Lab 10: One-Way ANOVA

Which Study Method Works Best?

Dave Brocker

Farmingdale State College

One-Way ANOVA

Concept Review

  • Compares means across 3+ groups

  • Used when you want to test if at least one group differs from the others

  • Tests the null hypothesis that all group means are equal: \(H_0: \mu_1 = \mu_2 = \mu_3\)

Scenario

Three groups of students used different methods to study for a quiz:

  • Video lectures
  • Reading the textbook
  • Flashcards

Each student then took the same 10-question quiz.

  • What is the independent variable (IV) here? What is the dependent variable (DV)?

Simulated Data in R

  method    score
1  Video 6.939524
2  Video 7.269823
3  Video 9.058708
4  Video 7.570508
5  Video 7.629288
6  Video 9.215065

Visualizing Scores

Running the ANOVA

anova_result <- aov(score ~ method, data = study_data)
summary(anova_result)
            Df Sum Sq Mean Sq F value   Pr(>F)    
method       2  32.84  16.420    16.9 4.12e-06 ***
Residuals   42  40.80   0.972                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

\[F = \frac{MS_B}{MS_E} = \frac{SS_B / (k - 1)}{SS_E / (N - k)}\]

  • F is the variance between group means (numerator) divided by the variance within groups (denominator); \(k\) = number of groups, \(N\) = total sample size

  • Look at the F value and p-value

  • If \(p < .05\), reject the null hypothesis

Post Hoc: Tukey HSD

TukeyHSD(anova_result)
  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = score ~ method, data = study_data)

$method
                          diff        lwr        upr     p adj
Textbook-Flashcards -2.0321418 -2.9065437 -1.1577400 0.0000038
Video-Flashcards    -0.5838473 -1.4582491  0.2905546 0.2476431
Video-Textbook       1.4482946  0.5738927  2.3226964 0.0006718

  • Shows which pairs of study methods differ significantly

  • Adjusts for multiple comparisons, so we don’t inflate our Type I error rate by running three separate t-tests

Discussion Prompts

  1. Which group performed best?

  2. Is the difference statistically significant?

  3. Is the difference practically meaningful? (Hint: look back at the boxplot — how much does a 1-point difference on a 10-question quiz actually matter?)

  4. What might influence quiz performance beyond study method?

Wrap-Up

  • One-way ANOVA compares 3+ means

  • A significant F-test tells you at least one group differs — Tukey HSD tells you which ones

  • Real-world applications: education, psychology, marketing, and beyond

Submit on Brightspace

Using study_data, answer:

  1. Report the F-statistic, degrees of freedom, and p-value from your ANOVA.

  2. Which pair(s) of study methods differ significantly per the Tukey HSD test?

  3. In your own words, explain what it would mean if this ANOVA had not been significant.