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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 computationWed, 10 Aug 2016 00:02:24 +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/2016/Aug/10/t14707837660xsgne26evkv5g6.htm/, Retrieved Tue, 30 Apr 2024 07:34:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296171, Retrieved Tue, 30 Apr 2024 07:34:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115

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] [] [2016-08-09 23:02:24] [3e69b53d94b342798d3f1a806941de01] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
29054.50
28543.50
28032.00
27009.50
37356.00
36844.50
29054.50
23881.50
24392.50
24392.50
24904.00
25982.00
22859.00
19731.00
17169.50
17169.50
27009.50
28032.00
20242.00
11429.50
16091.50
16091.50
19731.00
21831.50
21320.00
16091.50
18708.50
17681.00
26493.50
24392.50
16091.50
9891.00
15580.00
17169.50
18708.50
20753.50
16602.50
13019.00
14558.00
15069.00
28543.50
28543.50
20753.50
19731.00
22859.00
21320.00
25471.00
30644.00
31671.50
24392.50
22342.50
20242.00
34283.50
35311.00
32694.00
35311.00
34794.50
30644.00
35311.00
40484.00
42584.50
36333.50
32182.50
35311.00
48785.00
52936.00
51913.50
53958.00
53447.00
48274.00
57086.50
59187.00
62259.50
52936.00
49296.50
53447.00
63337.50
72150.00
70049.50
70049.50
71077.00
67488.00
76817.00
76817.00
75227.50
66410.00
67999.50
69027.00
75789.50
84602.00
78350.50
81479.00
78862.00
77328.00
89269.00
86652.00
83012.50
77839.50
83012.50
85629.50
88752.50
92903.00
88752.50
91314.00
88190.50
87679.50
100642.50
101720.50
97570.00
90291.50
96492.00
99104.00
102232.00
106894.00
102232.00
105871.50
104282.00
98592.50
110533.00
110533.00

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'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296171&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296171&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296171&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
128287.254521.8550824151413474.5
219782.29166666674717.8441313915916602.5
318573.41666666674352.1629096834416602.5
421426.16666666675951.0567561695717625
531456.79166666676076.5520182027820242
647666.54166666678987.6504146177627004.5
765477.04166666679330.6712719112427520.5
8775837287.5611084292722859
989120.756927.618184090823881
10102052.2916666676006.7847527847920241.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 28287.25 & 4521.85508241514 & 13474.5 \tabularnewline
2 & 19782.2916666667 & 4717.84413139159 & 16602.5 \tabularnewline
3 & 18573.4166666667 & 4352.16290968344 & 16602.5 \tabularnewline
4 & 21426.1666666667 & 5951.05675616957 & 17625 \tabularnewline
5 & 31456.7916666667 & 6076.55201820278 & 20242 \tabularnewline
6 & 47666.5416666667 & 8987.65041461776 & 27004.5 \tabularnewline
7 & 65477.0416666667 & 9330.67127191124 & 27520.5 \tabularnewline
8 & 77583 & 7287.56110842927 & 22859 \tabularnewline
9 & 89120.75 & 6927.6181840908 & 23881 \tabularnewline
10 & 102052.291666667 & 6006.78475278479 & 20241.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296171&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]28287.25[/C][C]4521.85508241514[/C][C]13474.5[/C][/ROW]
[ROW][C]2[/C][C]19782.2916666667[/C][C]4717.84413139159[/C][C]16602.5[/C][/ROW]
[ROW][C]3[/C][C]18573.4166666667[/C][C]4352.16290968344[/C][C]16602.5[/C][/ROW]
[ROW][C]4[/C][C]21426.1666666667[/C][C]5951.05675616957[/C][C]17625[/C][/ROW]
[ROW][C]5[/C][C]31456.7916666667[/C][C]6076.55201820278[/C][C]20242[/C][/ROW]
[ROW][C]6[/C][C]47666.5416666667[/C][C]8987.65041461776[/C][C]27004.5[/C][/ROW]
[ROW][C]7[/C][C]65477.0416666667[/C][C]9330.67127191124[/C][C]27520.5[/C][/ROW]
[ROW][C]8[/C][C]77583[/C][C]7287.56110842927[/C][C]22859[/C][/ROW]
[ROW][C]9[/C][C]89120.75[/C][C]6927.6181840908[/C][C]23881[/C][/ROW]
[ROW][C]10[/C][C]102052.291666667[/C][C]6006.78475278479[/C][C]20241.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296171&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296171&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
128287.254521.8550824151413474.5
219782.29166666674717.8441313915916602.5
318573.41666666674352.1629096834416602.5
421426.16666666675951.0567561695717625
531456.79166666676076.5520182027820242
647666.54166666678987.6504146177627004.5
765477.04166666679330.6712719112427520.5
8775837287.5611084292722859
989120.756927.618184090823881
10102052.2916666676006.7847527847920241.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5052.19058891118
beta0.0271981572682842
S.D.0.0172378096996492
T-STAT1.57781978929944
p-value0.153259023177621

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5052.19058891118 \tabularnewline
beta & 0.0271981572682842 \tabularnewline
S.D. & 0.0172378096996492 \tabularnewline
T-STAT & 1.57781978929944 \tabularnewline
p-value & 0.153259023177621 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296171&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5052.19058891118[/C][/ROW]
[ROW][C]beta[/C][C]0.0271981572682842[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0172378096996492[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.57781978929944[/C][/ROW]
[ROW][C]p-value[/C][C]0.153259023177621[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296171&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296171&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)
alpha5052.19058891118
beta0.0271981572682842
S.D.0.0172378096996492
T-STAT1.57781978929944
p-value0.153259023177621






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha5.88627898093399
beta0.267764826550773
S.D.0.109132888194764
T-STAT2.45356675682318
p-value0.0397151972182873
Lambda0.732235173449227

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.88627898093399 \tabularnewline
beta & 0.267764826550773 \tabularnewline
S.D. & 0.109132888194764 \tabularnewline
T-STAT & 2.45356675682318 \tabularnewline
p-value & 0.0397151972182873 \tabularnewline
Lambda & 0.732235173449227 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296171&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.88627898093399[/C][/ROW]
[ROW][C]beta[/C][C]0.267764826550773[/C][/ROW]
[ROW][C]S.D.[/C][C]0.109132888194764[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.45356675682318[/C][/ROW]
[ROW][C]p-value[/C][C]0.0397151972182873[/C][/ROW]
[ROW][C]Lambda[/C][C]0.732235173449227[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296171&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296171&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)
alpha5.88627898093399
beta0.267764826550773
S.D.0.109132888194764
T-STAT2.45356675682318
p-value0.0397151972182873
Lambda0.732235173449227


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')