Chapter 13
Inference for Tables: ChiSquare Procedures

2
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!
2
• Chi-Square (  ) test for goodness of fit.
(O  E )
 
E
2
2
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
–
H 0  p1  p2  p3  ...
• 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?