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ANALYSIS OF MENDELIAN
RATIOS:
PROBABILITY AND THE
CHI-SQUARE TEST
Genetic – BIOL 358
Lecture 5
24 January 2006
PROBABILITY AND GENETIC EVENTS
Probability Theory
1. Probability of occurrence (P)
P = # of defined outcomes / total # of possible outcomes
Example: P of getting 3 in a die toss
1 chance (of a 3) / 6 possible outcomes = 1/
Probability of Multiple Events
1. Product Rule
-probability of 2 independent events occurring together is equal to the product of their individual probabilities
- Example: A couple, both of whom are normal, have a child that is an albino. The couple was planning to have 2 more children; what is the probability that both will be albino?
Probability of Multiple Events
2. Sum Rule
-probability of either of 2 independent events occurring is equal to the sum of their individual probabilities -either or, but not both occur
Example: For the previous couple, what is the
probability that either both children will be albino or both will be normal?
EVALUATING GENETIC DATA
The Chi-Square Test
1. Compares an observed outcome to an
expected outcome (based on a genetic
hypothesis)
2. Asks if the difference between observed
and expected is due solely to chance
deviations
3. Dependent upon sample size
-chance deviations are more likely when sample size is small
Chance and Mendelian Ratios
4. Chance events can affect Mendelian
ratios
-segregation of alleles is affected by chance -independent assortment is affected by chance -fertilization is affected by chance
5. Chance deviations in any one of the above
can alter observed Mendelian ratios
Monohybrid Example
Use a Chi-Square Test:
-first calculate expected frequencies of each phenotype 3/4 should be tall 1/4 should be dwarf
-then calculate X 2 value
Monohybrid Example
Is your calculated X^2 significant?
Compare your calculated X 2 to the tabled X^2
-need to know degrees of freedom df = N - 1 Where N = the number of phenotypic classes Our example, df = 2 - 1 = 1
Critical Value of Chi-square
Need to set a critical value to interpret your X^2
5% is used by scientific convention -this means that if your calculated X^2 is larger than the tabled X^2 at 5% then the difference is REAL, not due to chance -if your calculated X 2 is less than the tabled X^2 at 5%, then the difference is due solely to CHANCE
X^2 , P < 0.05, 1 df = 3.841 (page 63 in text)
In our example, X 2 = 0.60, definitely less than 3.841, thus deviation is due to chance, these observed numbers fit a Mendelian 3:1 ratio
Dihybrid Example
Consider the following observed F2 offspring:
Round, Yellow Round, Green Wrinkled, Yellow Wrinkled, Green 315 108 101 32
Do these observed results fit a 9:3:3:1 ratio predicted if these traits are inherited in a Mendelian fashion?
