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Scale-Up and Masking (with 4 questions = 2 above + 2 extra)

Definitions

For a given NAME:

t = "total number of alters named NAME that the respondent knows"

k = "has name NAME and knows respondent uses drugs"

u = "has name NAME and respondent knows he uses drugs"

xy = x and y

~z = not z

Example

~k~u: alters who do not use drugs and have no knowledge of the respondent's use

Equations

ku + k~u + ~ku + ~k~u = t

ku + k~u = k

~ku + ~k~u = ~k

ku + ~ku = u

k~u + ~k~u = ~u

Questions

?t = T

?k = K

?u = U

?ku = KU

Examples

~k~u = ~u - k~u = t - u + ku - k = T - K - U + KU

k~u/~u = (k - ku) / (t - u) = (K - KU) / (T - U)