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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 computationMon, 06 Dec 2010 21:49:19 +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/t12916720763ts3dv8vcxityzl.htm/, Retrieved Sun, 28 Apr 2024 20:39:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105935, Retrieved Sun, 28 Apr 2024 20:39:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120

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] [Katrien Monnens] [2010-12-06 21:49:19] [3f9379635061ebc5737ab9ab2503b0b0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
103.6
103.5
110.9
115.8
117.8
121.1
128.7
112.7
111.3
116.2
109.8
137.9
98.7
100.5
128.7
98.7
115
121
125.9
117.3
115
113.8
115.7
145.5
101.7
106.9
116.4
114.6
122.5
120.4
116.5
117
114.3
111.5
117.8
141.5
102.6
103.8
119.8
113.6
121.8
123.9
122.7
120
111.6
117.6
121.3
143.7
107.1
107.7
126.4
111.5
127.9
124.9
122
124.9
113.9
120.8
123.3
143.5
107.1
106.5
114.6
122.2
120.2
123.1
127.1
118.5
116.1
120.6
115.7
146.5
108
106.6
122.2
115.8
115.6
124.5
121.7
118.7
113.7
113.4
115.1
143.9
101
103.4
121.5
111.9
117.4
124.3
122
119.7
115
112.2
115.3
142.6
104.1
105.3
124.4
113.9
124.8
131.8
125.6
125
119.7
116.1
120
148.1
109.2
109.4
135.1
114.9
129
138.5
125.6
130.4
120.3
126.2
127.6
150.9
114.6
118.6
131.4
124.5
136.8
136.8
136.6
131
125.8
129.4
124.8
157.1
116.6
114.2
128.4
127.3
133.5
137.2
137.7
131.2
127.7
133.9
124.3
160.6

