Types of biological data, scales of measurement, frequency distributions, histograms, boxplots, measures of central tendency and variability, and graphical summaries; random sampling, random number generation, basic numerical techniques in data handling, and interpretation of statistical tables; frequency/statistical interpretations of probability, basic parameter estimation methods (maximum likelihood, least squares), and microarray data as motivating examples.
Axioms of probability, probability rules, and interpretations; univariate and multivariate probability distributions including normal, binomial, multinomial, Poisson, and Cauchy; law of large numbers and the central limit theorem; standard errors, types of error and error propagation, confidence intervals (frequentist and Bayesian), significance testing, one- and two-tailed tests, p-values, Type I and II errors, and critical values; parameter estimation and inferential reasoning in biological contexts.
t-tests (one-sample, paired, two-sample), analysis of variance (ANOVA), and the F-distribution (with connections to χ² and t distributions); categorical data analysis including contingency tables, chi-squared tests (goodness-of-fit, homogeneity, independence), and Fisher’s Exact Test; non-parametric and distribution-free methods such as Mann–Whitney U, Wilcoxon Signed-Rank, and Kruskal–Wallis tests; introduction to classification (e.g., discriminant analysis) and clustering techniques (e.g., k-means, hierarchical) for biological data.
Pearson and Spearman correlation, partial correlation, simple and multiple linear regression, logistic regression basics, residual analysis, and model diagnostics; principal component analysis (PCA) for dimensionality reduction in high-throughput data such as microarrays; optimization techniques (linear and non-linear); design of experiments including randomization, replication, blocking, factorial experiments; real-world biological case studies involving gene expression and clinical trials.