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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 computationFri, 15 Dec 2017 12:02:31 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/15/t1513335768mlm97d3hm07qfor.htm/, Retrieved Wed, 15 May 2024 06:08:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309645, Retrieved Wed, 15 May 2024 06:08:40 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

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] [] [2017-12-15 11:02:31] [4a18882c9dbf23bd76c659f8b4f63e4f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
58.4
64.8
73.8
65
73
71.1
58.2
64
75
74.9
75
68.3
72.5
72.4
79.6
70.7
76.4
79.7
64.2
67.9
74.1
78.5
73.4
65.4
69.9
69.6
76.8
75.6
74
76
68.1
65.5
76.9
81.7
73.6
68.7
73.3
71.5
78.3
76.5
71.8
77.6
70
64
81.3
82.5
73.1
78.1
70.7
74.9
88
81.3
75.7
89.8
74.6
74.9
90
88.1
84.9
87.7
80.5
79
89.9
86.3
81.1
92.4
71.8
76.1
92.5
87
89.5
88.7
83.8
84.9
99
84.6
92.7
97.6
78
81.9
96.5
99.9
96.2
90.5
91.4
89.7
102.7
91.5
96.2
104.5
90.3
90.3
100.4
111.3
101.3
94.4
100.4
102
104.3
108.8
101.3
108.9
98.5
88.8
111.8
109.6
92.5
94.5
80.8
83.7
94.2
86.2
89
94.7
81.9
80.2
96.5
95.6
91.9
89.9
86.3
94
108
96.3
94.6
111.7
92
91.9
109.2
106.8
105.8
103.6
97.6
102.8
124.8
103.9
112.2
108.5
92.4
101.1
114.9
106.4
104
101.6
99.4
102.3
121.3
99.3
102.9
111.4
98.5
98.5
108.5
112.1
105.3
95.2
98.2
96.6
109.6
108
106.7
111.5
104.5
94.3
109.6
116.4
106.5
100.5
101.7
104.1
112.3
111.2
108.2
115.1
102.3
93.6
120.6
118.4
106.6
105.3
101.5
100.1
119.5
111.2
103.7
117.8
101.7
97.4
120
117
110.6
105.3
100.9
108.1
119.3
113
108.6
123.3
101.4
103.5
119.4
113.1
112
115.8
105.4
110.9
128.5
109
117.2
124.4
104.7
108.6