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'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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105935&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105935&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105935&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1108.456.0013887281750612.3
2120.0756.7083902689095216
3118.813.023312430663228.1
4106.6514.724469430169630
5119.84.758851402036710.9
6122.515.353392676104731.7
7109.96.8454364360499314.7
8119.12.853068523537426
9121.27513.727436031539230
10109.958.2095472875589617.2
11122.11.64316767251553.90000000000001
12123.5514.015348729161232.1
13113.1759.0293502903955819.3
14124.9252.408837894089185.9
15125.37512.72042321098929.6
16112.67.385120175054715.7
17122.2253.764195354477058.6
18124.72514.685678965123430.8
19113.157.2652139220626815.6
20120.1253.835253142449238.9
21121.52514.935053844339930.5
22109.459.2953393339529720.5
23120.852.969287232092356.89999999999999
24121.27514.285044627161630.4
25111.9259.3923284298055420.3
26126.83.350621832834427.00000000000001
27125.97514.856059369832932
28117.1512.254658977983325.9
29130.8755.4683178400674612.9
30131.2513.476522795835230.6
31122.2757.3172740826075416.8
32135.32.868216635239865.80000000000001
33134.27515.344352924338932.3
34121.6257.2683675379459614.2
35134.93.097310661417956.5
36136.62516.470048573091736.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 108.45 & 6.00138872817506 & 12.3 \tabularnewline
2 & 120.075 & 6.70839026890952 & 16 \tabularnewline
3 & 118.8 & 13.0233124306632 & 28.1 \tabularnewline
4 & 106.65 & 14.7244694301696 & 30 \tabularnewline
5 & 119.8 & 4.7588514020367 & 10.9 \tabularnewline
6 & 122.5 & 15.3533926761047 & 31.7 \tabularnewline
7 & 109.9 & 6.84543643604993 & 14.7 \tabularnewline
8 & 119.1 & 2.85306852353742 & 6 \tabularnewline
9 & 121.275 & 13.7274360315392 & 30 \tabularnewline
10 & 109.95 & 8.20954728755896 & 17.2 \tabularnewline
11 & 122.1 & 1.6431676725155 & 3.90000000000001 \tabularnewline
12 & 123.55 & 14.0153487291612 & 32.1 \tabularnewline
13 & 113.175 & 9.02935029039558 & 19.3 \tabularnewline
14 & 124.925 & 2.40883789408918 & 5.9 \tabularnewline
15 & 125.375 & 12.720423210989 & 29.6 \tabularnewline
16 & 112.6 & 7.3851201750547 & 15.7 \tabularnewline
17 & 122.225 & 3.76419535447705 & 8.6 \tabularnewline
18 & 124.725 & 14.6856789651234 & 30.8 \tabularnewline
19 & 113.15 & 7.26521392206268 & 15.6 \tabularnewline
20 & 120.125 & 3.83525314244923 & 8.9 \tabularnewline
21 & 121.525 & 14.9350538443399 & 30.5 \tabularnewline
22 & 109.45 & 9.29533933395297 & 20.5 \tabularnewline
23 & 120.85 & 2.96928723209235 & 6.89999999999999 \tabularnewline
24 & 121.275 & 14.2850446271616 & 30.4 \tabularnewline
25 & 111.925 & 9.39232842980554 & 20.3 \tabularnewline
26 & 126.8 & 3.35062183283442 & 7.00000000000001 \tabularnewline
27 & 125.975 & 14.8560593698329 & 32 \tabularnewline
28 & 117.15 & 12.2546589779833 & 25.9 \tabularnewline
29 & 130.875 & 5.46831784006746 & 12.9 \tabularnewline
30 & 131.25 & 13.4765227958352 & 30.6 \tabularnewline
31 & 122.275 & 7.31727408260754 & 16.8 \tabularnewline
32 & 135.3 & 2.86821663523986 & 5.80000000000001 \tabularnewline
33 & 134.275 & 15.3443529243389 & 32.3 \tabularnewline
34 & 121.625 & 7.26836753794596 & 14.2 \tabularnewline
35 & 134.9 & 3.09731066141795 & 6.5 \tabularnewline
36 & 136.625 & 16.4700485730917 & 36.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105935&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]108.45[/C][C]6.00138872817506[/C][C]12.3[/C][/ROW]
[ROW][C]2[/C][C]120.075[/C][C]6.70839026890952[/C][C]16[/C][/ROW]
[ROW][C]3[/C][C]118.8[/C][C]13.0233124306632[/C][C]28.1[/C][/ROW]
[ROW][C]4[/C][C]106.65[/C][C]14.7244694301696[/C][C]30[/C][/ROW]
[ROW][C]5[/C][C]119.8[/C][C]4.7588514020367[/C][C]10.9[/C][/ROW]
[ROW][C]6[/C][C]122.5[/C][C]15.3533926761047[/C][C]31.7[/C][/ROW]
[ROW][C]7[/C][C]109.9[/C][C]6.84543643604993[/C][C]14.7[/C][/ROW]
[ROW][C]8[/C][C]119.1[/C][C]2.85306852353742[/C][C]6[/C][/ROW]
[ROW][C]9[/C][C]121.275[/C][C]13.7274360315392[/C][C]30[/C][/ROW]
[ROW][C]10[/C][C]109.95[/C][C]8.20954728755896[/C][C]17.2[/C][/ROW]
[ROW][C]11[/C][C]122.1[/C][C]1.6431676725155[/C][C]3.90000000000001[/C][/ROW]
[ROW][C]12[/C][C]123.55[/C][C]14.0153487291612[/C][C]32.1[/C][/ROW]
[ROW][C]13[/C][C]113.175[/C][C]9.02935029039558[/C][C]19.3[/C][/ROW]
[ROW][C]14[/C][C]124.925[/C][C]2.40883789408918[/C][C]5.9[/C][/ROW]
[ROW][C]15[/C][C]125.375[/C][C]12.720423210989[/C][C]29.6[/C][/ROW]
[ROW][C]16[/C][C]112.6[/C][C]7.3851201750547[/C][C]15.7[/C][/ROW]
[ROW][C]17[/C][C]122.225[/C][C]3.76419535447705[/C][C]8.6[/C][/ROW]
[ROW][C]18[/C][C]124.725[/C][C]14.6856789651234[/C][C]30.8[/C][/ROW]
[ROW][C]19[/C][C]113.15[/C][C]7.26521392206268[/C][C]15.6[/C][/ROW]
[ROW][C]20[/C][C]120.125[/C][C]3.83525314244923[/C][C]8.9[/C][/ROW]
[ROW][C]21[/C][C]121.525[/C][C]14.9350538443399[/C][C]30.5[/C][/ROW]
[ROW][C]22[/C][C]109.45[/C][C]9.29533933395297[/C][C]20.5[/C][/ROW]
[ROW][C]23[/C][C]120.85[/C][C]2.96928723209235[/C][C]6.89999999999999[/C][/ROW]
[ROW][C]24[/C][C]121.275[/C][C]14.2850446271616[/C][C]30.4[/C][/ROW]
[ROW][C]25[/C][C]111.925[/C][C]9.39232842980554[/C][C]20.3[/C][/ROW]
[ROW][C]26[/C][C]126.8[/C][C]3.35062183283442[/C][C]7.00000000000001[/C][/ROW]
[ROW][C]27[/C][C]125.975[/C][C]14.8560593698329[/C][C]32[/C][/ROW]
[ROW][C]28[/C][C]117.15[/C][C]12.2546589779833[/C][C]25.9[/C][/ROW]
[ROW][C]29[/C][C]130.875[/C][C]5.46831784006746[/C][C]12.9[/C][/ROW]
[ROW][C]30[/C][C]131.25[/C][C]13.4765227958352[/C][C]30.6[/C][/ROW]
[ROW][C]31[/C][C]122.275[/C][C]7.31727408260754[/C][C]16.8[/C][/ROW]
[ROW][C]32[/C][C]135.3[/C][C]2.86821663523986[/C][C]5.80000000000001[/C][/ROW]
[ROW][C]33[/C][C]134.275[/C][C]15.3443529243389[/C][C]32.3[/C][/ROW]
[ROW][C]34[/C][C]121.625[/C][C]7.26836753794596[/C][C]14.2[/C][/ROW]
[ROW][C]35[/C][C]134.9[/C][C]3.09731066141795[/C][C]6.5[/C][/ROW]
[ROW][C]36[/C][C]136.625[/C][C]16.4700485730917[/C][C]36.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105935&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105935&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
1108.456.0013887281750612.3
2120.0756.7083902689095216
3118.813.023312430663228.1
4106.6514.724469430169630
5119.84.758851402036710.9
6122.515.353392676104731.7
7109.96.8454364360499314.7
8119.12.853068523537426
9121.27513.727436031539230
10109.958.2095472875589617.2
11122.11.64316767251553.90000000000001
12123.5514.015348729161232.1
13113.1759.0293502903955819.3
14124.9252.408837894089185.9
15125.37512.72042321098929.6
16112.67.385120175054715.7
17122.2253.764195354477058.6
18124.72514.685678965123430.8
19113.157.2652139220626815.6
20120.1253.835253142449238.9
21121.52514.935053844339930.5
22109.459.2953393339529720.5
23120.852.969287232092356.89999999999999
24121.27514.285044627161630.4
25111.9259.3923284298055420.3
26126.83.350621832834427.00000000000001
27125.97514.856059369832932
28117.1512.254658977983325.9
29130.8755.4683178400674612.9
30131.2513.476522795835230.6
31122.2757.3172740826075416.8
32135.32.868216635239865.80000000000001
33134.27515.344352924338932.3
34121.6257.2683675379459614.2
35134.93.097310661417956.5
36136.62516.470048573091736.3






