Lecture 6: Chi-Square Analysis, Introduction to Pedigrees.
1. What formula is used to calculate the value of chi-square?
2. How do you determine the expected value, E, for use in the calculation of chi-square?
3. Why is it usually necessary to employ two different expected values, E, when calculating chi-square for phenotypic ratios?
4. For one degree of freedom, the chi-square value is 1.64 for 0.2 probability, 3.84 for 0.05 probability, and 6.64 for 0.01 probability. .
a. You are testing a coin to see if it is unbiased. You toss it 100 times and obtain 53 heads and 47 tails. What conclusion do you reach based on a chi-square test?5. You are examining a dihybrid cross in which four different phenotypes can be observed. How many degrees of freedom do you use to evaluate your chi-square value?
b. You test a second coin that has been damaged and is somewhat bent. This time you obtain 57 heads and 43 tails. What is your conclusion?
c. Why might you recommend more testing in part b.
d. How would your answers to parts b and c differ if you had obtained 60 heads and 40 tails?
e. How much deviation from expected results would be needed to conclude that there was only a 1% chance that the observed deviation could have arisen by chance? .
6. Explain why chi-square values for a given probability become larger as the number of degrees of freedom increases.
7. Does failure to reject the null hypothesis indicate that you have proven it correct? Explain your answer. .
8. What two advantages are derived from squaring the difference between observed and expected values when doing chi-square analysis of data.
9. Why do the probability values read from the table become smaller as chi-square becomes larger?
10. Draw a human pedigree using correct symbols that demonstrates the occurrence of a homozygous recessive disease resulting from the marriage of first cousins. Trace the recessive gene back through the pedigree to its origin from a single individual.
11. In problem 10, what is the probability that a sibling of the diseased individual is not a carrier of the recessive gene?
12. You are examining the goodness of fit of actual data to the expected phenotypic ratios for the F2 generation of a trihybrid cross that started with true breeding individuals in the parental generation. Assume that there is independent assortment at the three loci.
a. How many different phenotypes would you expect to observe?
b. What phenotypic ratios would you expect
c. If you examine 1000 progeny, what are the expected numbers (E) for each of the phenotypes?
d. How many degrees of freedom will you use in a chi-square analysis of you data?
13. Identify the pedigree symbol for each of the following:
a. male14. A family has six sons in a row. They suspect that some type of rare genetic defect may be preventing the birth of daughters. Based on chi-square analysis, can they reject the null hypothesis that their family is simply a random chance deviation away from a 1:1 ratio of boys:girls? Do the chi-squared results compare favorably with the calculated odds of having six boys in a row? Explain the basis for your conclusions.
b. female
c. an afflicted individual
d. a consanguineous marriage.
e. twins
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