ANOVA

Provides a statistical test of whether two or more population means are equal. Generalizes the t-test beyond two means.

Type of general linear model

Subtypes of ANOVA

N-ANOVA
Repeated Measures ANOVA
MANOVA
ANCOVA

Violations and exceptions

• Robust against violations of normality (Normality assumption) if sample is large enough (ex. N>=15)
• Robust against violation of homogeneity (Homogeneity of variance assumption) where sample sizes are approximately equal
  • If differences in standard deviations become very large, this can no longer be taken for granted → if largest standard deviation is greater than twice the smallest
  • If that’s the case, your options are:
    • Data transformation
    • Adjust significance level
    • Choose Welch-procedure instead of conventional F-test
    • Choose non-parametric statistical test

Model Assumptions

• Quantitative dependent variable
• Independent groups
• Normality assumption:
  • dependent variable normally distributed in each population
• Homoegeneity of variance assumption:
  • variance of dependent variable is equal in each population

General Model Testing

• Box plots
  • If histogram shows an outlier, check it (check it either way!)
  • Check for outliers with 1IQR and 3IQR criterion Interquartile Range
• Z-scores
  • Check if any values are +/- 1.96 or 95% of probable sample statistics
  • 95% confidence interval: likely to find 5% of z-scores outside normal range
• Checking outliers:
  • Logistic Regression Analysis:
    • dependent variable: outlier according to 1.5*IQR criterion
    • Independent variables (as in study design)

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Related

References

PSY4106 Advanced Statistics I