Post on 05-Jan-2016
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?