Theories (Models) in Science *must* make predictions of observable events

. . -that we did not previous know about

. . -and must be testable predictions

In Biology, the *one* theory we have which meets the above test is
Mendel's Hypothesis,

. . -as well as Kepler's "Laws of Planetary Motion" explain gravity.

**Chi-square Test**

Used to test the "goodness of fit" of observed data (grouped into classes)

to expected (theoretical, predicted) data.

Expected values from Mendel's Hypothesis (Punnett Analysis)

Expected values from binomial expansion

. . -= pr(allele "A") ... in P-1 generation

offspring | |||||||

genotype | count | phenotype | prob | exp | obs | ||

AA | 1 | type A | 25% | 4.5 | . | ||

Aa | 2 | hybrid | 50% | 9.0 | . | ||

aa | 1 | type a | 25% | 4.5 | . | ||

total | 4 | 100% | 18.0 | 18 |

Record obs data; calculate dev, dev^{2}/exp

offspring | |||||||

phenotype | prob | exp | obs | dev | X^{2}
| ||

type A | 25% | 4.5 | 4 | -0.5 | .056 | ||

hybrid | 50% | 9.0 | 8 | -1.0 | .111 | ||

type a | 25% | 4.5 | 6 | +1.5. | .500 | ||

total | 100% | 18.0 | 18 | .667 | ns |

Total dev^{2}/exp contribution to X^{2} is compared to the tablulated
"critical values" (c.v.) to determine significance

. . -Eureka! there is no evidence to reject genetics explanation!

. . -Eureka, data cannot be explained by genetics explanation.

critical values, X^{2} |
|||

# phenotypes | df | 5% | 1% |

monohybrid dominance |
1 | 5.024 | 6.635 |

monohybrid no dominance |
2 | 5.991 | 9.210 |

dihybrid dominance |
3 | 7.815 | 11.345 |

dihybrid no dominance |
8 | 15.507 | 20.090 |

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© 2004 Prof. LaFrance, Ancilla College