Exploring Study Habits Through ANOVA

Dec 2, 2024

Lecture Notes: Analysis of Variance (ANOVA) and Study Habits

Introduction to ANOVA

  • In-class activity number: 14b
  • Main question: Who studies the most among college students with different majors?
  • Reference: A study claims college students spend 17 hours/week preparing and studying.
  • Question: Do students from different majors have different study habits? Focus on the mean number of hours spent preparing for classes each week.

Majors Considered

  1. Arts and Humanities
  2. STEM (Science, Technology, Engineering, Math)
  3. Education
  4. Business

Preconceived Notions from Past Students

  • STEM students believed to study the most.
  • Business students thought to be second.
  • Arts and Humanities, and Education perceived as similar in study habits.

ANOVA: One-Way ANOVA

  • Used to compare two or more means from different populations.
  • Helps determine if there are differences in mean study hours between different majors.
  • Requires technology to calculate test statistics and interpret results.

Survey and Research Questions

  • Survey Question: How many hours do students spend preparing for classes per week?
  • Research Question: Is there a difference in mean hours spent preparing based on major?

Groups and Variables

  • Four groups: Arts and Humanities, STEM, Education, Business
  • Variable compared: Number of hours students prepare for classes per week

Hypotheses in ANOVA

  • Null Hypothesis (H₀): All group means are equal (µ₁ = µ₂ = µ₃ = µ₄)
  • Alternative Hypothesis (Hₐ): At least two of the population means are different

Data Collection

  • Randomly selected 12 students from each major
  • Collected data on weekly preparation hours

Descriptive Statistics and Box Plots

  • Descriptive statistics help to initially assess differences.
  • Box plots illustrate variation within and between groups.
  • Observations:
    • STEM appears to have the highest mean study hours.
    • Education and Business are similar in terms of mean and spread.
    • STEM has the greatest variation (IQR) compared to others.

Test Statistic and P-Value

  • Test statistic: F-test statistic = 3.76
  • P-value indicates the probability of observing the data if H₀ is true.
  • Comparison: p-value (0.0173) vs. alpha (significance level, 0.05 or 5%)
  • Conclusion based on p-value: Reject H₀ if p-value < alpha. Here, reject H₀ at 5% but not at 1%.

Conclusion

  • Rejecting H₀ at 5% significance suggests at least two means are different.
  • The ANOVA test does not specify which means are different.

Implications

  • STEM majors generally study more compared to other majors, especially Business majors.
  • ANOVA does not confirm which specific groups differ.

Follow-Up Questions

  • Changing significance level to 1% impacts decision.
  • With 1% alpha, do not reject H₀; conclude all majors might have similar study habits.

Final Thoughts

  • ANOVA is useful for comparing means across multiple groups.
  • Technology simplifies calculations and interpretations.
  • Emphasizes the importance of using statistical evidence over preconceived notions.