Chapter 13 Inference for Tables: Chi-Square Procedures

1
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)

3

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

4
(No Transcript)
5
(No Transcript)
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
  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

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?

11
(No Transcript)
12
(No Transcript)
13
(No Transcript)