Regression, ANOVA and Beyond: Applied Statistics for Dissertations, Essays and Assignments

Statistical analysis turns data into evidence. Whether you’re writing a dissertation, an essay or an assignment, choosing and applying the right statistical techniques — and reporting them clearly — is essential to persuasive, reproducible research. This guide walks you through practical uses of regression, ANOVA, and advanced alternatives, with tips on assumptions, reporting, and resources tailored to thesis- and assignment-level work.

Why this matters (quick overview)

• Match method to research question: correlations, group comparisons, predictions and causal inference require different tools.
• Avoid common pitfalls: ignored assumptions or poor reporting can undermine valid results.
• Reproducibility and clarity are graded as much as findings in academic work.

If you’re unsure which test fits your study, see our decision tree: Selecting the Right Statistical Tests for Dissertations, Essays and Assignments: A Practical Decision Tree.

H2 — Regression: prediction, control and effect size

What regression does

Regression models quantify relationships between one dependent (outcome) variable and one or more independent (predictor) variables. Common types:

• Linear regression: continuous outcome (e.g., test score).
• Logistic regression: binary outcome (e.g., pass/fail).
• Poisson/Negative binomial: count outcomes (e.g., number of events).

When to use regression

Use regression when you want to:

• Predict an outcome from predictors.
• Control for confounders (e.g., age, gender).
• Estimate effect sizes and confidence intervals.

Key assumptions (linear regression)

• Linearity between predictors and outcome.
• Independent errors.
• Homoscedasticity (constant variance).
• Normally distributed residuals (for small samples).

Violations? Consider transformations, robust standard errors, or nonparametric/Bayesian alternatives.

H2 — ANOVA: comparing group means

What ANOVA does

Analysis of Variance (ANOVA) tests whether group means differ across three or more groups. Variants include:

• One-way ANOVA: single factor (e.g., teaching method).
• Two-way ANOVA: two factors, can test interaction effects.
• Repeated-measures ANOVA: within-subject designs over time.

When to use ANOVA

• Comparing outcomes across groups (e.g., treatment A vs B vs control).
• Testing interactions between categorical factors.

Assumptions

• Normality of residuals.
• Homogeneity of variances.
• Independent observations.

If assumptions fail, use Kruskal–Wallis, Friedman test, or generalized linear models.

H2 — Regression vs ANOVA vs other methods (quick comparison)

Purpose	Typical models	Strengths	Limitations
Compare group means	ANOVA, t-tests	Intuitive group comparisons, well-established	Assumes normality, limited to mean differences
Predict continuous outcome	Linear regression	Include continuous & categorical predictors, control confounders	Sensitive to outliers, linearity assumption
Predict binary outcome	Logistic regression	Models odds/probabilities	Interpretation requires care (odds ratios)
Non-normal data / ranks	Kruskal–Wallis, Spearman	Fewer distributional assumptions	Less power, fewer model options
Complex data structures	Mixed-effects models, multilevel models	Handles clustered/repeated data	Requires more advanced knowledge

H2 — Beyond the basics: advanced approaches and when to use them

• Mixed-effects (multilevel) models: use for nested or repeated measures (students within schools, repeated observations). Superior to aggregated ANOVA for hierarchical data.
• Multivariate analysis (MANOVA, PCA): for multiple correlated outcomes or dimension reduction.
• Robust and nonparametric methods: when assumptions are violated or sample sizes are small.
• Bayesian models: incorporate prior information and provide full posterior distributions — useful for complex inference and small samples.
• Machine learning (regularised regression, tree methods): for prediction-focused projects; include cross-validation and holdout samples to avoid overfitting.

For practical workflows, see: Reproducible Analysis Workflows for Dissertations, Essays and Assignments Using R and Python.

H3 — Handling messy data: missingness and outliers

• Missing data: never simply drop cases without justification. Prefer multiple imputation or full-information methods when data are missing at random. Guidance: Handling Missing Data and Outliers in Dissertations, Essays and Assignments: Strategies and Examples.
• Outliers: check influence (Cook’s distance), consider robust regression or sensitivity analyses.

H3 — Power, sample size and planning

Underpowered studies risk false negatives. Use power analysis during design to estimate required sample sizes for your chosen test. See: Power Analysis and Sample Size Planning for Dissertation and Assignment Studies.

H3 — Reporting and interpreting results (what examiners look for)

• Report test statistics, degrees of freedom, p-values, and effect sizes with confidence intervals (e.g., Cohen’s d, OR, R²).
• Provide diagnostic checks (residual plots, variance homogeneity tests).
• Avoid overclaiming causality from observational data — discuss limitations and potential confounders.
• Use clear, plain-language interpretations in results and link back to research questions.

For step-by-step guidance on turning output into readable results, see: Interpreting Statistical Output for Dissertations, Essays and Assignments: Writing Clear Results.

H3 — Visualisation and reproducibility

• Use appropriate plots: residual vs fitted, interaction plots, forest plots for effect sizes.
• Label axes and include sample sizes in figures. For visualization standards: Data Visualization Best Practices for Dissertations, Essays and Assignments: Charts, Tables and Figures That Communicate.
• Share code, scripts, and data (where ethics allow). Read: Reproducible Analysis Workflows for Dissertations, Essays and Assignments Using R and Python.

H3 — Mixed-methods and qualitative integration

Combine quantitative findings with qualitative insights for richer interpretation. Techniques and reporting standards are covered in:

• Mixed-Methods Data Integration: Techniques for Dissertations, Essays and Assignments
• Beginner’s Guide to Qualitative Coding and Thematic Analysis for Dissertations, Essays and Assignments

Also ensure trustworthiness and validity: Qualitative Trustworthiness and Quantitative Validity: Reporting Standards for Dissertations, Essays and Assignments.

H2 — Quick practical checklist before submitting

• Research question aligned with chosen statistical method.
• Assumptions checked and documented.
• Effect sizes and confidence intervals reported.
• Diagnostic plots and sensitivity analyses included.
• Data handling (missing/outliers) justified and documented.
• Code and data stored reproducibly (or described why not).
• Visuals clear, labelled, and interpretable.

For assistance with choosing the right test step-by-step, consult: Selecting the Right Statistical Tests for Dissertations, Essays and Assignments: A Practical Decision Tree.

Contact us — writing and proofreading support

Need help with statistical writing, analysis or proofreading of your dissertation, essay or assignment? Contact MzansiWriters:

• Click the WhatsApp icon on the page to message us directly.
• Email: info@mzansiwriters.co.za
• Or use the Contact Us page in the main menu.

Our team can help with statistical interpretation, result write-ups, figure polishing, and full proofreading to meet academic standards.

If you’d like a custom walkthrough for your dataset or help writing the results chapter, message us via WhatsApp or email and include your question, sample size, and the outcome variable you’re studying.