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Visual EDA for ANOVA etc.

🎯 Purpose

This guide outlines visual exploratory data analysis (EDA) techniques to prepare for conducting ANOVA, MANOVA, ANCOVA, and MANCOVA. Each method requires evaluating group differences in means, variance, and distributional assumptions.

🟦 ANOVA (Analysis of Variance)

✅ Use Case

Compare the means of a single continuous dependent variable across 2 or more categorical groups.

📈 Visual Tools

  • Box Plot: 

    sns.boxplot(x="group", y="outcome", data=df)
    ✔️ Highlights differences in medians and spread

  • Violin Plot: 

    sns.violinplot(x="group", y="outcome", data=df)
    ✔️ Combines KDE with boxplot for richer shape comparison

  • Strip/Swarm Plot: 

    sns.stripplot(x="group", y="outcome", data=df, jitter=True)
    ✔️ Reveals individual observations and clustering

  • Histogram by Group: 

    sns.histplot(data=df, x="outcome", hue="group", kde=True, element="step")
    ✔️ Compares distribution overlap

🟩 MANOVA (Multivariate ANOVA)

✅ Use Case

Compare the means of 2+ continuous dependent variables across groups.

📈 Visual Tools

  • Pair Plot by Group: 

    sns.pairplot(df, hue="group", vars=["outcome1", "outcome2"])
    ✔️ Visualize interactions between multiple DVs by group

  • Group Mean Plot (Centroids): Plot average values for each DV per group using scatter

  • Correlation Heatmap (DVs only): 

    sns.heatmap(df[["outcome1", "outcome2"]].corr(), annot=True)
    ✔️ Check for collinearity between dependent variables

🟨 ANCOVA (Analysis of Covariance)

✅ Use Case

Compare group means of a continuous DV while controlling for a continuous covariate.

📈 Visual Tools

  • Scatter Plot with Regression Lines: 

    sns.lmplot(x="covariate", y="outcome", hue="group", data=df)
    ✔️ Show linear trends by group, adjusting for covariate

  • Box Plot + Covariate Distribution:

  • Plot covariate distribution per group to ensure no confounding imbalance

  • Interaction Plot (optional): Shows how slope of DV vs covariate changes per group

🟥 MANCOVA (Multivariate ANCOVA)

✅ Use Case

Compare 2+ dependent variables across groups, controlling for one or more covariates.

📈 Visual Tools

  • Facet Grid Regression: Visualize each DV against covariate, by group

  • Multivariate Scatter or PCA Plot: Reduce DVs to 2D (via PCA) and color by group for pattern detection

  • Partial Residual Plot: Show adjusted effects of group differences post-covariate adjustment

📌 Summary Table

Method Visual Focus
ANOVA Box/violin plots, histograms, stripplots
MANOVA Pair plots, mean centroids, DV correlation map
ANCOVA lmplot (scatter w/ covariate), covariate hist
MANCOVA Faceted plots by DV, partial plots, PCA clustering

✅ Final Tips

  • Always start with distribution and spread checks
  • Use color to encode group membership
  • Ensure covariates are balanced and linear across groups (for ANCOVA/MANCOVA)
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