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ANOVA (ANALYSIS OF VARIANCE)

Concepts, Types, Steps, and Applications

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WHAT IS ANOVA?

  • - A statistical test used to compare the means of three or more groups.
  • - Determines whether observed differences are statistically significant.
  • - Helps analyze the effect of categorical variables on a continuous outcome.

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WHY USE ANOVA?

  • - More efficient than multiple t-tests.
  • - Controls Type I error rate.
  • - Commonly used in biological, medical, agricultural, and public health research.

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TYPES OF ANOVA

  • 1. **One-Way ANOVA**
  • - Tests mean differences among 3+ groups for one factor.

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  • 2. **Two-Way ANOVA**
  • - Tests effects of two independent variables and their interaction.

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  • 3. **Repeated Measures ANOVA**
  • - Same subjects measured multiple times or under different conditions.

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ASSUMPTIONS OF ANOVA

  • - Normal distribution of the dependent variable.
  • - Homogeneity of variances.
  • - Independent observations.
  • - Continuous outcome variable.

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ANOVA FORMULA (F-RATIO)

  • F = Variance Between Groups ÷ Variance Within Groups

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  • • A larger F-value indicates greater differences among group means.

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STEPS TO PERFORM ANOVA

  • 1. State the hypotheses.
  • 2. Calculate group means and overall mean.
  • 3. Compute Sum of Squares (SS).
  • 4. Compute Mean Squares (MS).
  • 5. Calculate F-statistic.
  • 6. Check p-value.
  • 7. If significant, perform post-hoc tests.

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EXAMPLE: PUBLIC HEALTH STUDY

  • Research Question:
  • - Does average BMI differ among three physical activity groups?

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  • Groups:
  • - Low activity
  • - Moderate activity
  • - High activity

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  • ANOVA checks if group differences are statistically significant.

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POST-HOC TESTS

  • - Tukey HSD
  • - Bonferroni
  • - Scheffé Test

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  • Used to identify which groups differ after ANOVA shows significance.

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APPLICATIONS OF ANOVA

  • - Drug comparison studies.
  • - Impact of fertilizers on crop yield.
  • - Education: comparing teaching methods.
  • - Public health program evaluation.
  • - Behavioral and psychological experiments.

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LIMITATIONS OF ANOVA

  • - Assumes normality and equal variances.
  • - Sensitive to outliers.
  • - Does not specify which groups differ (needs post-hoc tests).

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SUMMARY

  • - ANOVA compares means of 3+ groups.
  • - Widely used in science and public health.
  • - F-ratio determines statistical significance.
  • - Post-hoc tests identify group differences.