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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Tue, 06 Dec 2011 16:29:43 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/06/t1323207232rlkkgcn0obn9x33.htm/, Retrieved Mon, 29 Apr 2024 03:28:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151962, Retrieved Mon, 29 Apr 2024 03:28:55 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Spectral Analysis] [Unemployment] [2010-11-29 09:21:38] [b98453cac15ba1066b407e146608df68]
-    D    [Spectral Analysis] [Workshop 9, Cumul...] [2010-12-05 17:58:39] [3635fb7041b1998c5a1332cf9de22bce]
- R  D      [Spectral Analysis] [WS 9] [2011-12-06 15:52:12] [43239ed98a62e091c70785d80176537f]
- RMP           [Standard Deviation-Mean Plot] [WS 9] [2011-12-06 21:29:43] [6e647d331a8f33aa61a2d78ef323178e] [Current]

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Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151962&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151962&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151962&T=0

As an alternative you can also use a 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 Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	432.083333333333	37.1739359652905	94
2	516.25	30.6301248031174	83
3	579.583333333333	28.4427921316179	86
4	595.083333333333	31.2015685308909	90
5	574.833333333333	37.9421409597042	117
6	519.916666666667	25.1593406957023	75
7	508.25	24.7390930972161	74
8	471.75	28.1008734901442	87
9	428.083333333333	25.105082184991	76
10	402.25	23.6571150166095	63
11	420.583333333333	23.0551052651659	70
12	460.25	25.2842926447519	76
13	529.25	34.8663030863482	93
14	585.666666666667	21.9310213389549	68
15	592.666666666667	25.4248744819762	76
16	596.666666666667	26.4620941016093	79
17	573.583333333333	22.232074836037	70
18	551	25.2478621957295	79
19	515.416666666667	24.1075557123538	77
20	481.583333333333	26.2036025744322	82
21	466.75	26.7619981588548	82
22	483.583333333333	26.0818931735246	70
23	527.5	29.5988329008241	79
24	565.583333333333	26.1376020786958	76
25	595.916666666667	21.9191005677005	62
26	596.083333333333	19.4303339854949	53
27	545.916666666667	25.2387088465798	89
28	507.166666666667	20.4931622003462	65
29	540.25	31.340142715925	95
30	570	20.8675476626878	67
31	549.583333333333	19.3365331730255	62

