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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 28 Nov 2012 12:38:36 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/28/t1354124432yv3slwt81zs3tuh.htm/, Retrieved Fri, 19 Apr 2024 15:16:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=194197, Retrieved Fri, 19 Apr 2024 15:16:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88

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] [TS - SDMP - Grond...] [2012-11-28 17:38:36] [64435dfec13c3cda39d1733fd4b6eb52] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
54.3
55.9
63.9
64
60.7
67.8
70.5
76.6
76.2
71.8
67.8
69.7
76.7
74.2
75.8
84.3
84.9
84.4
89.4
88.5
76.5
71.4
72.1
75.8
66.6
71.7
75.4
80.9
80.7
85
91.5
87.7
95.3
102.4
114.2
111.7
113.7
118.8
129
136.4
155
166
168.7
145.5
127.3
91.5
69
54
56.3
54.2
59.3
63.4
73.3
86.7
81.3
89.6
85.3
92.4
96.8
93.6
97.6
94.2
99.9
106.4
96
94.9
94.8
95.9
96.2
103.1
106.9
114.2
118.2
123.9
137.1
146.2
136.4
133.2
135.9
127.1
128.5
126.6
132.6
130.9

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' @ fisher.wessa.net

\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' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194197&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194197&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194197&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' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
166.67.1448646529581622.3
279.56.3810799883861218
388.591666666666715.111793006747747.6
4122.90833333333336.2755479460735114.7
577.683333333333315.66599289331342.6
6100.0083333333336.3211705379381320
7131.3833333333337.2747175307028328

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 66.6 & 7.14486465295816 & 22.3 \tabularnewline
2 & 79.5 & 6.38107998838612 & 18 \tabularnewline
3 & 88.5916666666667 & 15.1117930067477 & 47.6 \tabularnewline
4 & 122.908333333333 & 36.2755479460735 & 114.7 \tabularnewline
5 & 77.6833333333333 & 15.665992893313 & 42.6 \tabularnewline
6 & 100.008333333333 & 6.32117053793813 & 20 \tabularnewline
7 & 131.383333333333 & 7.27471753070283 & 28 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194197&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]66.6[/C][C]7.14486465295816[/C][C]22.3[/C][/ROW]
[ROW][C]2[/C][C]79.5[/C][C]6.38107998838612[/C][C]18[/C][/ROW]
[ROW][C]3[/C][C]88.5916666666667[/C][C]15.1117930067477[/C][C]47.6[/C][/ROW]
[ROW][C]4[/C][C]122.908333333333[/C][C]36.2755479460735[/C][C]114.7[/C][/ROW]
[ROW][C]5[/C][C]77.6833333333333[/C][C]15.665992893313[/C][C]42.6[/C][/ROW]
[ROW][C]6[/C][C]100.008333333333[/C][C]6.32117053793813[/C][C]20[/C][/ROW]
[ROW][C]7[/C][C]131.383333333333[/C][C]7.27471753070283[/C][C]28[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194197&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194197&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
166.67.1448646529581622.3
279.56.3810799883861218
388.591666666666715.111793006747747.6
4122.90833333333336.2755479460735114.7
577.683333333333315.66599289331342.6
6100.0083333333336.3211705379381320
7131.3833333333337.2747175307028328






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-3.24345742036057
beta0.175316861287199
S.D.0.18466218421439
T-STAT0.949392329745535
p-value0.386018007327684

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -3.24345742036057 \tabularnewline
beta & 0.175316861287199 \tabularnewline
S.D. & 0.18466218421439 \tabularnewline
T-STAT & 0.949392329745535 \tabularnewline
p-value & 0.386018007327684 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194197&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.24345742036057[/C][/ROW]
[ROW][C]beta[/C][C]0.175316861287199[/C][/ROW]
[ROW][C]S.D.[/C][C]0.18466218421439[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.949392329745535[/C][/ROW]
[ROW][C]p-value[/C][C]0.386018007327684[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194197&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194197&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-3.24345742036057
beta0.175316861287199
S.D.0.18466218421439
T-STAT0.949392329745535
p-value0.386018007327684






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.25208886382971
beta0.803343628523587
S.D.1.12670030107119
T-STAT0.713005603850309
p-value0.507727004322418
Lambda0.196656371476413

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.25208886382971 \tabularnewline
beta & 0.803343628523587 \tabularnewline
S.D. & 1.12670030107119 \tabularnewline
T-STAT & 0.713005603850309 \tabularnewline
p-value & 0.507727004322418 \tabularnewline
Lambda & 0.196656371476413 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194197&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.25208886382971[/C][/ROW]
[ROW][C]beta[/C][C]0.803343628523587[/C][/ROW]
[ROW][C]S.D.[/C][C]1.12670030107119[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.713005603850309[/C][/ROW]
[ROW][C]p-value[/C][C]0.507727004322418[/C][/ROW]
[ROW][C]Lambda[/C][C]0.196656371476413[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194197&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194197&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-1.25208886382971
beta0.803343628523587
S.D.1.12670030107119
T-STAT0.713005603850309
p-value0.507727004322418
Lambda0.196656371476413


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
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')