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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Graduation and graduation tests

In a graduation test report, the signs test on 25 ages shows 17 positive deviations. Under the null hypothesis the number of positive deviations is Binomial(25, 0.5). Which statement describes the role of this test relative to the serial correlation test?

The signs test looks at the overall balance between positive and negative deviations, detecting bias, while the serial correlation test looks at how those signs are ordered across ages. A graduation can pass one and fail the other, so they are complementary rather than interchangeable.

  1. AThe signs test checks overall balance of positive and negative deviations, whereas serial correlation checks their ordering across agesCorrect
  2. BThe signs test checks the ordering of deviations, whereas serial correlation checks overall balance
  3. CBoth tests detect only the same problem, so one can replace the other
  4. DThe signs test checks smoothness of the graduated rates
  5. The signs test is valid only when the lag-1 autocorrelation is zero

Explanation

The signs test counts positives against a Binomial(n, 0.5) null and detects overall bias. A graduation could have an equal number of positive and negative deviations but have them in long runs, which only the serial correlation or runs test would detect. Thus they test different features.

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