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 432.083333333333 & 37.1739359652905 & 94 \tabularnewline
2 & 516.25 & 30.6301248031174 & 83 \tabularnewline
3 & 579.583333333333 & 28.4427921316179 & 86 \tabularnewline
4 & 595.083333333333 & 31.2015685308909 & 90 \tabularnewline
5 & 574.833333333333 & 37.9421409597042 & 117 \tabularnewline
6 & 519.916666666667 & 25.1593406957023 & 75 \tabularnewline
7 & 508.25 & 24.7390930972161 & 74 \tabularnewline
8 & 471.75 & 28.1008734901442 & 87 \tabularnewline
9 & 428.083333333333 & 25.105082184991 & 76 \tabularnewline
10 & 402.25 & 23.6571150166095 & 63 \tabularnewline
11 & 420.583333333333 & 23.0551052651659 & 70 \tabularnewline
12 & 460.25 & 25.2842926447519 & 76 \tabularnewline
13 & 529.25 & 34.8663030863482 & 93 \tabularnewline
14 & 585.666666666667 & 21.9310213389549 & 68 \tabularnewline
15 & 592.666666666667 & 25.4248744819762 & 76 \tabularnewline
16 & 596.666666666667 & 26.4620941016093 & 79 \tabularnewline
17 & 573.583333333333 & 22.232074836037 & 70 \tabularnewline
18 & 551 & 25.2478621957295 & 79 \tabularnewline
19 & 515.416666666667 & 24.1075557123538 & 77 \tabularnewline
20 & 481.583333333333 & 26.2036025744322 & 82 \tabularnewline
21 & 466.75 & 26.7619981588548 & 82 \tabularnewline
22 & 483.583333333333 & 26.0818931735246 & 70 \tabularnewline
23 & 527.5 & 29.5988329008241 & 79 \tabularnewline
24 & 565.583333333333 & 26.1376020786958 & 76 \tabularnewline
25 & 595.916666666667 & 21.9191005677005 & 62 \tabularnewline
26 & 596.083333333333 & 19.4303339854949 & 53 \tabularnewline
27 & 545.916666666667 & 25.2387088465798 & 89 \tabularnewline
28 & 507.166666666667 & 20.4931622003462 & 65 \tabularnewline
29 & 540.25 & 31.340142715925 & 95 \tabularnewline
30 & 570 & 20.8675476626878 & 67 \tabularnewline
31 & 549.583333333333 & 19.3365331730255 & 62 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151962&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]432.083333333333[/C][C]37.1739359652905[/C][C]94[/C][/ROW]
[ROW][C]2[/C][C]516.25[/C][C]30.6301248031174[/C][C]83[/C][/ROW]
[ROW][C]3[/C][C]579.583333333333[/C][C]28.4427921316179[/C][C]86[/C][/ROW]
[ROW][C]4[/C][C]595.083333333333[/C][C]31.2015685308909[/C][C]90[/C][/ROW]
[ROW][C]5[/C][C]574.833333333333[/C][C]37.9421409597042[/C][C]117[/C][/ROW]
[ROW][C]6[/C][C]519.916666666667[/C][C]25.1593406957023[/C][C]75[/C][/ROW]
[ROW][C]7[/C][C]508.25[/C][C]24.7390930972161[/C][C]74[/C][/ROW]
[ROW][C]8[/C][C]471.75[/C][C]28.1008734901442[/C][C]87[/C][/ROW]
[ROW][C]9[/C][C]428.083333333333[/C][C]25.105082184991[/C][C]76[/C][/ROW]
[ROW][C]10[/C][C]402.25[/C][C]23.6571150166095[/C][C]63[/C][/ROW]
[ROW][C]11[/C][C]420.583333333333[/C][C]23.0551052651659[/C][C]70[/C][/ROW]
[ROW][C]12[/C][C]460.25[/C][C]25.2842926447519[/C][C]76[/C][/ROW]
[ROW][C]13[/C][C]529.25[/C][C]34.8663030863482[/C][C]93[/C][/ROW]
[ROW][C]14[/C][C]585.666666666667[/C][C]21.9310213389549[/C][C]68[/C][/ROW]
[ROW][C]15[/C][C]592.666666666667[/C][C]25.4248744819762[/C][C]76[/C][/ROW]
[ROW][C]16[/C][C]596.666666666667[/C][C]26.4620941016093[/C][C]79[/C][/ROW]
[ROW][C]17[/C][C]573.583333333333[/C][C]22.232074836037[/C][C]70[/C][/ROW]
[ROW][C]18[/C][C]551[/C][C]25.2478621957295[/C][C]79[/C][/ROW]
[ROW][C]19[/C][C]515.416666666667[/C][C]24.1075557123538[/C][C]77[/C][/ROW]
[ROW][C]20[/C][C]481.583333333333[/C][C]26.2036025744322[/C][C]82[/C][/ROW]
[ROW][C]21[/C][C]466.75[/C][C]26.7619981588548[/C][C]82[/C][/ROW]
[ROW][C]22[/C][C]483.583333333333[/C][C]26.0818931735246[/C][C]70[/C][/ROW]
[ROW][C]23[/C][C]527.5[/C][C]29.5988329008241[/C][C]79[/C][/ROW]
[ROW][C]24[/C][C]565.583333333333[/C][C]26.1376020786958[/C][C]76[/C][/ROW]
[ROW][C]25[/C][C]595.916666666667[/C][C]21.9191005677005[/C][C]62[/C][/ROW]
[ROW][C]26[/C][C]596.083333333333[/C][C]19.4303339854949[/C][C]53[/C][/ROW]
[ROW][C]27[/C][C]545.916666666667[/C][C]25.2387088465798[/C][C]89[/C][/ROW]
[ROW][C]28[/C][C]507.166666666667[/C][C]20.4931622003462[/C][C]65[/C][/ROW]
[ROW][C]29[/C][C]540.25[/C][C]31.340142715925[/C][C]95[/C][/ROW]
[ROW][C]30[/C][C]570[/C][C]20.8675476626878[/C][C]67[/C][/ROW]
[ROW][C]31[/C][C]549.583333333333[/C][C]19.3365331730255[/C][C]62[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151962&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151962&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	432.083333333333	37.1739359652905	94
2	516.25	30.6301248031174	83
3	579.583333333333	28.4427921316179	86
4	595.083333333333	31.2015685308909	90
5	574.833333333333	37.9421409597042	117
6	519.916666666667	25.1593406957023	75
7	508.25	24.7390930972161	74
8	471.75	28.1008734901442	87
9	428.083333333333	25.105082184991	76
10	402.25	23.6571150166095	63
11	420.583333333333	23.0551052651659	70
12	460.25	25.2842926447519	76
13	529.25	34.8663030863482	93
14	585.666666666667	21.9310213389549	68
15	592.666666666667	25.4248744819762	76
16	596.666666666667	26.4620941016093	79
17	573.583333333333	22.232074836037	70
18	551	25.2478621957295	79
19	515.416666666667	24.1075557123538	77
20	481.583333333333	26.2036025744322	82
21	466.75	26.7619981588548	82
22	483.583333333333	26.0818931735246	70
23	527.5	29.5988329008241	79
24	565.583333333333	26.1376020786958	76
25	595.916666666667	21.9191005677005	62
26	596.083333333333	19.4303339854949	53
27	545.916666666667	25.2387088465798	89
28	507.166666666667	20.4931622003462	65
29	540.25	31.340142715925	95
30	570	20.8675476626878	67
31	549.583333333333	19.3365331730255	62

