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

Chapter 13Inference for Tables:

Chi-Square Procedures

AP Statistics

13 – Chi-Square Tests

2

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.2

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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 eyes r – white eyes• C – Curly wings c – 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)

...3210 pppH

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