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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 computationThu, 22 Nov 2007 05:57:41 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/22/t11957358375l6wklbigqg0ipb.htm/, Retrieved Thu, 02 May 2024 22:10:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5960, Retrieved Thu, 02 May 2024 22:10:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS10 G29 Q1
Estimated Impact193

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] [Standard deviatio...] [2007-11-22 12:57:41] [7a600ca82a81f1b71fd92dcbb183f5b4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
145,9
158,5
152,2
153,7
157,9
154,4
150,7
151,2
147,3
146,6
145,2
139,3
145,7
163,3
181,8
188,1
222,9
206,3
184,9
183,6
186,6
176,5
173,9
184,9
182,5
183,6
172,4
168,9
163,3
152,4
145,8
148,6
143,4
141,2
144,6
144,5
140,8
133,3
127,3
119,6
120,2
121,9
112,4
111
107,8
110,5
118,3
123
112,1
104,2
102,4
100,3
102,6
101,5
103,4
99,4
97,9
98
90,2
87,1
91,8
94,8
91,8
89,3
91,7
86,2
82,8
82,3
79,8
79,4
85,3
87,5
88,3
88,6
94,9
94,7
92,6
91,8
96,4
96,4
107,1
111,9
107,8
109,2
115,3
119,2
107,8
106,8
104,2
94,8
97,5
98,3
100,6
94,9
93,6
98
104,3
103,9
105,3
102,6
103,3
107,9
107,8
109,8
110,6
110,8
119,3
128,1
127,6
137,9
151,4
143,6
143,4
141,9
135,2
133,1
129,6
134,1
136,8
143,5
162,5
163,1
157,2
158,8
155,4
148,5
154,2
153,3
149,4
147,9
156
163
159,1
159,5
157,3
156,4
156,6
162,4
166,8
162,6
168,1

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5960&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5960&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5960&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1150.2416666666675.6162844937869370.2
2183.20833333333319.2750643594413134.3
3157.615.764517119150891.8
4120.5083333333339.785281928705151.5
599.9256.4780924521175120.4
686.89166666666675.110320810661388.6
798.30833333333338.377617184914229.1
8102.5833333333338.2840299079102536.9
9109.4757.4621621287910748.3
10138.1756.8251040618107472
11155.7755.4492910297829377.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 150.241666666667 & 5.61628449378693 & 70.2 \tabularnewline
2 & 183.208333333333 & 19.2750643594413 & 134.3 \tabularnewline
3 & 157.6 & 15.7645171191508 & 91.8 \tabularnewline
4 & 120.508333333333 & 9.7852819287051 & 51.5 \tabularnewline
5 & 99.925 & 6.47809245211751 & 20.4 \tabularnewline
6 & 86.8916666666667 & 5.11032081066138 & 8.6 \tabularnewline
7 & 98.3083333333333 & 8.3776171849142 & 29.1 \tabularnewline
8 & 102.583333333333 & 8.28402990791025 & 36.9 \tabularnewline
9 & 109.475 & 7.46216212879107 & 48.3 \tabularnewline
10 & 138.175 & 6.82510406181074 & 72 \tabularnewline
11 & 155.775 & 5.44929102978293 & 77.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5960&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]150.241666666667[/C][C]5.61628449378693[/C][C]70.2[/C][/ROW]
[ROW][C]2[/C][C]183.208333333333[/C][C]19.2750643594413[/C][C]134.3[/C][/ROW]
[ROW][C]3[/C][C]157.6[/C][C]15.7645171191508[/C][C]91.8[/C][/ROW]
[ROW][C]4[/C][C]120.508333333333[/C][C]9.7852819287051[/C][C]51.5[/C][/ROW]
[ROW][C]5[/C][C]99.925[/C][C]6.47809245211751[/C][C]20.4[/C][/ROW]
[ROW][C]6[/C][C]86.8916666666667[/C][C]5.11032081066138[/C][C]8.6[/C][/ROW]
[ROW][C]7[/C][C]98.3083333333333[/C][C]8.3776171849142[/C][C]29.1[/C][/ROW]
[ROW][C]8[/C][C]102.583333333333[/C][C]8.28402990791025[/C][C]36.9[/C][/ROW]
[ROW][C]9[/C][C]109.475[/C][C]7.46216212879107[/C][C]48.3[/C][/ROW]
[ROW][C]10[/C][C]138.175[/C][C]6.82510406181074[/C][C]72[/C][/ROW]
[ROW][C]11[/C][C]155.775[/C][C]5.44929102978293[/C][C]77.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5960&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5960&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
1150.2416666666675.6162844937869370.2
2183.20833333333319.2750643594413134.3
3157.615.764517119150891.8
4120.5083333333339.785281928705151.5
599.9256.4780924521175120.4
686.89166666666675.110320810661388.6
798.30833333333338.377617184914229.1
8102.5833333333338.2840299079102536.9
9109.4757.4621621287910748.3
10138.1756.8251040618107472
11155.7755.4492910297829377.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.3778098877228
beta0.0888175763801903
S.D.0.0384441177874714
T-STAT2.31030340899473
p-value0.0462135461460341

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.3778098877228 \tabularnewline
beta & 0.0888175763801903 \tabularnewline
S.D. & 0.0384441177874714 \tabularnewline
T-STAT & 2.31030340899473 \tabularnewline
p-value & 0.0462135461460341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5960&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.3778098877228[/C][/ROW]
[ROW][C]beta[/C][C]0.0888175763801903[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0384441177874714[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.31030340899473[/C][/ROW]
[ROW][C]p-value[/C][C]0.0462135461460341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5960&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5960&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-2.3778098877228
beta0.0888175763801903
S.D.0.0384441177874714
T-STAT2.31030340899473
p-value0.0462135461460341






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.18105456706794
beta0.887717836305606
S.D.0.505548697538176
T-STAT1.75594921048841
p-value0.112980766274478
Lambda0.112282163694394

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.18105456706794 \tabularnewline
beta & 0.887717836305606 \tabularnewline
S.D. & 0.505548697538176 \tabularnewline
T-STAT & 1.75594921048841 \tabularnewline
p-value & 0.112980766274478 \tabularnewline
Lambda & 0.112282163694394 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5960&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.18105456706794[/C][/ROW]
[ROW][C]beta[/C][C]0.887717836305606[/C][/ROW]
[ROW][C]S.D.[/C][C]0.505548697538176[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.75594921048841[/C][/ROW]
[ROW][C]p-value[/C][C]0.112980766274478[/C][/ROW]
[ROW][C]Lambda[/C][C]0.112282163694394[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5960&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5960&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-2.18105456706794
beta0.887717836305606
S.D.0.505548697538176
T-STAT1.75594921048841
p-value0.112980766274478
Lambda0.112282163694394


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')