chi­square.notebook
November 14, 2013
What is a chi­square test?
• The chi­square test is a “goodness of fit” test: it answers the question of how well does experimental data fit expectations.
• We start with a theory for how the offspring will be distributed: the “null hypothesis”. • For example the offspring of 2 heterozygous parents we would expect a 3:1 ratio. The null hypothesis is that the offspring will appear in a ratio of 3/4 dominant to 1/4 recessive.
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chi­square.notebook
November 14, 2013
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 observed individuals
• “exp” is the number of that phenotype expected • Note that you must use the number of individuals, the counts, and NOT proportions, ratios, or frequencies.
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chi­square.notebook
November 14, 2013
White leghorn chickens, having white feathers and large "single" combs, were crossed to Indian Game Fowl, having dark feathers and small "pea" combs. The F1 were white with pea combs (these would be heterozygous) and the F2 distribution was: 111 white pea, 37 white single, 34 dark pea, and 8 dark single. What phenotypic ratio would you expect? Test your prediction using chi­square.
Phenotype Observed
Expected Ratio
Expected
White/Pea
White/
Single
Dark/Pea
Dark/
Single
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chi­square.notebook
November 14, 2013
Degrees of Freedom
• A critical factor in using the chi­square test is the “degrees of freedom”, which is essentially the number of independent random variables involved.
• Degrees of freedom is simply the number of classes of offspring minus 1. • For our example, there are 2 classes of offspring: purple and white. Thus, degrees of freedom (d.f.) = 2 ­1 = 1.
www.bios.niu.edu/johns/genetics/chi_square.ppt 4
chi­square.notebook
November 14, 2013
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chi­square.notebook
November 14, 2013
If P > .05 we accept the hypothesis
If P < .05 we reject the hypothesis because there is something affecting the outcome other than random chance.
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chi­square.notebook
November 14, 2013
http://waynesword.palomar.edu/lmexer4.htm Chi Square Problem: An ear of corn has a total of 381 grains, including 216 Purple & Smooth, 79 Purple & Shrunken, 65 Yellow & Smooth, and 21 Yellow & Shrunken. These phenotypes and numbers are entered in Columns 1 and 2 of the following Table 2. Your Tentative Hypothesis: This ear of corn was produced by a dihybrid cross (PpSs x PpSs) involving two pairs of heterozygous genes resulting in a theoretical (expected) ratio of 9:3:3:1. 7