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# statistics_new.tcl --
# Implementation of the Wilcoxon test: test if the medians
# of two samples are the same
#
# test-Wilcoxon
# Compute the statistic that indicates if the medians of two
# samples are the same
#
# Arguments:
# sample_a List of values in the first sample
# sample_b List of values in the second sample
#
# Result:
# Statistic for the test (if both samples have 10 or more
# values, the statistic behaves as a standard normal variable)
#
proc ::math::statistics::test-Wilcoxon {sample_a sample_b} {
#
# Construct the sorted list for both
#
set sorted {}
set count_a 0
set count_b 0
foreach sample {sample_a sample_b} code {0 1} count {count_a count_b} {
foreach v [set $sample] {
if { $v ne {} } {
incr $count
lappend sorted [list $v $code]
}
}
}
set raw_sorted [lsort -index 0 -real $sorted]
#
# Resolve the ties (TODO)
# - Make sure the previous value is never equal to the first
# - Take care of the last part of the sorted samples
#
set previous [expr {0.5*[lindex $raw_sorted 0 0] - 1.0}]
set sorted $raw_sorted
set rank 0
set sum_ranks 0
set count 0
set first 0
set index 0
foreach v [concat $raw_sorted {{} -1}] {
set sum_ranks [expr {$sum_ranks + $rank}]
incr count
set current [lindex $v 0]
if { $current != $previous } {
set new_rank [expr {$sum_ranks / $count}]
if { $index > [llength $raw_sorted] } {
set index [llength $raw_sorted]
}
for {set elem $first} {$elem < $index} {incr elem} {
lset sorted $elem 0 $new_rank
}
set previous $current
set first $index
set count 0
set sum_ranks 0
}
incr index
incr rank
}
#
# Sum the ranks for the first sample and determine
# the statistic
#
if { $count_a < 2 || $count_b < 2 } {
return -code error \
-errorcode DATA -errorinfo {Too few data in one or both samples}
}
set sum 0
foreach v $sorted {
if { [lindex $v 1] == 0 } {
set rank [lindex $v 0]
set sum [expr {$sum + $rank}]
}
}
set expected [expr {$count_a * ($count_a + $count_b + 1)/2.0}]
set stdev [expr {sqrt($count_b * $expected/6.0)}]
set statistic [expr {($sum-$expected)/$stdev}]
return $statistic
}
# SpearmanRankData --
# Auxiliary procedure to rank the data
#
# Arguments:
# sample Series of data to be ranked
#
# Returns:
# Ranks of the data
#
proc ::math::statistics::SpearmanRankData {sample} {
set counted_sample {}
set count 0
foreach v $sample {
if { $v ne {} } {
incr count
lappend counted_sample [list $v 0 $count]
}
}
set raw_sorted [lsort -index 0 -real $counted_sample]
#
# Resolve the ties (TODO)
# - Make sure the previous value is never equal to the first
# - Take care of the last part of the sorted samples
#
set previous [expr {0.5*[lindex $raw_sorted 0 0] - 1.0}]
set sorted $raw_sorted
set rank 0
set sum_ranks 0
set count 0
set first 0
set index 0
foreach v [concat $raw_sorted {{} -1}] {
set sum_ranks [expr {$sum_ranks + $rank}]
incr count
set current [lindex $v 0]
if { $current != $previous } {
set new_rank [expr {$sum_ranks / $count}]
if { $index > [llength $raw_sorted] } {
set index [llength $raw_sorted]
}
for {set elem $first} {$elem < $index} {incr elem} {
lset sorted $elem 1 $new_rank
}
set previous $current
set first $index
set count 0
set sum_ranks 0
}
incr index
incr rank
}
#
# Return the ranks of the data in the original order
#
set ranks {}
foreach values [lsort -index 2 -integer $sorted] {
lappend ranks [lindex $values 1]
}
return $ranks
}
# spearman-rank-extended --
# Compute the Spearman's rank correlation coefficient and
# associated parameters
#
# Arguments:
# sample_a List of values in the first sample
# sample_b List of values in the second sample
#
# Result:
# List of:
# - Rank correlation coefficient
# - Number of data
# - z-score to test the null hyothesis
#
proc ::math::statistics::spearman-rank-extended {sample_a sample_b} {
#
# Filter out missing data
#
if { [llength $sample_a] != [llength $sample_b] } {
return -code error \
-errorcode DATA -errorinfo {The two samples should have the same number of data}
}
set new_sample_a {}
set new_sample_b {}
foreach a $sample_a b $sample_b {
if { $a != {} && $b != {} } {
lappend new_sample_a $a
lappend new_sample_b $b
}
}
#
# Construct the ranks
#
set rank_a [SpearmanRankData $new_sample_a]
set rank_b [SpearmanRankData $new_sample_b]
set rcorr [corr $rank_a $rank_b]
set number [llength $new_sample_a]
set zscore [expr {sqrt(($number-3)/1.06) * 0.5 * log((1.0+$rcorr)/(1.0-$rcorr))}]
return [list $rcorr $number $zscore]
}
# spearman-rank --
# Compute the Spearman's rank correlation coefficient
#
# Arguments:
# sample_a List of values in the first sample
# sample_b List of values in the second sample
#
# Result:
# Rank correlation coefficient
#
proc ::math::statistics::spearman-rank {sample_a sample_b} {
return [lindex [spearman-rank-extended $sample_a $sample_b] 0]
}
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