Biostatistics-CDFD-2026

A Biostatistics course offered to PhD students at BRIC-Centre for DNA Fingerprinting and Diagnostics - CDFD during August-December 2026.

Lecture notes

Lecture 01

Lecture 01 introduces R:

1. R Basics — basic syntax, variables, vectors, data frames, descriptive statistics, plots, statistical tests, correlation, and linear regression.
2. Reading data files — reading CSV/TSV files, inspecting data, selecting rows and columns, modifying data, and saving results.
3. ggplot2 — introduction to plotting with ggplot2, including scatter plots and fitted regression lines.
4. Bioconductor — a first example using Biostrings to work with DNA sequences.

Lecture 02

Lecture 02 introduces discrete probability distributions and hypothesis testing using biological examples:

1. Discrete random variables — introduction to discrete data, probability distributions, and biological examples involving counts.
2. Binomial distribution — modeling repeated independent trials with two possible outcomes, illustrated using coin tosses and implemented in R with dbinom() and pbinom().
3. Poisson distribution — modeling counts of rare events and understanding the Poisson approximation to the binomial distribution when $n$ is large and $p$ is small.
4. HIV mutation example — modeling the number of mutations in an HIV genome using the binomial distribution and comparing it with the Poisson approximation.
5. Cumulative probability — calculating probabilities such as $P(X\leq x)$ by summing individual probabilities and using cumulative distribution functions.
6. Hypothesis testing — introducing the null and alternative hypotheses, p-values, significance levels, rejection regions, and left-tailed tests using the HIV mutation example.
7. Confidence and significance levels — connecting $\alpha=0.05$ with a corresponding 95% probability level and interpreting significance thresholds in discrete probability distributions.

Lecture 03

Lecture 03 develops exact binomial hypothesis testing using biological examples:

1. When to use the binomial distribution — recognizing situations with a fixed number of independent trials, two possible outcomes per trial, and a constant probability of success.
2. Null model and observed proportion — distinguishing between the null probability $p_0$, the unknown underlying probability $p$, the observed proportion $\hat p$, and the expected count $np_0$.
3. Hypothesis testing and compatibility regions — interpreting $\alpha=0.05$ as defining an approximately 95% central region of outcomes expected under $H_0$ and rejection regions in the tails.
4. p-values and the CDF — calculating left- and right-tailed p-values using cumulative probabilities with pbinom() and understanding the connection between the CDF and hypothesis testing.
5. Exact binomial test in R — using binom.test() for left-tailed, right-tailed, and two-sided tests and extracting the p-value using result$p.value.
6. Mendel’s pea experiment — testing whether the observed proportion of round seeds differs from the Mendelian expectation of $p_0=0.75$.
7. Allele-specific expression — testing whether allele-specific sequencing reads deviate from the 50:50 expectation using a two-sided exact binomial test.
8. EXACT precision-oncology trial — performing a right-tailed exact binomial test with $\alpha=0.025$ and connecting the p-value with the critical rejection region.

Additional content will be added as the course progresses.

Repository

The repository https://github.com/raghurama123/Biostatistics-CDFD-2026 contains R scripts, data, and notes.

The repository is organized lecture-wise. Each lecture folder contains the corresponding R scripts, data files, and lecture notes.

Biostatistics-CDFD-2026/
│
├── README.md
│
└── Lec01/
|   ├── Lec01.md
|   ├── Lec01.html
|   ├── Rbasics.R
|   ├── ...
└── Lec02/
|   ├── ...

Interactive plots

• Normal distribution
• Binomial distribution

How to do various things in R programming?

The HowToR folder contains short manuals and examples explaining how to perform various tasks in R.

General reference

The main general reference for the course is the online book: Modern Statistics for Modern Biology by Susan Holmes and Wolfgang Huber

The book provides a modern introduction to statistical thinking and data analysis for biological applications, with extensive use of R.

Contact

Raghunathan Ramakrishnan
Tata Institute of Fundamental Research Hyderabad, India
Email: ramakrishnan@tifr.res.in