Chapter 25: Chi-Square Tests for Goodness-of-Fit

Question 1

Chi-Square Statistic (χ²)

Answer 1

Σ(Observed-Expected)^2/Expected

Question 2

Chi-Square Degrees Of Freedom

Answer 2

df=number of categories-1

Question 3

Chi-Square Distribution

Answer 3

1. Only nonegative
2. Right skew (less pronounced as df increases)

Question 4

χ²GOF-Test Hypotheses

Answer 4

H0: “The distribution of [context] is the same across all [groups in context].”
Ha: “The distribution of [context] is not the same across all [groups in context].”

Question 5

χ²GOF-Test Conditions

Answer 5

1. Random sample
2. Sample≤10% of pop.
3. All expected counts>5

Question 6

χ²GOF-Test p-value Interpretation

Answer 6

“Assuming the proportions of [a single categorical variable as stated in the null hypothesis] are true, there is a [p-value] probability of getting a chi-square statistic as extreme as the one in the study or more extreme, by chance alone.”

Question 7

χ²GOF-Test On Calculator

Answer 7

Observed: List on L1
Expected: List on L2
df: degrees of freedom

Question 8

χ²-Test (Homogeneity) Hypotheses

Answer 8

H0: “There is no difference in the distribution of [categorical variable in context] across populations or treatments.”
Ha: “There is a difference in the distribution of [categorical variable in context] across populations or treatments.”

Question 9

χ²-Test (Independence)

Answer 9

H0: “There is no association between [categorical variable in context] and [other categorical variable in context] in a given population.”
Ha: “There is an association between [categorical variable in context] and [other categorical variable in context] in a given population.”

Question 10

χ²-Test (Homogeneity & Independence)

Answer 10

1. Stratified random sample (homogeneity) or single random sample (independence)
2. Sample size ≤ 10% of pop.
3. All expected counts>5

Question 11

χ²-Test On Calculator

Answer 11

Observed: Data on matrix [A]
Expected: Will fill in data on matrix [B] as long as it is empty