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IAI Actuarial Core Principles · Actuarial Statistics · Purpose and function of data analysis

A pension scheme dataset has 500 members, and salary is missing for 100 of them. Among the 400 members with salary recorded, the mean salary is ₹60,000. It is known that higher-paid members are more likely to leave salary blank. Which statement is correct about using the 400-record mean as an estimate for all 500 members?

The complete-case mean is likely biased downwards. Because higher earners are more likely to leave salary blank, they are under-represented in the observed records, so missingness is related to the value itself and the sample mean understates the true average.

  1. AIt is unbiased, because the missing values are random
  2. BIt is likely to be biased downwards, because the data are not missing completely at randomCorrect
  3. CIt is likely to be biased upwards, because missing members are low earners
  4. DIt is exactly ₹60,000 for all members by the law of large numbers
  5. It is unbiased provided the 400 records are not duplicated

Explanation

If higher earners are more likely to omit salary, the observed sample under-represents them, so the complete-case mean tends to underestimate the true mean. The missingness depends on the value itself, so it is not missing completely at random and complete-case analysis is biased. A large sample does not remove this bias.

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