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309645&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309645&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309645&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
168.45833333333336.2875719165716616.8
272.95.2103044754863115.5
373.03333333333334.6939677601506116.2
474.83333333333335.22325801032518.5
581.71666666666677.1442072317155619.3
684.56666666666676.7238156555409120.7
790.46666666666677.5414410647656321.9
8976.9763235954971921.6
9101.7833333333337.3138515327031523
1088.71666666666676.0197905933577816.3
11100.0166666666678.3911027916839425.4
12105.858.500106951198832.4
13104.5583333333337.5266143944288926.1
14105.26.6056449688539522.1
15108.2833333333337.6819544545918927
16108.8166666666678.2284244966439222.6
17111.5333333333337.2886378991031222.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 68.4583333333333 & 6.28757191657166 & 16.8 \tabularnewline
2 & 72.9 & 5.21030447548631 & 15.5 \tabularnewline
3 & 73.0333333333333 & 4.69396776015061 & 16.2 \tabularnewline
4 & 74.8333333333333 & 5.223258010325 & 18.5 \tabularnewline
5 & 81.7166666666667 & 7.14420723171556 & 19.3 \tabularnewline
6 & 84.5666666666667 & 6.72381565554091 & 20.7 \tabularnewline
7 & 90.4666666666667 & 7.54144106476563 & 21.9 \tabularnewline
8 & 97 & 6.97632359549719 & 21.6 \tabularnewline
9 & 101.783333333333 & 7.31385153270315 & 23 \tabularnewline
10 & 88.7166666666667 & 6.01979059335778 & 16.3 \tabularnewline
11 & 100.016666666667 & 8.39110279168394 & 25.4 \tabularnewline
12 & 105.85 & 8.5001069511988 & 32.4 \tabularnewline
13 & 104.558333333333 & 7.52661439442889 & 26.1 \tabularnewline
14 & 105.2 & 6.60564496885395 & 22.1 \tabularnewline
15 & 108.283333333333 & 7.68195445459189 & 27 \tabularnewline
16 & 108.816666666667 & 8.22842449664392 & 22.6 \tabularnewline
17 & 111.533333333333 & 7.28863789910312 & 22.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309645&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]68.4583333333333[/C][C]6.28757191657166[/C][C]16.8[/C][/ROW]
[ROW][C]2[/C][C]72.9[/C][C]5.21030447548631[/C][C]15.5[/C][/ROW]
[ROW][C]3[/C][C]73.0333333333333[/C][C]4.69396776015061[/C][C]16.2[/C][/ROW]
[ROW][C]4[/C][C]74.8333333333333[/C][C]5.223258010325[/C][C]18.5[/C][/ROW]
[ROW][C]5[/C][C]81.7166666666667[/C][C]7.14420723171556[/C][C]19.3[/C][/ROW]
[ROW][C]6[/C][C]84.5666666666667[/C][C]6.72381565554091[/C][C]20.7[/C][/ROW]
[ROW][C]7[/C][C]90.4666666666667[/C][C]7.54144106476563[/C][C]21.9[/C][/ROW]
[ROW][C]8[/C][C]97[/C][C]6.97632359549719[/C][C]21.6[/C][/ROW]
[ROW][C]9[/C][C]101.783333333333[/C][C]7.31385153270315[/C][C]23[/C][/ROW]
[ROW][C]10[/C][C]88.7166666666667[/C][C]6.01979059335778[/C][C]16.3[/C][/ROW]
[ROW][C]11[/C][C]100.016666666667[/C][C]8.39110279168394[/C][C]25.4[/C][/ROW]
[ROW][C]12[/C][C]105.85[/C][C]8.5001069511988[/C][C]32.4[/C][/ROW]
[ROW][C]13[/C][C]104.558333333333[/C][C]7.52661439442889[/C][C]26.1[/C][/ROW]
[ROW][C]14[/C][C]105.2[/C][C]6.60564496885395[/C][C]22.1[/C][/ROW]
[ROW][C]15[/C][C]108.283333333333[/C][C]7.68195445459189[/C][C]27[/C][/ROW]
[ROW][C]16[/C][C]108.816666666667[/C][C]8.22842449664392[/C][C]22.6[/C][/ROW]
[ROW][C]17[/C][C]111.533333333333[/C][C]7.28863789910312[/C][C]22.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309645&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309645&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
168.45833333333336.2875719165716616.8
272.95.2103044754863115.5
373.03333333333334.6939677601506116.2
474.83333333333335.22325801032518.5
581.71666666666677.1442072317155619.3
684.56666666666676.7238156555409120.7
790.46666666666677.5414410647656321.9
8976.9763235954971921.6
9101.7833333333337.3138515327031523
1088.71666666666676.0197905933577816.3
11100.0166666666678.3911027916839425.4
12105.858.500106951198832.4
13104.5583333333337.5266143944288926.1
14105.26.6056449688539522.1
15108.2833333333337.6819544545918927
16108.8166666666678.2284244966439222.6
17111.5333333333337.2886378991031222.4






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.31608585301862
beta0.060202542650618
S.D.0.0125090285445845
T-STAT4.81272725823951
p-value0.000228123653217031

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.31608585301862 \tabularnewline
beta & 0.060202542650618 \tabularnewline
S.D. & 0.0125090285445845 \tabularnewline
T-STAT & 4.81272725823951 \tabularnewline
p-value & 0.000228123653217031 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309645&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.31608585301862[/C][/ROW]
[ROW][C]beta[/C][C]0.060202542650618[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0125090285445845[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.81272725823951[/C][/ROW]
[ROW][C]p-value[/C][C]0.000228123653217031[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309645&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309645&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)
alpha1.31608585301862
beta0.060202542650618
S.D.0.0125090285445845
T-STAT4.81272725823951
p-value0.000228123653217031






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.84803835371443
beta0.833611912822325
S.D.0.169422001210972
T-STAT4.9203285692764
p-value0.000184876932557774
Lambda0.166388087177675

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.84803835371443 \tabularnewline
beta & 0.833611912822325 \tabularnewline
S.D. & 0.169422001210972 \tabularnewline
T-STAT & 4.9203285692764 \tabularnewline
p-value & 0.000184876932557774 \tabularnewline
Lambda & 0.166388087177675 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309645&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.84803835371443[/C][/ROW]
[ROW][C]beta[/C][C]0.833611912822325[/C][/ROW]
[ROW][C]S.D.[/C][C]0.169422001210972[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.9203285692764[/C][/ROW]
[ROW][C]p-value[/C][C]0.000184876932557774[/C][/ROW]
[ROW][C]Lambda[/C][C]0.166388087177675[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309645&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309645&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-1.84803835371443
beta0.833611912822325
S.D.0.169422001210972
T-STAT4.9203285692764
p-value0.000184876932557774
Lambda0.166388087177675


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 0.2 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 1 ; par9 = 1 ;
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')