1. Chapter 13 Inference 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)

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

6. 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)

7. Conditions
Null Hyp: the actual population proportions are EQUAL 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

8. 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?

9. 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)

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