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	30.3081617958497
beta	-0.00770003472489582
S.D.	0.0149631124993069
T-STAT	-0.514601138316144
p-value	0.610731705976892

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 30.3081617958497 \tabularnewline
beta & -0.00770003472489582 \tabularnewline
S.D. & 0.0149631124993069 \tabularnewline
T-STAT & -0.514601138316144 \tabularnewline
p-value & 0.610731705976892 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151962&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]30.3081617958497[/C][/ROW]
[ROW][C]beta[/C][C]-0.00770003472489582[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0149631124993069[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.514601138316144[/C][/ROW]
[ROW][C]p-value[/C][C]0.610731705976892[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151962&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151962&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	30.3081617958497
beta	-0.00770003472489582
S.D.	0.0149631124993069
T-STAT	-0.514601138316144
p-value	0.610731705976892

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.24797395438736
beta	-0.158897386127125
S.D.	0.275871356414415
T-STAT	-0.575983633068554
p-value	0.569069665274485
Lambda	1.15889738612713

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.24797395438736 \tabularnewline
beta & -0.158897386127125 \tabularnewline
S.D. & 0.275871356414415 \tabularnewline
T-STAT & -0.575983633068554 \tabularnewline
p-value & 0.569069665274485 \tabularnewline
Lambda & 1.15889738612713 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151962&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.24797395438736[/C][/ROW]
[ROW][C]beta[/C][C]-0.158897386127125[/C][/ROW]
[ROW][C]S.D.[/C][C]0.275871356414415[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.575983633068554[/C][/ROW]
[ROW][C]p-value[/C][C]0.569069665274485[/C][/ROW]
[ROW][C]Lambda[/C][C]1.15889738612713[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151962&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151962&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.24797395438736
beta	-0.158897386127125
S.D.	0.275871356414415
T-STAT	-0.575983633068554
p-value	0.569069665274485
Lambda	1.15889738612713

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code