Stats Studio: Statistical Analysis & Interpretation (Tutorials)
A practical tutorial series for people who are tired of running tests blindly. This studio teaches the logic first, then the steps, then the interpretation — so your results are not “numbers”, they’re evidence.
What you’ll be able to do (without guessing)
The tutorial design follows a repeatable pattern: What’s the question? → What test fits the data? → What assumptions must hold? → What to read on the output? → What is the conclusion?
Test Selection Matrix (how to choose correctly)
Selection is driven by the research intent (association, prediction, or group differences) and the measurement level of the dependent variable.
| Situation | Typical Tests | What it answers | What you must check |
|---|---|---|---|
| Group differences (2 groups)DV continuous | Two-sample t-test • Paired t-test | Do two means differ? | Normality (reasonable) • equality of variance (if independent) • pairing logic |
| Group differences (3+ groups)DV continuous | ANOVA • ANCOVA | Do 3+ means differ (with/without covariates)? | Independence • normality of errors • homoscedasticity (Levene/Bartlett) • post-hoc (Tukey/Bonferroni/Scheffé) |
| Multiple outcomesDVs continuous | MANOVA • MANCOVA | Do groups differ across related outcomes? | DV correlations • assumptions as above • covariate control (if used) |
| Association (continuous) | Pearson • Spearman • Kendall | How strong and what direction is the relationship? | Linearity (Pearson) • ranks/long tails (Spearman) • faster normal approximation (Kendall) |
| Agreement (methods) | Bland–Altman | Do two methods agree (not just correlate)? | Interpret limits of agreement; correlation ≠ agreement |
| Prediction (continuous DV) | Simple / Multiple Regression • Path logic | How much variance is explained? Which predictors matter? | Residual patterns • outliers (leverage/DFITS/DFBETAS/covratio) • multicollinearity (VIF/CI) |
| Prediction (binary DV) | Logistic Regression | What are the odds of the outcome as predictors change? | Interpret odds/probabilities correctly; model fit checks |
| Categorical association | Chi-square (GOF / Association) | Is the distribution/association due to chance? | Observed vs expected frequencies • correct hypothesis framing |
| When assumptions are doubtful | Wilcoxon Signed Rank • Mann–Whitney U • Kruskal–Wallis • Friedman | Robust conclusions when parametric assumptions are violated | Compare outcomes: if parametric & nonparametric agree → stronger confidence; if they disagree → investigate distribution/plots |
Course Modules (12 chapters • 12 lessons • 12 practicals)
This is a full tutorial programme: each chapter is taught, executed, and interpreted — then converted into reporting language you can use in a dissertation, report, or journal-style write-up.
1) Foundations: Scales, Variables, Research Intent Setup
Measurement scales (nominal/ordinal/interval/ratio), independent vs dependent variables, covariates, and the question that decides the method: description (association), explanation (prediction), intervention (group differences).
2) Hypothesis Testing Workflow (H0/H1, p-values, α) Core
Four-step hypothesis process: set H0/H1, identify a test statistic, compute p-value, compare to alpha. Decision rules that stay consistent across tests.
3) Descriptives & Distribution Thinking (Mean/Median/Mode, Variance/SD) Clarity
Central tendency, spread, frequency tables, and reading what your data is “doing” before you test anything.
4) One-Sample & Two-Sample t-tests (Independent / Paired) Comparisons
Correct framing of hypotheses, what to read on SAS output, and how to conclude. Paired logic versus independent samples logic.
5) Power & Sample Size (Why n matters) Planning
How power increases sample needs; how effect size and SD shift your required n; typical choices (80–90% power; 5% alpha).
6) Categorical Data (Proportions & Chi-square) Counts
Single proportion tests, two-proportion comparisons, chi-square goodness-of-fit, and chi-square tests of association.
7) Nonparametric Toolkit (When normality/equal variance is not safe) Robust
Sign test, Wilcoxon signed rank, Mann–Whitney U, Kruskal–Wallis, Friedman, and when to trust nonparametric outcomes.
8) ANOVA & Post-hoc Logic (Tukey/Bonferroni/Scheffé) 3+ Groups
Model rationale, assumptions (independence, normality of errors, equal variances), interpretation of Pr>F, R², MSE, and post-hoc location of differences.
9) Two-Factor & Multi-Factor ANOVA (Interactions) Design
Interaction meaning, why it matters, how to read interaction plots, and how it changes what conclusions are valid.
10) Correlation vs Agreement (Pearson/Spearman/Kendall + Bland–Altman) Relationships
Relationship strength/direction, rank correlation for long tails, Kendall’s rapid normal approximation, and why agreement is a different question to correlation.
11) Regression (Simple → Multiple) + Diagnostics Prediction
Residual patterns (fan/parabola/curvature/double bow), outliers (leverage, DFITS, DFBETAS, covratio), multicollinearity (VIF, condition indices), and defensible reporting.
12) ANCOVA / Indicator Regression + Transformations Control
Covariates for reducing error and eliminating confounds, indicator variables (dummy coding), transformation choices (log, sqrt, reciprocal, logit), and model comparison logic (R² before/after).
How Stats Studio is delivered
Tutorial Mode (Teach-You)
Walkthrough lessons + guided practicals. The goal is competence: you should be able to run the analysis again alone and interpret outputs without copying templates.
- Weekly chapter rhythm (12 chapters / 12 weeks).
- Focus on test choice + output reading.
- Interpretation language that fits academic and professional reporting.
Analysis Support (Do-For-You)
For students/teams under pressure: we analyse, interpret, and structure the findings in a way that is defendable — then show you how the conclusions were reached.
- Clean outputs and defensible conclusions.
- Assumptions checks and diagnostics included.
- Write-up support aligned to your chapter structure.
