In: Statistics and Probability
Hair type is an example of incomplete dominance (HCHC = Curly, HCHS = Wavy, HSHS = Straight). A population contains 80 curly, 5 wavy, and 15 straight individuals. Perform a chi-square analysis to determine whether or not this population is in Hardy-Weinberg equilibrium.
a) Calculate your expected values
b) Perform a chi-square analysis
Given:
Hair type is an example of incomplete dominance (HCHC = Curly, HCHS = Wavy, HSHS = Straight). A population contains 80 curly, 5 wavy, and 15 straight individuals.
Hypothesis test:
The null and alternative hypothesis is
Ho : p1 = p2 = p3 = 1/3
Ha : At least one of population is not in Hardy-Weinberg equilibrium.
Table for calculating Chi square test statistic :
Expected frequency E = Total frequency/number of categories
Hair type | Observed frequency O | Expected frequency E | (O-E)2/E |
Curly | 80 | 100/3 = 33.33 | 65.3492 |
Wavy | 5 | 100/3 = 33.33 | 24.0801 |
Straight | 15 | 100/3 = 33.33 | 10.0807 |
Total | 100 | 100 | (O-E)2/E = 99.51 |
Test statistics:
2 = (O-E)2/E = 99.51
Degree of freedom, df = k-1 = 3-1 = 2
P-value:
P-value corresponding to Chi square test statistic 99.51 with degree of freedom , df = 2 is
P-value = 0.00001
Since P-value is less than significance level, = 0.05, we reject null hypothesis.
Conclusion : There is sufficient evidence to conclude that this population is in Hardy-Weinberg equilibrium.