AP Biology Name:
Jones Period: Date:
Chi-Square Statistical Analysis with Genetics
v Example: Monohybrid Cross
Assuming purple is dominant to white flower color
· P Generation: Cross two true breeders; one purple (PP) and one white (pp) flower
· Next, cross two F1 (Pp X Pp); we would expect a 3:1 ratio in the F2 offspring.
Total flowers produced = 150
· We now calculate the chi-square value based on the 3:1 hypothesis.
You should understand that the chi-square compares the NUMBER (not ratio) observed to the NUMBER (not ratio) expected.
· We look up the critical value for the 0.05 probability level from the chi-square table for 1 degree of freedom (2-1=1). The table value is 3.841.
· Because 2.0 < 3.841, we accept the hypothesis. This means that the difference between the predicted and actual cross results is not significant (at the 5% probability level).
v Example: Dihybrid Cross
Now let’s try it! We’ll take it slow and walk you through each step. SHOW YOUR WORK.
- Mendel’s data from one of his experiments was…
- P = smooth seeds crossed with wrinkled seed
- F1 = all smooth seeds (so smooth is dominant and wrinkled is recessive)
- F2 = 5,474 smooth seeds and 1,850 wrinkled seeds
1. What ratio did he observe?
2. What ratio did he expect?
® You already know the number observed: smooth =5,474 & wrinkled = 1,850
3. What is the total number of seeds?
4. What number of wrinkled is expected?
5. What number of smooth is expected?
6. What is the difference between observed and expected smooth?
7. What is the difference between observed and expected wrinkled?
8. What is the square of the difference between the observed and expected smooth?
9. What is the square of the difference between the observed and expected wrinkled?
10. What is the square of the difference between the observed and expected smooth, divided by the expected number of smooth?
11. What is the square of the difference between the observed and expected wrinkled, divided by the expected number of wrinkled?
12. What is the sum of the “squared difference per expected”? In other words, the chi-square value is?
® Any chi-square larger than the value form the 5% Table indicated an experiment in which the ratios observed are so far off the expected that we have to conclude that the ratios expected are wrong!
13. List the different classes/categories in the experiment. ______
14. How many degrees of freedom are there in this experiment? ______
15. Is the chi-square you calculated within the boundary of “the possible”? Explain.
- One more monohybrid cross without the baby steps J: Consider these results among the F2 = 4,400 yellow seeds and 1,624 green seeds (yellow is dominant to green). Use the space below to work out the chi-square value. Will you accept or reject the null hypothesis? Explain.
Phenotypes / O / E / O-E / (O-E)2 / (O-E)2
E
Total / XXXXXXX / XXXXXXXX
Do you accept or reject that these results are within acceptable range of a 3:1 ratio (the null hypothesis)? Explain.
- Let’s try one for a Dihybrid cross using the results below:
Cross two flowers that are both heterozygous for two traits: Flower color and flower height.
White and Short are dominant to red and tall (WwSs X WwSs)
1. Use the space below to show the Punnett square:
® Use these observed results to calculate the chi-square value for this cross
- 206 white short
- 65 white tall
- 83 red short
- 30 red tall
Phenotypes / O / E / O-E / (O-E)2 / (O-E)2E
Total / XXXXXX / XXXXXX
2. How many classes/categories are in this experiment?
3. How many degrees of freedom are in this experiment?
4. Does the 9:3:3:1 ratio fit the data? In other words, do you accept or reject the null hypothesis? Explain.