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 ofFreedom 0.9 0.5 0.1 0.05 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