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IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit

In a chi-square goodness of fit test, an expected frequency in one tail cell is only 1.2 while all others exceed 5. What is the standard recommended remedy?

Combine the small-expectation cell with an adjacent cell, because the chi-square approximation needs expected frequencies of about 5 or more. The degrees of freedom are then based on the reduced number of cells.

  1. ACombine the cell with an adjacent cellCorrect
  2. BDelete the cell and reduce the sample size
  3. CIncrease the significance level to 10%
  4. DReplace the chi-square test with a t-test
  5. Add 0.5 to every observed frequency

Explanation

The chi-square approximation requires expected counts of roughly 5 or more. Cells with small expected counts are combined with neighbours, and the degrees of freedom are reduced accordingly. Deleting the cell biases the test.

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