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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, 04 Dec 2010 17:22:07 +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/04/t1291483233s5o4w4fpgdbvev9.htm/, Retrieved Sat, 04 May 2024 22:46:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105230, Retrieved Sat, 04 May 2024 22:46:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact170

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] [Opgave 8] [2010-12-04 17:22:07] [781993a4dd4effefeecf3b39fd55765b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
96.1
96.5
96.9
97.8
98.9
100.2
101.2
101
101.6
102.4
103.7
103.7
104.6
104.5
104.5
105.6
106.1
107.6
107.7
108.3
108.1
108.1
108
108.2
108.9
109.8
109.9
109.8
110.9
111.1
112.2
112.7
114.6
114.2
114.7
114.7
116
116.3
116.4
116.6
118.1
117.2
108.3
109.5
110.5
110.6
111.2
111.1
111
112.4
112.5
112.4
111.8
111.6
112.9
112.8
113.7
113.8
114
113.8
113.9
114.4
114.4
114.5
113.8
114.3
115
115.4
115.3
114.9
114.3
114.5
115.5
115.8
115.8
116
114.9
114.1
114.1
113.5
115
114.7
115.4
116.1
116.6
117.2
118.2
118
117.7
118.5
117.5
118
117.7
116.3
115
115.7
113.6
114.8
114.9
117.3
117.3
117.7
120
119.6
119.2
117.3
117.5
119
112.5
118.9
118.4
119.4
120.6
118.6
122
122.6
120.6
117.4
116.4
122.2
121
122.4
124.9
126.1
124.5
123.2
126.4
123.9
116
126.6
125.9
126.6
116.7
126.4
129
128.7
128.4
129.2
133.3
128.9
132.7
127.7
131.8
133.9

