Using the Chi-Squared Test on Data from Dihybrid Crosses
- Consider a scientist studying inheritance patterns in pea plants.
- They've performed a dihybrid cross and predicted a 9:3:3:1 phenotypic ratio in the F2 generation.
- But when they count the offspring, the numbers don't match perfectly.
- The scientist now needs to determine if this deviation is due to chance or if something else is at play.
- The chi-squared test helps you answer this question by comparing your observed results to the expected ones.
Why Use the Chi-Squared Test?
- In genetics, the chi-squared test is used to:
- Compare observed results (actual data) to expected results (based on predictions).
- Determine if deviations are due to chance or if they suggest other factors, like gene linkage.
Observed vs. Expected Results
- In a dihybrid cross, the expected phenotypic ratio for unlinked genes is 9:3:3:1.
- This means:
- 9/16 of the offspring should show both dominant traits.
- 3/16 should show one dominant and one recessive trait.
- 3/16 should show the other dominant and recessive trait.
- 1/16 should show both recessive traits.
The null hypothesis assumes that the traits assort independently, following Mendelian ratios.
Calculating Chi-Squared ($\chi^2$)
The chi-squared formula is:
$$\chi^2 = \sum \frac{(O - E)^2}{E}$$
where $O$ is the observed frequency and $E$ is the expected frequency.
