| vijfde opdracht | *The author of this computation has been verified* | R Software Module: /rwasp_variability.wasp (opens new window with default values) | Title produced by software: Variability | Date of computation: Mon, 04 Oct 2010 11:13:15 +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/Oct/04/t1286191127cnpgxzf82w2575s.htm/, Retrieved Mon, 04 Oct 2010 13:18:47 +0200 | | 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/Oct/04/t1286191127cnpgxzf82w2575s.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 « | 33.999
37.028
39.047
57.47
59.609
62.156
64.016
70.939
72.844
85.094
86.58
103.898
109.215
131.812
136.452
136.813
137.55
140.321
150.034
156.187
158.047
169.861
171.26
171.328
180.818
183.186
183.613
184.641
187.881
190.157
190.379
191.835
192.797
193.299
197.549
198.296
199.297
199.746
200.156
203.077
204.386
206.771
206.893
207.533
208.108
211.655
213.361
213.511
213.923
216.046
216.548
216.886
217.465
218.761
220.553
221.588
223.166
226.731
229.641
232.444
232.669
235.577
236.302
236.71
238.502
239.89
240.755
241.171
242.205
242.344
246.542
249.148
250.407
251.422
252.64
257.102
257.567
259.7
260.642
261.596
262.517
262.875
263.906
265.777
266.793
274.482
275.562
278.741
287.069
289.714
293.671
295.281
308.16
308.174
308.532
313.906
315.955
324.04
330.563
348.821
350.089
356.725
366.936
380.155
380.531
383.703
386.688
388.3
392.25
401.422
401.915
403.064
403.556
406.167
421.403
426.113
435.9 etc... | | Output produced by software: |
| | Charts produced by software: | | | Parameters (Session): | | | Parameters (R input): | | | R code (references can be found in the software module): | num <- 50
res <- array(NA,dim=c(num,3))
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
iqd <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
iqdiff <- qvalue3 - qvalue1
return(c(iqdiff,iqdiff/2,iqdiff/(qvalue3 + qvalue1)))
}
range <- max(x) - min(x)
lx <- length(x)
biasf <- (lx-1)/lx
varx <- var(x)
bvarx <- varx*biasf
sdx <- sqrt(varx)
mx <- mean(x)
bsdx <- sqrt(bvarx)
x2 <- x*x
mse0 <- sum(x2)/lx
xmm <- x-mx
xmm2 <- xmm*xmm
msem <- sum(xmm2)/lx
axmm <- abs(x - mx)
medx <- median(x)
axmmed <- abs(x - medx)
xmmed <- x - medx
xmmed2 <- xmmed*xmmed
msemed <- sum(xmmed2)/lx
qarr <- array(NA,dim=c(8,3))
for (j in 1:8) {
qarr[j,] <- iqd(x,j)
}
sdpo <- 0
adpo <- 0
for (i in 1:(lx-1)) {
for (j in (i+1):lx) {
ldi <- x[i]-x[j]
aldi <- abs(ldi)
sdpo = sdpo + ldi * ldi
adpo = adpo + aldi
}
}
denom <- (lx*(lx-1)/2)
sdpo = sdpo / denom
adpo = adpo / denom
gmd <- 0
for (i in 1:lx) {
for (j in 1:lx) {
ldi <- abs(x[i]-x[j])
gmd = gmd + ldi
}
}
gmd <- gmd / (lx*(lx-1))
sumx <- sum(x)
pk <- x / sumx
ck <- cumsum(pk)
dk <- array(NA,dim=lx)
for (i in 1:lx) {
if (ck[i] <= 0.5) dk[i] <- ck[i] else dk[i] <- 1 - ck[i]
}
bigd <- sum(dk) * 2 / (lx-1)
iod <- 1 - sum(pk*pk)
res[1,] <- c('Absolute range','http://www.xycoon.com/absolute.htm', range)
res[2,] <- c('Relative range (unbiased)','http://www.xycoon.com/relative.htm', range/sd(x))
res[3,] <- c('Relative range (biased)','http://www.xycoon.com/relative.htm', range/sqrt(varx*biasf))
res[4,] <- c('Variance (unbiased)','http://www.xycoon.com/unbiased.htm', varx)
res[5,] <- c('Variance (biased)','http://www.xycoon.com/biased.htm', bvarx)
res[6,] <- c('Standard Deviation (unbiased)','http://www.xycoon.com/unbiased1.htm', sdx)
res[7,] <- c('Standard Deviation (biased)','http://www.xycoon.com/biased1.htm', bsdx)
res[8,] <- c('Coefficient of Variation (unbiased)','http://www.xycoon.com/variation.htm', sdx/mx)
res[9,] <- c('Coefficient of Variation (biased)','http://www.xycoon.com/variation.htm', bsdx/mx)
res[10,] <- c('Mean Squared Error (MSE versus 0)','http://www.xycoon.com/mse.htm', mse0)
res[11,] <- c('Mean Squared Error (MSE versus Mean)','http://www.xycoon.com/mse.htm', msem)
res[12,] <- c('Mean Absolute Deviation from Mean (MAD Mean)', 'http://www.xycoon.com/mean2.htm', sum(axmm)/lx)
res[13,] <- c('Mean Absolute Deviation from Median (MAD Median)', 'http://www.xycoon.com/median1.htm', sum(axmmed)/lx)