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4.9436787347441
beta0.0329396696083206
S.D.0.10353819647582
T-STAT0.318140268321296
p-value0.752324473491293

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4.9436787347441 \tabularnewline
beta & 0.0329396696083206 \tabularnewline
S.D. & 0.10353819647582 \tabularnewline
T-STAT & 0.318140268321296 \tabularnewline
p-value & 0.752324473491293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105935&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.9436787347441[/C][/ROW]
[ROW][C]beta[/C][C]0.0329396696083206[/C][/ROW]
[ROW][C]S.D.[/C][C]0.10353819647582[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.318140268321296[/C][/ROW]
[ROW][C]p-value[/C][C]0.752324473491293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105935&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105935&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)
alpha4.9436787347441
beta0.0329396696083206
S.D.0.10353819647582
T-STAT0.318140268321296
p-value0.752324473491293






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha5.8596193774501
beta-0.802864558325808
S.D.1.71597253256789
T-STAT-0.46787727838764
p-value0.642857704219085
Lambda1.80286455832581

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.8596193774501 \tabularnewline
beta & -0.802864558325808 \tabularnewline
S.D. & 1.71597253256789 \tabularnewline
T-STAT & -0.46787727838764 \tabularnewline
p-value & 0.642857704219085 \tabularnewline
Lambda & 1.80286455832581 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105935&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.8596193774501[/C][/ROW]
[ROW][C]beta[/C][C]-0.802864558325808[/C][/ROW]
[ROW][C]S.D.[/C][C]1.71597253256789[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.46787727838764[/C][/ROW]
[ROW][C]p-value[/C][C]0.642857704219085[/C][/ROW]
[ROW][C]Lambda[/C][C]1.80286455832581[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105935&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105935&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)
alpha5.8596193774501
beta-0.802864558325808
S.D.1.71597253256789
T-STAT-0.46787727838764
p-value0.642857704219085
Lambda1.80286455832581


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')