Chi-Square Test Activity
Goal: Use the chi-square goodness-of-fit test to decide whether offspring counts fit an expected Mendelian ratio, and explain what the result does and does not show.
What to do
- On the 3 : 1 tab, press “Mendel: 705 purple : 224 white” and then “Poor fit: 250 : 150”. Record χ², the degrees of freedom, the critical value and the verdict.
- Switch to the 1 : 2 : 1 tab and press “Snapdragons: 28 red : 55 pink : 17 white”. Record the same readouts.
- Switch to the 9 : 3 : 3 : 1 tab and press “Mendel dihybrid: 315 : 108 : 101 : 32”. Record the same readouts.
Record your results
| Data | χ² | Degrees of freedom | Critical value | Verdict |
|---|---|---|---|---|
| Mendel: 705 purple : 224 white | ||||
| Poor fit: 250 : 150 | ||||
| Snapdragons: 28 red : 55 pink : 17 white | ||||
| Mendel dihybrid: 315 : 108 : 101 : 32 |
Questions
For 705 purple : 224 white, calculate the expected counts for a 3 : 1 ratio and then χ².
Why is the 250 : 150 result rejected, even though it may not look far from 3 : 1?
How do you find the degrees of freedom? Why does the critical value change between the 3 : 1, 1 : 2 : 1 and 9 : 3 : 3 : 1 tests?
Do the snapdragon counts (28 red : 55 pink : 17 white) support incomplete dominance with a 1 : 2 : 1 ratio?
A “fits” verdict does not prove the hypothesis is true. Explain what it does tell you.
Challenge: Mendel’s dihybrid counts give χ² = 0.47. Is that a good fit? What would a χ² of exactly 0 mean?
Free from Biology Lab · thebiologylab.org · HS-LS3-3: Apply concepts of statistics and probability to explain the variation and distribution of expressed traits in a population.