Teacher Guide for Chi Squared

Prerequisites	Students must be familiar with the concept of testing deviations for significance. This also involves ways to express the probability of an event occurring randomly.

Completed	By now students have determined the expected frequencies for the alleles controlling the six traits surveyed during the project.

Rationale	Students complete this activity in order to compare their results with the results expected according to the Hardy-Weinberg Equilibrium Equation.

Objective	The primary reason for doing this activity is to test the hypothesis that there is no significant difference between the observed and expected results of the survey conducted during the project. While the Chi Squared technique is not the only statistical test for significance, it appears to be the one favored by geneticists.

1.	Your students are working with calculators. They will need hard copies of the project data, the Chi Squared Critical Values Table and tables for recording their results.

2.	The students are given the hypothesis here, but later, they will be asked to formulate their own. In essence, their hypothesis suggests that the numbers of individuals showing the recessive trait are not significantly different from the number of individuals expected (from the Hardy - Weinberg Equation) to show the recessive trait.

3.	Students are to fill out Table 3. They need the information from the last row of Table 2 and the project data. The current project data are from this semester only.

	Help with Table 3?

4.	In the Chi Squared Table, df stands for degrees of freedom. The value of df is one less than the number of possibilities (n): df = (n -1). The recessive trait is one possibility and the dominant trait is the other. Therefore, n = 2 and df = 1.

	The p value is the probability of an event occurring by chance.

5.	Students should have little difficulty in completing Table #4. When they are done, have them work out the answers to the questions. Please include a summary of your findings in your final report. You are encouraged to use the general discussion area to discuss these questions with other participants. Feel free to consult with the project leader as well.

6.	Explaining this part to the students may be your greatest challenge. Just remember this: Values of p greater than 10% (p > 0.1) mean that students should reject the hypothesis and conclude that the differences between the observed and expected values are important.

7.	Suppose you and the students determine that the expected and observed values do not match. What might this mean? (HINT: Under what conditions does the Hardy-Weinberg Equilibrium apply?) Again, feel free to consult.

Linked from	analysis.html and index.html
Recommended Level	High School
Prerequisites	Basic Statistics
Completed	Hardy-Weinberg Activity
Rationale	Need to determine whether the survey results match expectations
Objective	Determine whether or not the differences between the observed numbers of individuals with each phenotype and the expected numbers of individuals with each phenotype