## Chi-squared data: flies

Six datasets based on reproduction experiments with fruit flies – used for chi-squared statistics calculations…

Winged | Vestigial |

40 | 23 |

58 | 18 |

53 | 24 |

52 | 19 |

52 | 21 |

49 | 16 |

The Winged flies had well-formed wings that result from double dominant genes or dominant and recessive (both ways round). The Vestigial flies had the stump wings associated with a double recessive gene.

There are worked examples of the calculation and plenty of information on the genetic context available in a laboratory manual designed for US undergraduates published by the University of South Florida. Page 19 has the contextual material and detailed examples.

One student came up with the idea of calculating the chi^{2} statistic based on expected values calculated both for the Mendelian 1:3 ratio *and* the alternative ratio of 1:2. Many of the data sets result in calculated chi^{2} statistics for both ratios that are *less than* the critical value of chi^{2} for 5% and 1 degree of freedom, so we can conclude that the sample is too small to distinguish between the two hypotheses.

A motivation for the 1:2 hypothesis could be along the lines that aA and Aa genotypes were regarded as one outcome, so that there were three possible genotypes, AA, Aa and aa. Only the aa leads to vestigial wings, so you get the 1:2 ratio in the offspring. I’m trying to find a historical reference for Aa and aA not being recognised as different equally likely outcomes.