Module Quiz

Quiz Instructions

15 questions covering all four lessons
Passing score: 70% (11 out of 15 correct)
Mix of conceptual understanding and calculations
You can review explanations after submitting
Take your time and read each question carefully

What is the primary purpose of ANOVA?

A) To test if two population means are equal B) To test if three or more population means are equal C) To test if two variables are correlated D) To test if two categorical variables are independent

Why shouldn't we use multiple t-tests when comparing 5 groups?

A) T-tests are too difficult to calculate B) Multiple t-tests inflate the Type I error rate C) T-tests can only be used with normal data D) ANOVA is always more powerful than t-tests

The F-statistic in ANOVA is calculated as:

A) F = SSB / SSW B) F = MSB / MSW C) F = (x̄₁ - x̄₂) / s D) F = SST / df_total

Given k = 4 groups and N = 48 total observations, what are df_between and df_within?

A) df_between = 3, df_within = 44 B) df_between = 4, df_within = 44 C) df_between = 3, df_within = 47 D) df_between = 4, df_within = 48

Which relationship is ALWAYS true in ANOVA?

A) SST = SSB - SSW B) SST = SSB + SSW C) MSB = MSW D) F = 1

Given SSB = 150, SSW = 250, df_between = 2, df_within = 27, calculate F.

A) F = 0.6 B) F = 1.67 C) F = 8.1 D) F = 27.0

An ANOVA yields F = 12.5 with p = 0.0002. What can we conclude?

A) All group means are significantly different from each other B) At least one group mean is significantly different C) All group means are equal D) Exactly two groups differ significantly

When should post-hoc tests be conducted?

A) Always, regardless of ANOVA results B) Only when ANOVA is significant AND there are 3+ groups C) Only when ANOVA is not significant D) Before running ANOVA

Tukey's HSD = 5.2. Group means are: x̄₁ = 42, x̄₂ = 48, x̄₃ = 45. Which groups differ significantly?

A) Only groups 1 and 2 B) Only groups 2 and 3 C) All three groups differ from each other D) No groups differ significantly

If comparing 6 groups with α = 0.05, what is the Bonferroni-adjusted α?

A) 0.05 B) 0.0083 C) 0.0033 D) 0.30

Which is NOT an assumption of one-way ANOVA?

A) Observations are independent B) Populations are normally distributed C) All groups have equal variances D) All groups must have the same sample size

Three groups have variances: s₁² = 10, s₂² = 15, s₃² = 22. Is equal variance reasonable?

A) Yes, because 22/10 = 2.2 < 3 B) No, because 22/10 = 2.2 > 2 C) Yes, because all variances are positive D) Cannot determine without knowing sample sizes

What is the appropriate test for comparing median incomes across 4 cities when data is highly skewed?

A) One-way ANOVA B) Kruskal-Wallis test C) Chi-square test D) Two-sample t-test

ANOVA is most robust to violations of normality when:

A) Sample sizes are small (n < 10 per group) B) Sample sizes are large (n ≥ 30 per group) C) Variances are very different across groups D) The F-statistic is small

A study compares stress levels of 40 employees at three time points (morning, afternoon, evening). Which test is appropriate?

A) One-way ANOVA (independent groups) B) Repeated measures ANOVA (dependent groups) C) Two-sample t-test D) Kruskal-Wallis test