Variations to Mendel's First Law
Chi-Square Test
The Chi-Square Test
An important question to answer in any genetic experiment is how can we decide if our data fits any of the Mendelian ratios we have discussed. A statistical test that can test out ratios is the Chi-Square or Goodness of Fit test.
Chi-Square Formula
Degrees of freedom (df) = n-1 where n is the number of classes
Let's test the following data to determine if it fits a 9:3:3:1 ratio.
| Observed Values | Expected Values |
|---|---|
| 315 Round, Yellow Seed | (9/16)(556) = 312.75 Round, Yellow Seed |
| 108 Round, Green Seed | (3/16)(556) = 104.25 Round, Green Seed |
| 101 Wrinkled, Yellow Seed | (3/16)(556) = 104.25 Wrinkled, Yellow |
| 32 Wrinkled, Green | (1/16)(556) = 34.75 Wrinkled, Green |
| 556 Total Seeds | 556.00 Total Seeds |
Number of classes (n) = 4
df = n-1 + 4-1 = 3
Chi-square value = 0.47
Enter the Chi-Square table at df = 3 and we see the probability of our chi-square value is greater than 0.90. By statistical convention, we use the 0.05 probability level as our critical value. If the calculated chi-square value is less than the 0 .05 value, we accept the hypothesis. If the value is greater than the value, we reject the hypothesis. Threrefore, because the calculated chi-square value is greater than the we accept the hypothesis that the data fits a 9:3:3:1 ratio.
A Chi-Square Table
| Probability | |||||
|---|---|---|---|---|---|
| Degrees of Freedom |
0.9 | 0.5 | 0.1 | 0.05 | 0.01 |
| 1 | 0.02 | 0.46 | 2.71 | 3.84 | 6.64 |
| 2 | 0.21 | 1.39 | 4.61 | 5.99 | 9.21 |
| 3 | 0.58 | 2.37 | 6.25 | 7.82 | 11.35 |
| 4 | 1.06 | 3.36 | 7.78 | 9.49 | 13.28 |
| 5 | 1.61 | 4.35 | 9.24 | 11.07 | 15.09 |
Copyright © 2000. Phillip McClean