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*The author of this computation has been verified*

R Software Module: /rwasp_smp.wasp (opens new window with default values)

Title produced by software: Standard Deviation-Mean Plot

Date of computation: Sun, 19 Dec 2010 18:51:08 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/19/t129278457308y6pwhub7f01f8.htm/, Retrieved Sun, 19 Dec 2010 19:49:35 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/19/t129278457308y6pwhub7f01f8.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

5 4 5 6 6 6 7 8 7 8 7 8 8 9 9 8 9 9 10 11 12 13 13 13 14 14 15 15 16 16 17 18 19 20 22 20 22 25 24 25 28 26 27 26 25 27 28 30 31 32 34 34 33 32 34 36 37 40 38 38 36 40 40 42 44 45 47 49 47 49 52 50 50 57 58 58 58 61 61 64 68 40 34 46 36 34 45 55 50 56 72 76 78 77 90 88 97 93 84 67 72 75 71 75 90 78 73 62 65 61 58 33 39 56 79 82 79 73 87 85 83 82 83 92 95 97 87 84 84 89 103 106 109 106 105 115 120 124 121 131 139 133 119 123 120 128 134 126 115 106 99 100 99 99 100 100 108 109 115 114 108 113 118 122 118 121 118 121 121 112 119 116 110 111 106 108

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	5	0.816496580927726	2
2	6.75	0.957427107756338	2
3	7.5	0.577350269189626	1
4	8.5	0.577350269189626	1
5	9.75	0.957427107756338	2
6	12.75	0.5	1
7	14.5	0.577350269189626	1
8	16.75	0.957427107756338	2
9	20.25	1.25830573921179	3
10	24	1.41421356237310	3
11	26.75	0.957427107756338	2
12	27.5	2.08166599946613	5
13	32.75	1.5	3
14	33.75	1.70782512765993	4
15	38.25	1.25830573921179	3
16	39.5	2.51661147842358	6
17	46.25	2.21735578260835	5
18	49.5	2.08166599946613	5
19	55.75	3.86221007541882	8
20	61	2.44948974278318	6
21	47	14.8323969741913	34
22	42.5	9.60902353693305	21
23	63.5	12.4766448481419	26
24	83.25	6.70198975429437	13
25	85.25	13.3260396717604	30
26	73.25	2.06155281280883	4
27	75.75	11.6153633893506	28
28	54.25	14.4539498638492	32
29	64	20.3141986469235	43
30	81	6.32455532033676	14
31	85	4.69041575982343	10
32	90.75	6.23832242407097	13
33	95.5	10.6614570611463	22
34	108.75	4.5	10
35	124	4.96655480858378	11
36	128.5	9.1469484893415	20
37	127	5.77350269189626	14
38	105	7.34846922834953	16
39	99.5	0.577350269189626	1
40	111.5	3.51188458428425	7
41	115.25	6.07590871118606	14
42	119.5	1.73205080756888	3
43	117	3.91578004149024	9
44	108.75	2.21735578260835	5

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	2.18246687026624
beta	0.0423952883327472
S.D.	0.0175591399422823
T-STAT	2.41442852395404
p-value	0.0201951800080296

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.96607958072566
beta	0.793692118958827
S.D.	0.130903559933309
T-STAT	6.06318208124507
p-value	3.22180606847752e-07
Lambda	0.206307881041173

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t129278457308y6pwhub7f01f8/1t3821292784666.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129278457308y6pwhub7f01f8/1t3821292784666.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129278457308y6pwhub7f01f8/2t3821292784666.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t129278457308y6pwhub7f01f8/2t3821292784666.ps (open in new window)

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 4 ;

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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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