Biology 212 General Genetics
Lecture 7: “Chi-Square”
Spring 2007
Reading: Chap. 3. pp. 107-111
Lecture Outline:
1. Chi-square test
Lecture:
1. Chi-Square test: Statistical test used to decide if experimentally observed results
are consistent with hypothesis.
Used in Genetics to
a. test fit of observed results to predicted ratio (laboratory, Chap. 3)
b. test whether genes are linked on the same chromosome (Chap. 4)
c. test whether population is in Hardy Weinberg equilibrium (Chap. 14)
Equation:
χ2 = Σ (observed-expected)2/expected
Chi-square sum
experimental results
predicted results based on Mendelian ratios
for same sample size
Chi-square test example: Problem 3.16
State hypothesis (here a predicted Mendelian phenotypic ratio):
Do the actual results from a testcross (188 tall red, 203 tall white, 175 short red, 178 short
white) fit the genetic hypothesis of 1:1:1:1 segregation?
1. Complete table with phenotypes and observed results.
Phenotypes
Observed
Expected
Obs-Exp
(Obs-Exp)2
Tall red
Tall white
Short red
Short white
188
203
175
178
744 total
¼(744)=186
¼(744)=186
¼(744)=186
¼(744)=186
744 total
2
17
-11
-8
4
289
121
64
(Obs-Exp)2/
Exp
0.022
1.55
0.65
0.34
χ2=1.977
2. Calculate the expected values. This is the number you would predict from a sample of
the same size given the stated hypothesis. Here we hypothesize a 1:1:1:1 ratio of
phenotypes, thus ¼ of the total is expected for each type.
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3. Use the table to prompt you for the other calculations. Subtract expected# from
observed#, square that, then divide that number by the expected#.
4. Chi-square is the sum of the last column of numbers (sum of observed#expected#/expected#).
5. Interpret Chi-square as indicated below:
Interpretation of χ2
1. Calculate # degrees of freedom. Usually df=#phenotypes-1
2. Use a chi-square graph or table to find the “critical value” for the #df and p=0.05 (5%
level)
for example, for a dihybrid cross producing 4 phenotypes, df=3, p=0.05
χ2 critical value =7.815
3. Compare calculated value to critical value


if critical value is greater than calculated χ2 then accept hypothesis (or fail to
reject, if you are a statistical purist)
if critical value is less than calculated χ2 then reject hypothesis
For example given χ2=1.977; this is less than 7.815, so you would accept the hypothesis.
A 1:1:1:1 phenotypic ratio is thus consistent with these data.
4. It is stronger in this test to reject a hypothesis, rather than accept a hypothesis
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