Using the Chi-Squared Test

When should you use the chi-squared test in biology?

• When you have categorical data (counting frequencies of individuals in different groups, like phenotypes).

• When you want to compare observed frequencies against expected frequencies (e.g., testing if a genetic cross fits a 9:3:3:1 ratio).

What are the conditions required to use the chi-squared test?

• The sample size must be relatively large (usually >20).

• The data must be discrete/categorical (counted in whole numbers, not percentages or continuous measurements).

• The expected frequency in any single category should be strictly greater than 5.

What is the standard null hypothesis (H₀) for a chi-squared test in genetics?

"There is no significant difference between the observed and expected frequencies of phenotypes. Any difference is purely due to chance."

How do you calculate the degrees of freedom (df) for a chi-squared test?

• df = n - 1

• Where n is the number of categories (or possible phenotypes).

• Example: If a cross produces 4 different phenotypes, df = 4-1=3.

At what probability level do biologists usually look up the critical value?

• At p = 0.05 (the 5% significance level).

• This means there is a 5% probability that the difference between observed and expected results is simply due to chance.

What is your conclusion if your calculated chi² value is GREATER than or equal to the critical value?

• The difference is significant.

• You reject the null hypothesis.

• The results do not fit the expected ratio (this could indicate that genes are linked or epistasis is occurring).

What is your conclusion if your calculated chi² value is LESS than the critical value?

• The difference is not significant.

• You accept the null hypothesis.

• Any difference is just due to chance, and the data fits the expected ratio.

A genetic cross between two heterozygous plants produces offspring with three different flower colours: red, pink, and white. Calculate the degrees of freedom for a chi-squared test on these data. (1 mark)

Answer: df = 2 (Because there are 3 categories/phenotypes, and 3 - 1 = 2).

Question: In a monohybrid cross of two heterozygous mice, the expected ratio of black to brown fur is 3:1. If exactly 120 offspring are produced in total, calculate the expected frequency for brown mice. (2 marks)

Answer: 1. The total ratio parts = 3 + 1 = 4. 2. 120 / 4 = 30. 3. Therefore, the expected frequency for the recessive brown mice (the "1" in the ratio) is 30.