# 4: Hypothesis Testing

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• 4.1: Phenotypic Ratios May Not Be As Expected
For a variety of reasons, the phenotypic ratios observed from real crosses rarely match the exact ratios expected based on a Punnett Square or other prediction techniques. There are many possible explanations for deviations from expected ratios. Sometimes these deviations are due to sampling effects, in other words, the random selection of a non-representative subset of individuals for observation. On the other hand, it may be because certain genotypes have a less than 100% survival rate.
• 4.2: Probability
When dealing with probabilities in biology, you are often working with theoretical expectations, not population samples. For example, in a genetic cross of two individual Drosophila melanogaster that are heterozygous at the vestigial locus, Mendel's theory predicts that the probability of an offspring individual being a recessive homozygote (having teeny-tiny wings) is one-fourth, or 0.25. This is equivalent to saying that one-fourth of a population of offspring will have tiny wings.
• 4.3: Chi-Square Test of Goodness-of-Fit
Use the chi-square test of goodness-of-fit when you have one nominal variable with two or more values. You compare the observed counts of observations in each category with the expected counts, which you calculate using some kind of theoretical expectation. If the expected number of observations in any category is too small, the chi-square test may give inaccurate results, and you should use an exact test instead.

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