001
40.9764250.02906628917950600.0681999999999999
50.9248750.02323938825930380.046
60.8688750.02098703965149280.0458000000000000
70.9147250.01907745178651140.0451
80.87280.02116553802765240.0484
90.8989750.01103158344632960.0231
100.87910.006902173570694940.0154000000000000
110.9611750.03320917292957880.0765
120.9956250.01854083331460590.0388000000000001
131.076850.01029708696671050.024
141.143750.02273301563805380.0519000000000001
151.17470.04232493354985920.1032
161.23820.03168543303580790.0651
171.2150750.01120278983110900.0266000000000000
181.278350.052363505102950.1182






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.0243782292399154
beta0.0467835582731542
S.D.0.0194546661133964
T-STAT2.40474742668234
p-value0.0286472672686761

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0243782292399154 \tabularnewline
beta & 0.0467835582731542 \tabularnewline
S.D. & 0.0194546661133964 \tabularnewline
T-STAT & 2.40474742668234 \tabularnewline
p-value & 0.0286472672686761 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12639&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0243782292399154[/C][/ROW]
[ROW][C]beta[/C][C]0.0467835582731542[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0194546661133964[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.40474742668234[/C][/ROW]
[ROW][C]p-value[/C][C]0.0286472672686761[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12639&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12639&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-0.0243782292399154
beta0.0467835582731542
S.D.0.0194546661133964
T-STAT2.40474742668234
p-value0.0286472672686761






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.9047853457954
beta1.78666886303345
S.D.0.958679638099591
T-STAT1.86367665696457
p-value0.0808247794064633
Lambda-0.78666886303345

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.9047853457954 \tabularnewline
beta & 1.78666886303345 \tabularnewline
S.D. & 0.958679638099591 \tabularnewline
T-STAT & 1.86367665696457 \tabularnewline
p-value & 0.0808247794064633 \tabularnewline
Lambda & -0.78666886303345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12639&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.9047853457954[/C][/ROW]
[ROW][C]beta[/C][C]1.78666886303345[/C][/ROW]
[ROW][C]S.D.[/C][C]0.958679638099591[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.86367665696457[/C][/ROW]
[ROW][C]p-value[/C][C]0.0808247794064633[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.78666886303345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12639&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12639&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-3.9047853457954
beta1.78666886303345
S.D.0.958679638099591
T-STAT1.86367665696457
p-value0.0808247794064633
Lambda-0.78666886303345


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')