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93.2
96
95.2
77.1
70.9
64.8
70.1
77.3
79.5
100.6
100.7
107.1
95.9
82.8
83.3
80
80.4
67.5
75.7
71.1
89.3
101.1
105.2
114.1
96.3
84.4
91.2
81.9
80.5
70.4
74.8
75.9
86.3
98.7
100.9
113.8
89.8
84.4
87.2
85.6
72
69.2
77.5
78.1
94.3
97.7
100.2
116.4
97.1
93
96
80.5
76.1
69.9
73.6
92.6
94.2
93.5
108.5
109.4
105.1
92.5
97.1
81.4
79.1
72.1
78.7
87.1
91.4
109.9
116.3
113
100
84.8
94.3
87.1
90.3
72.4
84.9
92.7
92.2
114.9
112.5
118.3
106
91.2
96.6
96.3
88.2
70.2
86.5
88.2
102.8
119.1
119.2
125.1
106.1
102.1
105.2
101
84.3
87.5
92.7
94.4
113
113.9
122.9
132.7
106.9
96.6
127.3
98.2
100.2
89.4
95.3
104.2
106.4
116.2
135.9
134
104.6
107.1
123.5
98.8
98.6
90.6
89.1
105.2
114
122.1
138
142.2
116.4
112.6
123.8
103.6
113.9
98.6
95
116
113.9
127.5
131.4
145.9
131.5
131
130.5
118.9
114.3
85.7
104.6
105.1
117.3
142.5
140
159.8
131.2
125.4
126.5
119.4
113.5
98.7
114.5
113.8
133.1
143.4
137.3
165.2
126.9
124
135.7
130
109.4
117.8
120.3
121
132.3
142.9
147.4
175.9
132.6
123.7
153.3
134
119.6
116.2
118.6
130.7
129.3
144.4
163.2
179.4
128.1
138.4
152.7
120
140.5
116.2
121.4
127.8
143.6
157.6
166.2
182.3
153.1
147.6
157.7
137.2
151.5
98.7
145.8
151.7
129.4
174.1
197
193.9
164.1
142.8
157.9
159.2
162.2
123.1
130
150.1
169.4
179.7
182.1
194.3
161.4
169.4
168.8
158.1
158.5
135.3
149.3
143.4
142.2
188.4
166.2
199.2
182.7
145.2
182.1
158.7
141.6
132.6
139.6
147
166.6
157
180.4
210.2
159.8
157.8
168.2
158.4
152
142.2
137.2
152.6
166.8
165.6
198.6
201.5
170.7
164.4
179.7
157
168
139.3
138.6
153.4
138.9
172.1
198.4
217.8
173.7
153.8
175.6
147.1
160.3
135.2
148.8
151
148.2
182.2
189.2
183.1
170
158.4
176.1
156.2
153.2
117.9
149.8
156.6
166.7
156.8
158.6
210.8
203.6
175.2
168.7
155.9
147.3
137
141.1
167.4
160.2
191.9
174.4
208.2
159.4
161.1
172.1
158.4
114.6
159.6
159.7
159.4
160.7
165.5
205
205.2
141.6
148.1
184.9
132.5
137.3
135.5
121.7
166.1
146.8
162.8
186.8
185.5
151.5
158.1
143
151.2
147.6
130.7
137.5
146.1
133.6
167.9
181.9
202
166.5
151.3
146.2
148.3
144.7
123.6
151.6
133.9
137.4
181.6
182
190
161.2
155.5
141.9
164.6
136.2
126.8
152.5
126.6
150.1
186.3
147.5
200.4
177.2
127.4
177.1
154.4
135.2
126.4
147.3
140.6
152.3
151.2
172.2
215.3
154.1
159.3
160.4
151.9
148.4
139.6
148.2
153.5
145.1
183.7
210.5
203.3
153.3
144.3
169.6
143.7
160.1
135.6
141.8
159.9
145.7
183.5
198.2
186.8
172
150.6
163.3
153.7
152.9
135.5
148.5
148.4
133.6
194.1
208.6
197.3
164.4
148.1
152
144.1
155
124.5
153
146
138
190
192
192
147
133
163
150
129
131
145
137
138
168
176
188
139
143
150
154
137
129
128
140
143
151
177
184
151
134
164
126
131
125
127
143
143
160
190
182
138
136
152
127
151
130
119
153

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')