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'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105230&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105230&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105230&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
196.8250.7274384280931741.70000000000000
2100.3251.043631480296882.30000000000000
3102.851.034408043278862.10000000000001
4104.80.5354126134736321.09999999999999
5107.4250.9358596760910992.20000000000000
6108.10.08164965809277380.200000000000003
7109.60.4690415759823411
8111.7250.865544144839921.80000000000000
9114.550.2380476142847610.5
10116.3250.2499999999999990.599999999999994
11113.2755.088794880257349.8
12110.850.3511884584284260.700000000000003
13112.0750.718215380880511.5
14112.2750.670198975429441.30000000000001
15113.8250.1258305739211790.299999999999997
16114.30.2708012801545310.599999999999994
17114.6250.7135591542869251.60000000000001
18114.750.4434711565216691
19115.7750.2061552812808830.5
20114.150.5744562646538061.40000000000001
21115.30.6055300708194951.39999999999999
22117.50.7393691004272971.60000000000001
23117.9250.4349329450233291
24116.1751.147097787171322.70000000000000
25115.151.550268793897803.7
26118.651.347837774610382.70000000000000
27118.250.9882644720249081.90000000000001
28117.33.225936556516066.9
29120.951.776701062831524
30119.152.709858544893685.8
31123.62.319482700948645.09999999999999
32124.51.373559851869103.2
33123.7755.1938264635366210.6
34125.25.7844619455918312.3
35129.952.257579825092944.90000000000001
36131.5252.691189328159586.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 96.825 & 0.727438428093174 & 1.70000000000000 \tabularnewline
2 & 100.325 & 1.04363148029688 & 2.30000000000000 \tabularnewline
3 & 102.85 & 1.03440804327886 & 2.10000000000001 \tabularnewline
4 & 104.8 & 0.535412613473632 & 1.09999999999999 \tabularnewline
5 & 107.425 & 0.935859676091099 & 2.20000000000000 \tabularnewline
6 & 108.1 & 0.0816496580927738 & 0.200000000000003 \tabularnewline
7 & 109.6 & 0.469041575982341 & 1 \tabularnewline
8 & 111.725 & 0.86554414483992 & 1.80000000000000 \tabularnewline
9 & 114.55 & 0.238047614284761 & 0.5 \tabularnewline
10 & 116.325 & 0.249999999999999 & 0.599999999999994 \tabularnewline
11 & 113.275 & 5.08879488025734 & 9.8 \tabularnewline
12 & 110.85 & 0.351188458428426 & 0.700000000000003 \tabularnewline
13 & 112.075 & 0.71821538088051 & 1.5 \tabularnewline
14 & 112.275 & 0.67019897542944 & 1.30000000000001 \tabularnewline
15 & 113.825 & 0.125830573921179 & 0.299999999999997 \tabularnewline
16 & 114.3 & 0.270801280154531 & 0.599999999999994 \tabularnewline
17 & 114.625 & 0.713559154286925 & 1.60000000000001 \tabularnewline
18 & 114.75 & 0.443471156521669 & 1 \tabularnewline
19 & 115.775 & 0.206155281280883 & 0.5 \tabularnewline
20 & 114.15 & 0.574456264653806 & 1.40000000000001 \tabularnewline
21 & 115.3 & 0.605530070819495 & 1.39999999999999 \tabularnewline
22 & 117.5 & 0.739369100427297 & 1.60000000000001 \tabularnewline
23 & 117.925 & 0.434932945023329 & 1 \tabularnewline
24 & 116.175 & 1.14709778717132 & 2.70000000000000 \tabularnewline
25 & 115.15 & 1.55026879389780 & 3.7 \tabularnewline
26 & 118.65 & 1.34783777461038 & 2.70000000000000 \tabularnewline
27 & 118.25 & 0.988264472024908 & 1.90000000000001 \tabularnewline
28 & 117.3 & 3.22593655651606 & 6.9 \tabularnewline
29 & 120.95 & 1.77670106283152 & 4 \tabularnewline
30 & 119.15 & 2.70985854489368 & 5.8 \tabularnewline
31 & 123.6 & 2.31948270094864 & 5.09999999999999 \tabularnewline
32 & 124.5 & 1.37355985186910 & 3.2 \tabularnewline
33 & 123.775 & 5.19382646353662 & 10.6 \tabularnewline
34 & 125.2 & 5.78446194559183 & 12.3 \tabularnewline
35 & 129.95 & 2.25757982509294 & 4.90000000000001 \tabularnewline
36 & 131.525 & 2.69118932815958 & 6.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105230&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]96.825[/C][C]0.727438428093174[/C][C]1.70000000000000[/C][/ROW]
[ROW][C]2[/C][C]100.325[/C][C]1.04363148029688[/C][C]2.30000000000000[/C][/ROW]
[ROW][C]3[/C][C]102.85[/C][C]1.03440804327886[/C][C]2.10000000000001[/C][/ROW]
[ROW][C]4[/C][C]104.8[/C][C]0.535412613473632[/C][C]1.09999999999999[/C][/ROW]
[ROW][C]5[/C][C]107.425[/C][C]0.935859676091099[/C][C]2.20000000000000[/C][/ROW]
[ROW][C]6[/C][C]108.1[/C][C]0.0816496580927738[/C][C]0.200000000000003[/C][/ROW]
[ROW][C]7[/C][C]109.6[/C][C]0.469041575982341[/C][C]1[/C][/ROW]
[ROW][C]8[/C][C]111.725[/C][C]0.86554414483992[/C][C]1.80000000000000[/C][/ROW]
[ROW][C]9[/C][C]114.55[/C][C]0.238047614284761[/C][C]0.5[/C][/ROW]
[ROW][C]10[/C][C]116.325[/C][C]0.249999999999999[/C][C]0.599999999999994[/C][/ROW]
[ROW][C]11[/C][C]113.275[/C][C]5.08879488025734[/C][C]9.8[/C][/ROW]
[ROW][C]12[/C][C]110.85[/C][C]0.351188458428426[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]13[/C][C]112.075[/C][C]0.71821538088051[/C][C]1.5[/C][/ROW]
[ROW][C]14[/C][C]112.275[/C][C]0.67019897542944[/C][C]1.30000000000001[/C][/ROW]
[ROW][C]15[/C][C]113.825[/C][C]0.125830573921179[/C][C]0.299999999999997[/C][/ROW]
[ROW][C]16[/C][C]114.3[/C][C]0.270801280154531[/C][C]0.599999999999994[/C][/ROW]
[ROW][C]17[/C][C]114.625[/C][C]0.713559154286925[/C][C]1.60000000000001[/C][/ROW]
[ROW][C]18[/C][C]114.75[/C][C]0.443471156521669[/C][C]1[/C][/ROW]
[ROW][C]19[/C][C]115.775[/C][C]0.206155281280883[/C][C]0.5[/C][/ROW]
[ROW][C]20[/C][C]114.15[/C][C]0.574456264653806[/C][C]1.40000000000001[/C][/ROW]
[ROW][C]21[/C][C]115.3[/C][C]0.605530070819495[/C][C]1.39999999999999[/C][/ROW]
[ROW][C]22[/C][C]117.5[/C][C]0.739369100427297[/C][C]1.60000000000001[/C][/ROW]
[ROW][C]23[/C][C]117.925[/C][C]0.434932945023329[/C][C]1[/C][/ROW]
[ROW][C]24[/C][C]116.175[/C][C]1.14709778717132[/C][C]2.70000000000000[/C][/ROW]
[ROW][C]25[/C][C]115.15[/C][C]1.55026879389780[/C][C]3.7[/C][/ROW]
[ROW][C]26[/C][C]118.65[/C][C]1.34783777461038[/C][C]2.70000000000000[/C][/ROW]
[ROW][C]27[/C][C]118.25[/C][C]0.988264472024908[/C][C]1.90000000000001[/C][/ROW]
[ROW][C]28[/C][C]117.3[/C][C]3.22593655651606[/C][C]6.9[/C][/ROW]
[ROW][C]29[/C][C]120.95[/C][C]1.77670106283152[/C][C]4[/C][/ROW]
[ROW][C]30[/C][C]119.15[/C][C]2.70985854489368[/C][C]5.8[/C][/ROW]
[ROW][C]31[/C][C]123.6[/C][C]2.31948270094864[/C][C]5.09999999999999[/C][/ROW]
[ROW][C]32[/C][C]124.5[/C][C]1.37355985186910[/C][C]3.2[/C][/ROW]
[ROW][C]33[/C][C]123.775[/C][C]5.19382646353662[/C][C]10.6[/C][/ROW]
[ROW][C]34[/C][C]125.2[/C][C]5.78446194559183[/C][C]12.3[/C][/ROW]
[ROW][C]35[/C][C]129.95[/C][C]2.25757982509294[/C][C]4.90000000000001[/C][/ROW]
[ROW][C]36[/C][C]131.525[/C][C]2.69118932815958[/C][C]6.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105230&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105230&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
196.8250.7274384280931741.70000000000000
2100.3251.043631480296882.30000000000000
3102.851.034408043278862.10000000000001
4104.80.5354126134736321.09999999999999
5107.4250.9358596760910992.20000000000000
6108.10.08164965809277380.200000000000003
7109.60.4690415759823411
8111.7250.865544144839921.80000000000000
9114.550.2380476142847610.5
10116.3250.2499999999999990.599999999999994
11113.2755.088794880257349.8
12110.850.3511884584284260.700000000000003
13112.0750.718215380880511.5
14112.2750.670198975429441.30000000000001
15113.8250.1258305739211790.299999999999997
16114.30.2708012801545310.599999999999994
17114.6250.7135591542869251.60000000000001
18114.750.4434711565216691
19115.7750.2061552812808830.5
20114.150.5744562646538061.40000000000001
21115.30.6055300708194951.39999999999999
22117.50.7393691004272971.60000000000001
23117.9250.4349329450233291
24116.1751.147097787171322.70000000000000
25115.151.550268793897803.7
26118.651.347837774610382.70000000000000
27118.250.9882644720249081.90000000000001
28117.33.225936556516066.9
29120.951.776701062831524
30119.152.709858544893685.8
31123.62.319482700948645.09999999999999
32124.51.373559851869103.2
33123.7755.1938264635366210.6
34125.25.7844619455918312.3
35129.952.257579825092944.90000000000001
36131.5252.691189328159586.2






