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

A actuary graduates crude mortality rates for ages 40 to 60 and wants to check whether the graduated rates are too far from the crude rates in total across the age range. Which test is designed to detect this overall lack of fit?

The chi-squared test is the right choice. It adds up squared standardised deviations across all ages, so it detects whether graduated rates are collectively too far from crude rates, unlike signs, runs or serial correlation tests, which examine the pattern of deviations.

  1. AChi-squared test, comparing observed and expected deaths using standardised deviationsCorrect
  2. BSigns test, counting the number of positive deviations
  3. CRuns test, counting groups of consecutive same-sign deviations
  4. DSerial correlations test, using lag-one correlation of deviations
  5. Individual standardised deviations test applied to one age only

Explanation

The chi-squared test sums the squared standardised deviations over all ages, so it picks up overall poor fit. The signs, runs and serial correlation tests look at the pattern of signs and are aimed at bias and clumping rather than overall size of deviations. Testing a single age cannot assess the whole range.

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