Statistical Computing and Data Analysis
Core concepts
Understand the workflow of a statistical analysis: data acquisition, cleaning, exploratory analysis, modelling, diagnostics, and reporting. Know reproducibility practices: scripts, version control, documented seeds for random number generation, and literate programming. Be familiar with data structures, missing data mechanisms (MCAR, MAR, MNAR), imputation, outlier detection, and the use of simulation and resampling (bootstrap, permutation tests). Understand numerical issues such as floating-point precision, convergence failures, and overfitting.
Traps
- Dropping incomplete cases without checking whether missingness is related to the outcome.
- Reporting results from a model that failed to converge without checking diagnostics.
- Forgetting to set or record a random seed, making simulation results irreproducible.
- Treating an outlier as an error without investigation; it may be a genuine extreme value.
- Confusing the bootstrap (resampling with replacement from the sample) with permutation tests (reshuffling labels under a null).
- Overfitting a model to training data and reporting training error as performance.
Worked example
To estimate the standard error of a median with no closed-form formula, draw 1,000 bootstrap samples with replacement, compute the median in each, and take the standard deviation of those 1,000 medians. Rule of thumb: the bootstrap works well for smooth statistics with reasonably large samples; for very small samples or extreme quantiles, use caution and consider alternative methods.