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-9.33088673527087
beta0.0930174495926373
S.D.0.0295195482323912
T-STAT3.15104583784148
p-value0.00338584288079182

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -9.33088673527087 \tabularnewline
beta & 0.0930174495926373 \tabularnewline
S.D. & 0.0295195482323912 \tabularnewline
T-STAT & 3.15104583784148 \tabularnewline
p-value & 0.00338584288079182 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105230&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-9.33088673527087[/C][/ROW]
[ROW][C]beta[/C][C]0.0930174495926373[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0295195482323912[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.15104583784148[/C][/ROW]
[ROW][C]p-value[/C][C]0.00338584288079182[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105230&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105230&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-9.33088673527087
beta0.0930174495926373
S.D.0.0295195482323912
T-STAT3.15104583784148
p-value0.00338584288079182






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-32.1968698691165
beta6.75427634760799
S.D.2.42118334224771
T-STAT2.78965918431342
p-value0.00858485247969788
Lambda-5.75427634760799

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -32.1968698691165 \tabularnewline
beta & 6.75427634760799 \tabularnewline
S.D. & 2.42118334224771 \tabularnewline
T-STAT & 2.78965918431342 \tabularnewline
p-value & 0.00858485247969788 \tabularnewline
Lambda & -5.75427634760799 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105230&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-32.1968698691165[/C][/ROW]
[ROW][C]beta[/C][C]6.75427634760799[/C][/ROW]
[ROW][C]S.D.[/C][C]2.42118334224771[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.78965918431342[/C][/ROW]
[ROW][C]p-value[/C][C]0.00858485247969788[/C][/ROW]
[ROW][C]Lambda[/C][C]-5.75427634760799[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105230&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105230&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-32.1968698691165
beta6.75427634760799
S.D.2.42118334224771
T-STAT2.78965918431342
p-value0.00858485247969788
Lambda-5.75427634760799


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')