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ANOVA for GPA and Seating

Jul 25, 2025

Overview

This lecture demonstrates how to use ANOVA to test whether students' GPAs differ based on their classroom seating choice (front, middle, back), including hypotheses, calculations, and interpretation.

Study Type & Hypotheses

  • This was an observational study, so no cause-and-effect relationship can be established.
  • Null Hypothesis (H₀): The mean GPA is equal for all seating rows (Ό₁ = Ό₂ = Ό₃).
  • Alternative Hypothesis (H₁): At least one row's mean GPA is different from the others.
  • Significance level (alpha) is set at 0.05.

ANOVA Procedure

  • Data collected: GPAs grouped by seating row (front, middle, back).
  • Condition checks: Random sampling and normality assumed (Central Limit Theorem applies).
  • Used one-way ANOVA since GPA (numerical) is compared across a categorical variable (row choice).
  • Calculated F statistic: 7.7780 (rounded to four decimal places).
  • Calculated p-value: 0.0021.

Decision & Interpretation

  • Since p-value (0.0021) < alpha (0.05), reject the null hypothesis.
  • There is statistical evidence that at least one seating row has a different mean GPA.

Post Hoc Analysis

  • Conducted pairwise two-sample t-interval comparisons between rows.
  • No significant difference between the middle and back rows (interval captured zero).
  • Significant differences found between front and both middle and back rows.
  • Front row GPAs are estimated to be 0.13 to 0.4 points higher than the other rows.

Key Terms & Definitions

  • Observational Study — A study where the researcher observes subjects without intervention.
  • ANOVA (Analysis of Variance) — A statistical test to compare means across three or more groups.
  • F Statistic — The ratio used in ANOVA to determine group differences.
  • p-value — Probability of obtaining results at least as extreme as the observed results, given that the null hypothesis is true.
  • Post Hoc Test — Additional tests following ANOVA to identify which specific means differ.
  • Significance Level (alpha) — Threshold probability for rejecting the null hypothesis, commonly set at 0.05.

Action Items / Next Steps

  • Review ANOVA calculation steps and interpretation.
  • Practice setting up hypotheses and interpreting output for categorical group comparisons.
  • Remember the limitations of observational studies regarding causation.

Full transcript