
The careless responding measure is calculated as  a weighted sum of all the averages of the sub_measures.  

cr_measure=
    w_mls*avg(mls)+
    w_pagetime*avg(pagetime<2*number_of_questions_on_page)+
    w_syn*avg(syn_a==syn_b)+
    w_ant*avg(ant_a!=ant_b)+
    w_infreq*avg(infreq==infreq_ans)
    
where:
    w_... is the weight for each measure
    mls is the max long string measure, which is between 1 and the number of questions on the page
    pagetime is the time spent on each page
    syn is for semantic synonyms, where syn_a and syn_b represent synonymous item pairs
    ant is for semantic antonyms, where ant_a and ant_b represent antonymous item pairs
    infreq is for infrequency (bogus) questions, where infreq is the item and infreq_ans is the expected response
    
    
avg represents a calculation of the arithmetic mean (aka average)
    (computed as sum(n)/count(n))
    avg's for mls and pagetime are calculated over all completed pages
    avg's for syn, ant, and infrq are calculated over all completed items
    If there are no entries for a submeasure, it returns 0
    
    
comparison operators ==, !=, < (equals, not equals, less than, resp.) evaluate to a true or false, 
    which is cast to a 1 or a 0
    e.g. if syn_a==syn_b, that counts as a 1
    but  if syn_a!=syn_b, that counts as a 0