res[14,] <- c('Median Absolute Deviation from Mean', 'http://www.xycoon.com/mean3.htm', median(axmm))
res[15,] <- c('Median Absolute Deviation from Median', 'http://www.xycoon.com/median2.htm', median(axmmed))
res[16,] <- c('Mean Squared Deviation from Mean', 'http://www.xycoon.com/mean1.htm', msem)
res[17,] <- c('Mean Squared Deviation from Median', 'http://www.xycoon.com/median.htm', msemed)
load(file='createtable')
mylink1 <- hyperlink('http://www.xycoon.com/difference.htm','Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[18,] <- c('', mylink2, qarr[1,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[19,] <- c('', mylink2, qarr[2,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[20,] <- c('', mylink2, qarr[3,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[21,] <- c('', mylink2, qarr[4,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[22,] <- c('', mylink2, qarr[5,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ')
res[23,] <- c('', mylink2, qarr[6,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[24,] <- c('', mylink2, qarr[7,1])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[25,] <- c('', mylink2, qarr[8,1])
mylink1 <- hyperlink('http://www.xycoon.com/deviation.htm','Semi Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[26,] <- c('', mylink2, qarr[1,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[27,] <- c('', mylink2, qarr[2,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[28,] <- c('', mylink2, qarr[3,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[29,] <- c('', mylink2, qarr[4,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[30,] <- c('', mylink2, qarr[5,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ')
res[31,] <- c('', mylink2, qarr[6,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[32,] <- c('', mylink2, qarr[7,2])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[33,] <- c('', mylink2, qarr[8,2])
mylink1 <- hyperlink('http://www.xycoon.com/variation1.htm','Coefficient of Quartile Variation','')
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[34,] <- c('', mylink2, qarr[1,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[35,] <- c('', mylink2, qarr[2,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[36,] <- c('', mylink2, qarr[3,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[37,] <- c('', mylink2, qarr[4,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[38,] <- c('', mylink2, qarr[5,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_6.htm','(Closest Observation)',''),sep=' ')
res[39,] <- c('', mylink2, qarr[6,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[40,] <- c('', mylink2, qarr[7,3])
mylink2 <- paste(mylink1,hyperlink('http://www.xycoon.com/method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[41,] <- c('', mylink2, qarr[8,3])
res[42,] <- c('Number of all Pairs of Observations', 'http://www.xycoon.com/pair_numbers.htm', lx*(lx-1)/2)
res[43,] <- c('Squared Differences between all Pairs of Observations', 'http://www.xycoon.com/squared_differences.htm', sdpo)
res[44,] <- c('Mean Absolute Differences between all Pairs of Observations', 'http://www.xycoon.com/mean_abs_differences.htm', adpo)
res[45,] <- c('Gini Mean Difference', 'http://www.xycoon.com/gini_mean_difference.htm', gmd)
res[46,] <- c('Leik Measure of Dispersion', 'http://www.xycoon.com/leiks_d.htm', bigd)
res[47,] <- c('Index of Diversity', 'http://www.xycoon.com/diversity.htm', iod)
res[48,] <- c('Index of Qualitative Variation', 'http://www.xycoon.com/qualitative_variation.htm', iod*lx/(lx-1))
res[49,] <- c('Coefficient of Dispersion', 'http://www.xycoon.com/dispersion.htm', sum(axmm)/lx/medx)
res[50,] <- c('Observations', '', lx)
res
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variability - Ungrouped Data',2,TRUE)
a<-table.row.end(a)
for (i in 1:num) {
a<-table.row.start(a)
if (res[i,1] != '') {
a<-table.element(a,hyperlink(res[i,2],res[i,1],''),header=TRUE)
} else {
a<-table.element(a,res[i,2],header=TRUE)
}
a<-table.element(a,res[i,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
| |
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