AP Statistics; Spring 2016
Chapter 11: Chi-Square () Procedures
Inference for Distributions of Categorical Variables
Goodness of Fit Test(one-way table) / Test of Homogeneity
(two-way table) / Test of Independence/Association
(two-way table)
Is observed sample distribution significantly different in some way from hypothesized distribution? / Separate & Independent SRS’s from each population; this test attempts to determine if the distribution of a given categorical variable is the same for each population / One SRS from only one population; this test attempts to determine if there is a relationship between the given categorical variables from the one SRS from the one population
: x = x = x = … = x (or as claimed)
: different from claim in some way / : Distribution of variables is the same in all populations
: Distributions are not all the same; at least one is different / : Variables are independent/ there is no association
: Variables are not independent/ dependent; they are associated
Conditions:
All individual expected counts must be ≥5;
NOTE: We are interested in expected counts, not observed counts; conditions are checked for expected counts only / Conditions:
Independent SRS’s from each population;
All individual expected counts must be
≥ 5 (NOTE: check this later in matrix [B]); / Conditions:
One SRS, one population;
All individual expected counts must be
≥ 5 (NOTE: check this later in matrix [B]);
Calculations:
State Test Name ( GOF)
Input observed counts into
Input expected counts into
Input formula into as
( (these are components of statistic)
Sum components (sum function; list, math, sum) --this is your statistic
OR
State Test Name ( GOF)
Input observed counts into
Input expected counts into
Stat-test-GOF Test
NOTE: OK to have decimals for expected counts; observed counts should only be whole numbers (no decimals) / Calculations:
State Test Name ( Test of Homogeneity)
Input observed counts into matrix [A]
Stat-test- test
Observed [A]
Expected [B]
(calculator automatically
calculates expected matrix)
NOTE: Now that you have done the test, you can go back and check matrix [B] for the expected count condition above
NOTE: OK to have decimals for expected counts; observed counts should only be whole numbers (no decimals) / Calculations:
State Test Name ( Test of Independence/Association)
Input observed counts into matrix [A]
Stat-test- test
Observed [A]
Expected [B]
(calculator automatically
calculates expected matrix)
NOTE: Now that you have done the test, you can go back and check matrix [B] for the expected count condition above
NOTE: OK to have decimals for expected counts; observed counts should only be whole numbers (no decimals)
Interpretation:
Use 5% α if not otherwise stated; like usual state conclusion, reference α, statistic, & p-value; tie into context of problem / Interpretation:
Use 5% α if not otherwise stated; like usual state conclusion, reference α, statistic, & p-value; tie into context of problem; caution using the word “cause” / Interpretation:
Use 5% α if not otherwise stated; like usual state conclusion, referenceα, statistic, & p-value; tie into context of problem; caution using the word, “cause”
Follow-Up Analysis (if applicable):
Which component contributes largest amount to statistic? Look at CNTRB on calculator screen (same screen as p-value, statistic, and df); arrow to right to see all entries / Follow-Up Analysis (if applicable):
Which component contributes largest amount to statistic? Calculator does not give this info for this test; but if you are given computer output (like Mini-Tab, Crunch-It, etc.), this information will be provided. / Follow-Up Analysis (if applicable):
Which component contributes largest amount to statistic? Calculator does not give this info for this test; but if you are given computer output (like Mini-Tab, Crunch-It, etc.), this information will be provided.