Relative Age Effect and chi-squared statistics

Traditionally, the Relative Age Effect (RAE) is determined with a chi-squared goodness-of-fit test based on a theoretical expected distribution of birthdates. This distribution must be that of the parent population, but many authors choose to replace it by a uniform distribution in order to simplify calculations. The consequences of this simplification are: (a) the actual Type 1 risk is no longer controlled at the conventional threshold of significance; (b) this risk increases with the sample size; and (c) the associated goodness-of-fit test is biased. The importance of these problems is tested on a national population and on a population of registered players.