Applications in Data Science
Overview
Statistics powers the complete data science lifecycle. A/B testing uses two-sample proportion or mean tests to compare treatment and control groups, enabling data-driven product decisions. Power analysis determines required sample sizes before experiments, preventing wasted resources on underpowered studies. Causal inference distinguishes correlation from causation using randomized experiments (gold standard), propensity scores, instrumental variables, and difference-in-differences for observational data. Feature selection uses chi-square tests, permutation importance, and mutual information. Model evaluation relies on cross-validation, AUC-ROC, and calibration curves. Understanding how these pieces fit together transforms data analysis from ad hoc number-crunching into rigorous, reproducible science.
Key Concepts
Causal Inference Methods
| Method | Description | Key Assumption | When to Use |
|---|---|---|---|
| Randomized Experiment | Gold standard | Random assignment | When feasible |
| Propensity Score Matching | Match treated and control on covariates | No unmeasured confounders | Observational, pre-treatment covariates available |
| Instrumental Variables | Use exogenous variation | Exclusion restriction | When confounders are unmeasurable |
| Difference-in-Differences | Compare pre/post changes | Parallel trends | Before/after with control group |
A/B Testing Workflow
- Define the metric: Choose what to measure (conversion rate, revenue, latency)
- Formulate hypotheses: : no difference, : difference exists
- Power analysis: Determine sample size before collecting data
- Random assignment: Users randomly assigned to control (A) and treatment (B)
- Collect data: Run experiment for predetermined duration
- Compute test statistic: Z-test for proportions or t-test for means
- Make decision: Reject if p-value β€ and effect is practically meaningful
Quick Example
Common Pitfalls in Applied Statistics
| Pitfall | Why It's Wrong | Correct Approach |
|---|---|---|
| Stopping experiment when p < 0.05 | Inflates false positive rate | Pre-specify sample size, run to completion |
| Ignoring practical significance | Trivial effects become "significant" with large | Report effect sizes and confidence intervals |
| Cherry-picking subgroups | Inflates false discovery rate | Pre-specify subgroups, adjust for multiple testing |
| Using accuracy for imbalanced classes | 95% accuracy by always predicting majority class | Use F1, AUC-ROC, or precision-recall curves |
| Correlation β Causation | Observational association doesn't imply causation | Use experiments or causal inference methods |
Key Takeaways
Deep Dive
For detailed explanations, worked examples, and Python implementations, explore the dedicated statistics lessons:
Machine Learning Applications
- Statistics in Machine Learning β How statistical methods power ML: hypothesis testing for model comparison, confidence intervals for metrics, and Bayesian approaches
Review and Roadmap
- Statistics Review and Roadmap β Comprehensive review of all statistical concepts with a structured learning roadmap
Related Topics
- Hypothesis Testing β The engine behind A/B testing and feature selection
- Confidence Intervals β Quantifying uncertainty in model performance
- Effect Size β Why practical significance matters more than statistical significance
- Multiple Testing Problem β Controlling false discoveries in large-scale experiments
- Propensity Score Matching β Causal inference from observational data
- Randomized Controlled Trials β Designing and analyzing experiments
- Power of a Test β Determining sample size before running experiments