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132.8
132.5
131.4
131.4
130.7
131.5
131.2
130.1
130.5
129
128.2
128.4
127.3
127.7
127
123.9
125.4
124.6
124.5
124.8
124.1
124.2
122.8
122.3
121.1
121.7
122.2
122.2
122.7
121.7
121
119.8
120.2
116.6
116
118
117.1
116.2
113.3
114.3
113.6
113
112.9
112.7
112.5
113
111.9
110.9
109.8
108.3
109.2
109.2
108.7
109.8
110.8
110
109.6
109.5
110.8
111.6
113.1
114.3
114.1
113.8
112.6
112.7
111.5
110.7
110.4
109.7
110
111.3
109
108.2
107.2
108.7
110.3
110.3
109.5
109.5
109.4
109.6
111.3
110
109.5
110.693
109.195
108.095
108.199
106.87
105.278
108.711
111.192
109.641
109.42
109.935
111.126
110.733
110.34
111.766
111.294
111.54
112.008
111.007
114.963
112.045
110.703
108.894
107.51
111.35
112.964
115.203
115.182
115.191
112.346
110.774
113.07
111.138
109.092
107.971
107.051

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','absolute.htm', range)
res[2,] <- c('Relative range (unbiased)','relative.htm', range/sd(x))
res[3,] <- c('Relative range (biased)','relative.htm', range/sqrt(varx*biasf))
res[4,] <- c('Variance (unbiased)','unbiased.htm', varx)
res[5,] <- c('Variance (biased)','biased.htm', bvarx)
res[6,] <- c('Standard Deviation (unbiased)','unbiased1.htm', sdx)
res[7,] <- c('Standard Deviation (biased)','biased1.htm', bsdx)
res[8,] <- c('Coefficient of Variation (unbiased)','variation.htm', sdx/mx)
res[9,] <- c('Coefficient of Variation (biased)','variation.htm', bsdx/mx)
res[10,] <- c('Mean Squared Error (MSE versus 0)','mse.htm', mse0)
res[11,] <- c('Mean Squared Error (MSE versus Mean)','mse.htm', msem)
res[12,] <- c('Mean Absolute Deviation from Mean (MAD Mean)', 'mean2.htm', sum(axmm)/lx)
res[13,] <- c('Mean Absolute Deviation from Median (MAD Median)', 'median1.htm', sum(axmmed)/lx)
res[14,] <- c('Median Absolute Deviation from Mean', 'mean3.htm', median(axmm))
res[15,] <- c('Median Absolute Deviation from Median', 'median2.htm', median(axmmed))
res[16,] <- c('Mean Squared Deviation from Mean', 'mean1.htm', msem)
res[17,] <- c('Mean Squared Deviation from Median', 'median.htm', msemed)
load(file='createtable')
mylink1 <- hyperlink('difference.htm','Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[18,] <- c('', mylink2, qarr[1,1])
mylink2 <- paste(mylink1,hyperlink('method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[19,] <- c('', mylink2, qarr[2,1])
mylink2 <- paste(mylink1,hyperlink('method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[20,] <- c('', mylink2, qarr[3,1])
mylink2 <- paste(mylink1,hyperlink('method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[21,] <- c('', mylink2, qarr[4,1])
mylink2 <- paste(mylink1,hyperlink('method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[22,] <- c('', mylink2, qarr[5,1])
mylink2 <- paste(mylink1,hyperlink('method_6.htm','(Closest Observation)',''),sep=' ')
res[23,] <- c('', mylink2, qarr[6,1])
mylink2 <- paste(mylink1,hyperlink('method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[24,] <- c('', mylink2, qarr[7,1])
mylink2 <- paste(mylink1,hyperlink('method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[25,] <- c('', mylink2, qarr[8,1])
mylink1 <- hyperlink('deviation.htm','Semi Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[26,] <- c('', mylink2, qarr[1,2])
mylink2 <- paste(mylink1,hyperlink('method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[27,] <- c('', mylink2, qarr[2,2])
mylink2 <- paste(mylink1,hyperlink('method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[28,] <- c('', mylink2, qarr[3,2])
mylink2 <- paste(mylink1,hyperlink('method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[29,] <- c('', mylink2, qarr[4,2])
mylink2 <- paste(mylink1,hyperlink('method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[30,] <- c('', mylink2, qarr[5,2])
mylink2 <- paste(mylink1,hyperlink('method_6.htm','(Closest Observation)',''),sep=' ')
res[31,] <- c('', mylink2, qarr[6,2])
mylink2 <- paste(mylink1,hyperlink('method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[32,] <- c('', mylink2, qarr[7,2])
mylink2 <- paste(mylink1,hyperlink('method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[33,] <- c('', mylink2, qarr[8,2])
mylink1 <- hyperlink('variation1.htm','Coefficient of Quartile Variation','')
mylink2 <- paste(mylink1,hyperlink('method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[34,] <- c('', mylink2, qarr[1,3])
mylink2 <- paste(mylink1,hyperlink('method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[35,] <- c('', mylink2, qarr[2,3])
mylink2 <- paste(mylink1,hyperlink('method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[36,] <- c('', mylink2, qarr[3,3])
mylink2 <- paste(mylink1,hyperlink('method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[37,] <- c('', mylink2, qarr[4,3])
mylink2 <- paste(mylink1,hyperlink('method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[38,] <- c('', mylink2, qarr[5,3])
mylink2 <- paste(mylink1,hyperlink('method_6.htm','(Closest Observation)',''),sep=' ')
res[39,] <- c('', mylink2, qarr[6,3])
mylink2 <- paste(mylink1,hyperlink('method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[40,] <- c('', mylink2, qarr[7,3])
mylink2 <- paste(mylink1,hyperlink('method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[41,] <- c('', mylink2, qarr[8,3])
res[42,] <- c('Number of all Pairs of Observations', 'pair_numbers.htm', lx*(lx-1)/2)
res[43,] <- c('Squared Differences between all Pairs of Observations', 'squared_differences.htm', sdpo)
res[44,] <- c('Mean Absolute Differences between all Pairs of Observations', 'mean_abs_differences.htm', adpo)
res[45,] <- c('Gini Mean Difference', 'gini_mean_difference.htm', gmd)
res[46,] <- c('Leik Measure of Dispersion', 'leiks_d.htm', bigd)
res[47,] <- c('Index of Diversity', 'diversity.htm', iod)
res[48,] <- c('Index of Qualitative Variation', 'qualitative_variation.htm', iod*lx/(lx-1))
res[49,] <- c('Coefficient of Dispersion', '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')