Appendix B: Statistical Decision Flowchart

The hardest part of statistics is choosing the right test. This appendix is your map.

When you have data and a question, the path to the correct statistical test follows a decision tree based on three things: what kind of data you have, how many groups you are comparing, and what assumptions your data meets. This appendix lays out that tree in a series of tables you can consult whenever you are unsure.

The Master Decision Guide

Start here. Find your question type, then follow the table to the right test.

Comparing Two Groups

Use this when you have one outcome variable and two groups (e.g., control vs. treated, male vs. female, wildtype vs. knockout).

Step 1: What type is your outcome variable?

Step 2: Are the observations paired or independent?

Step 3: Choose your test

Key insight: Welch’s t-test is almost always preferred over Student’s t-test because it does not assume equal variances. When variances are actually equal, Welch’s test gives nearly identical results. When they are not, Student’s test can be dangerously wrong. BioLang uses Welch’s by default.

How to check normality

let data = [2.3, 4.1, 3.7, 5.2, 4.8, 3.1, 6.0, 4.4]

# Visual check — Q-Q plot (best for small samples)
qq_plot(data, {title: "Normality Check"})

Common pitfall: With small samples (n < 30), normality tests have low power and may fail to reject normality even when the data is non-normal. With large samples (n > 5000), normality tests reject normality for trivially small deviations. Use Q-Q plots as a visual supplement.

Comparing Multiple Groups

Use this when you have three or more groups (e.g., three drug doses, four tissue types, five time points).

Post-hoc Tests

When ANOVA is significant, you know some groups differ but not which ones. Use post-hoc tests:

Key insight: ANOVA is an omnibus test — it tells you that at least one group differs, but not which one. Always follow a significant ANOVA with post-hoc comparisons. Reporting only the ANOVA p-value is incomplete.

Associations and Correlations

Use this when you have two continuous variables and want to know if they are related (e.g., gene expression vs. methylation, age vs. telomere length).

Interpreting Correlation Strength

| |r| value | Interpretation | |—|—| | 0.0 - 0.1 | Negligible | | 0.1 - 0.3 | Weak | | 0.3 - 0.5 | Moderate | | 0.5 - 0.7 | Strong | | 0.7 - 1.0 | Very strong |

Common pitfall: Correlation does not imply causation, but more subtly, absence of Pearson correlation does not imply absence of relationship. Pearson only detects linear associations. Two variables can have a perfect quadratic relationship with r = 0. Always plot your data.

Categorical Data

Use this when both your variables are categorical (e.g., mutation status vs. disease outcome, genotype vs. phenotype).

Measures of Association for Categorical Data

Regression

Use this when you want to predict an outcome from one or more predictor variables.

Checking Regression Assumptions

let model = lm(expression, [age, sex, batch])

# Check residuals with Q-Q plot
let residuals = model.residuals
qq_plot(residuals, {title: "Residual Normality Check"})
print("R-squared: " + str(round(model.r_squared, 3)))

Common pitfall: Adding more predictors always improves R-squared, even if the predictors are noise. Use adjusted R-squared or AIC/BIC for model comparison. Report both R-squared and adjusted R-squared.

Time-to-Event Analysis

Use this when your outcome is the time until something happens (death, relapse, response) and some observations are censored (the event has not yet occurred).

Clinical relevance: In clinical trials, the hazard ratio from a Cox model is the primary efficacy endpoint. A hazard ratio of 0.65 means the treatment group has a 35% lower instantaneous risk of the event at any time point. Always report the 95% confidence interval alongside the point estimate.

Dimensionality Reduction

Use this when you have many variables (genes, proteins, metabolites) and want to find the main patterns.

Key insight: PCA is deterministic — you get the same answer every time. t-SNE and UMAP are stochastic — different runs give different layouts. Always set a random seed before running stochastic methods for reproducibility.

Clustering

Use this when you want to group similar observations (samples, genes, cells) together.

Multiple Testing Correction

Use this whenever you perform more than one statistical test on the same dataset.

Key insight: For genomics (testing thousands of genes), Benjamini-Hochberg FDR correction at q = 0.05 is the standard. Bonferroni is too conservative for genome-wide studies — it controls the family-wise error rate, which is the wrong quantity when you expect hundreds of true positives.

Quick Reference: Common Biological Scenarios