Abstract:
This work compares different randomized response designs by their measures of efficiency using
the concept of Jeopardy Function. A population is divided into two sensitive groups, 𝐴 𝑎𝑛𝑑 𝐴𝐶
with unknown proportion 𝜋 𝑎𝑛𝑑 (1 − 𝜋), respectively. Considering a dichotomous response
model where a typical response R is yes (say, y) or no (say, n). The conditional probabilities that a
person R comes from individual of groups, 𝐴 𝑎𝑛𝑑 𝐴𝐶 , are 𝑃(𝑅|𝐴) 𝑎𝑛𝑑 𝑃(𝑅|𝐴𝐶 ), respectively.
These probabilities are at the researcher’s disposal and are called Design probabilities. Taking into
consideration these design probabilities, a natural measure was proposed and it was carried
by 𝑅 𝑎𝑏𝑜𝑢𝑡 𝐴 𝑎𝑛𝑑 𝐴𝐶 , respectively. These measure are as follows: 𝑔(𝑅|𝐴) =
𝑃(𝑅|𝐴)
𝑃(𝑅|𝐴𝐶
)
; 𝑔(𝑅|𝐴𝐶 ) =
1
𝑔(𝑅|𝐴)
.
Considering the Percentage Relative Efficiency of Mangat et al. (1995) and Bhargava and Singh
(2002), defined by; 𝑃𝑅𝐸 =
𝑉(𝜋̂𝐵𝑆)
𝑉(𝜋̂𝑀)
× 100,
It is found that the Bhargava and Singh model is better than Mangat et al.’s model when
𝜋 >
1
2
, and when 𝜋 <
1
2
, Mangat et al.’s model is better than Bhargava and Singh’s model.
