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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, 12 May 2008 07:34:04 -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/12/t1210599379knjia37io29fvtd.htm/, Retrieved Mon, 13 May 2024 22:37:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12344, Retrieved Mon, 13 May 2024 22:37:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176

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] [Mathieu Demoor - ...] [2008-05-12 13:34:04] [8c69c5b6690db7c1e43065ff98235337] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
113
110
107
103
98
98
137
148
147
139
130
128
127
123
118
114
108
111
151
159
158
148
138
137
136
133
126
120
114
116
153
162
161
149
139
135
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105

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=12344&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=12344&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12344&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
1121.518.768929838238750
2132.66666666666718.391368199305551
313716.53096268439148
4133.33333333333316.188286075449945
5126.514.317821063276439
6110.58333333333311.704376285920837

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 121.5 & 18.7689298382387 & 50 \tabularnewline
2 & 132.666666666667 & 18.3913681993055 & 51 \tabularnewline
3 & 137 & 16.530962684391 & 48 \tabularnewline
4 & 133.333333333333 & 16.1882860754499 & 45 \tabularnewline
5 & 126.5 & 14.3178210632764 & 39 \tabularnewline
6 & 110.583333333333 & 11.7043762859208 & 37 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12344&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]121.5[/C][C]18.7689298382387[/C][C]50[/C][/ROW]
[ROW][C]2[/C][C]132.666666666667[/C][C]18.3913681993055[/C][C]51[/C][/ROW]
[ROW][C]3[/C][C]137[/C][C]16.530962684391[/C][C]48[/C][/ROW]
[ROW][C]4[/C][C]133.333333333333[/C][C]16.1882860754499[/C][C]45[/C][/ROW]
[ROW][C]5[/C][C]126.5[/C][C]14.3178210632764[/C][C]39[/C][/ROW]
[ROW][C]6[/C][C]110.583333333333[/C][C]11.7043762859208[/C][C]37[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12344&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12344&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
1121.518.768929838238750
2132.66666666666718.391368199305551
313716.53096268439148
4133.33333333333316.188286075449945
5126.514.317821063276439
6110.58333333333311.704376285920837






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.49357260778901
beta0.161325982877754
S.D.0.109613019828151
T-STAT1.47177756009896
p-value0.215054518047367

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.49357260778901 \tabularnewline
beta & 0.161325982877754 \tabularnewline
S.D. & 0.109613019828151 \tabularnewline
T-STAT & 1.47177756009896 \tabularnewline
p-value & 0.215054518047367 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12344&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.49357260778901[/C][/ROW]
[ROW][C]beta[/C][C]0.161325982877754[/C][/ROW]
[ROW][C]S.D.[/C][C]0.109613019828151[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.47177756009896[/C][/ROW]
[ROW][C]p-value[/C][C]0.215054518047367[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12344&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12344&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-4.49357260778901
beta0.161325982877754
S.D.0.109613019828151
T-STAT1.47177756009896
p-value0.215054518047367






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.32744294669611
beta1.46384549222119
S.D.0.843228146359448
T-STAT1.73600169603113
p-value0.157572798180607
Lambda-0.46384549222119

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.32744294669611 \tabularnewline
beta & 1.46384549222119 \tabularnewline
S.D. & 0.843228146359448 \tabularnewline
T-STAT & 1.73600169603113 \tabularnewline
p-value & 0.157572798180607 \tabularnewline
Lambda & -0.46384549222119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12344&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.32744294669611[/C][/ROW]
[ROW][C]beta[/C][C]1.46384549222119[/C][/ROW]
[ROW][C]S.D.[/C][C]0.843228146359448[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.73600169603113[/C][/ROW]
[ROW][C]p-value[/C][C]0.157572798180607[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.46384549222119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12344&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12344&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-4.32744294669611
beta1.46384549222119
S.D.0.843228146359448
T-STAT1.73600169603113
p-value0.157572798180607
Lambda-0.46384549222119


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')