Chapter 13 Inference for Tables: Chi-Square Procedures AP Statistics 13 – Chi-Square Tests

Chi-Square Procedures Ch 12: Comparing 2 population proportions Chi-Square Tests: –1. Goodness of Fit – examining the distribution of proportions within a single population (13.1) –2. Homogeneity of Populations – 2 or more (13.2) population proportions (2-way tables  Matrices) –3. Association/Independence – Matrices  (13.2) (determine whether the distribution of one variable has been influenced by another)

Then we could perform additional tests of significance for each of the remaining colors. Very Inefficient! Chi-Square ( ) test for goodness of fit.

Properties of Chi-Square Distributions Family of distributions that take only positive values and are Skewed Right! A specific Chi-Square Distribution is specified by one parameter –Degrees of Freedom! Area under the curve = 1 Table E (in back of our book)

Conditions Null Hyp: the actual population proportions are EQAUL to the hypothesized proportions. Alternative Hyp: DIFFERENT The sample was obtained randomly (SRS) All Expected counts are at least 1 No more than 20% of the Expected counts are less than 5

Goodness of Fit - Most commonly used in field of Genetics Example 13.2: Mating 2 Red-Eyed Fruit Flies –Mate 2 fruit flies having genetic makeup RrCc R – Red eyesr – white eyes C – Curly wingsc – straight wings Punnett Square baby! Of 200 offspring: 101 RC, 42 Rc, 49 rC, 8 rc Do these data differ significantly from what the biologist predicted?

13.2 – Inference for Two-way tables Now, we can compare more than 2 groups –Use Chi-Square test for Homogeneity of populations – Chi-Square test for Association/Independence – Use for 2 classifications, 2 categorical variables. – H(0): There is NO ASSOCIATION b/w the 2 variables. Note: –df for a two-way table: (rows - 1)x(columns - 1)

Are these data good evidence that the proportions of successes for the three treatments differ in the population of all cocaine users?