The Chi-Square Distribution (College Board AP® Statistics)

Chi-square distributions

What is the chi-square distribution?

• The chi-square distribution is a continuous probability distribution of the sum of the squares of independent variables

  • Each of these independent variables follows a standard normal disctribution

• If a continuous random variable follows the chi-square distribution, then its shape will be:

  • positively-skewed

  • non-negative

• Degrees of freedom ('dof') is a parameter that defines the shape of the chi-square distribution curve

  • The dof is the number of independent standard normal random variables,

  • The chi-square distribution curve approximates a normal curve more closely as the degrees of freedom increase

When is the chi-square distribution used?

• The chi-square distribution is used for:

  • Goodness of fit tests

  • Tests of independence

  • Tests of homogeneity

How is a critical value found from the chi-square tables?

• The chi-square tables are given to you in the exam

• A critical value, , can be found from the chi-square tables

  • Find the row that corresponds to the number of degrees of freedom

  • Find the column that corresponds to the relevant significance level

  • The cell where these intersect contains the critical chi-square value,