chi_square - Chi-Square Test A fundamental problem is...

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Chi-Square Test A fundamental problem is genetics is determining whether the experimentally determined data fits the results expected from theory (i.e. Mendel’s laws as expressed in the Punnett square). How can you tell if an observed set of offspring counts is legitimately the result of a given underlying simple ratio? For example, you do a cross and see 290 purple flowers and 110 white flowers in the offspring. This is pretty close to a 3/4 : 1/4 ratio, but how do you formally define "pretty close"? What about 250:150?
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Goodness of Fit Mendel has no way of solving this problem. Shortly after the rediscovery of his work in 1900, Karl Pearson and R.A. Fisher developed the “chi-square” test for this purpose. The chi-square test is a “goodness of fit” test: it answers the question of how well do experimental data fit expectations. We start with a theory for how the offspring will be distributed: the “null hypothesis”. We will discuss the offspring of a self-pollination of a heterozygote. The null hypothesis is that the offspring will appear in a ratio of 3/4 dominant to 1/4 recessive.
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Formula First determine the number of each phenotype that have been observed and how many would be expected given basic genetic theory. Then calculate the chi-square statistic using this formula. You need to memorize the formula! The “Χ” is the Greek letter chi; the “∑” is a sigma; it means to sum the following terms for all phenotypes. “obs” is the number of individuals of the given phenotype observed; “exp” is the number of that phenotype expected from the null hypothesis. Note that you must use the number of individuals, the counts, and NOT proportions, ratios, or frequencies. - = Χ exp exp) ( 2 2 obs
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Example As an example, you count F2 offspring, and get 290 purple and 110 white flowers. This is a total of 400 (290 + 110) offspring. We expect a 3/4 : 1/4 ratio. We need to calculate the expected numbers (you MUST use the numbers of offspring, NOT the proportion!!!); this is done by multiplying the total offspring by the expected proportions.
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chi_square - Chi-Square Test A fundamental problem is...

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