---
title: "Differential Expression from Counts: Dispersion, Fit and Shrinkage"
description: "Sequencing gives counts, not measurements, and counts carry a mean-variance relationship that a normal model gets wrong. This stop fits a count model, borrows information across genes to estimate disp"
canonical: https://lightmysky.com/learn/science/differential-expression-from-counts-dispersion-fit-and-shrinkage-mt_nEV9547kSN
source: https://lightmysky.com/learn/science/differential-expression-from-counts-dispersion-fit-and-shrinkage-mt_nEV9547kSN.md
retrieved: 2026-09-12
---

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# Differential Expression from Counts: Dispersion, Fit and Shrinkage

Sequencing gives counts, not measurements, and counts carry a mean-variance relationship that a normal model gets wrong. This stop fits a count model, borrows information across genes to estimate dispersion, and reads the result honestly.

Subject: Science · Area: Genetics & Evolution · Ages 22 to 24
Page: https://lightmysky.com/learn/science/differential-expression-from-counts-dispersion-fit-and-shrinkage-mt_nEV9547kSN

## Ready when they can

- Explain why read counts need a negative binomial rather than a normal or Poisson model
- Say what library-size normalisation corrects and what composition effects it cannot fix
- Interpret shrunken fold changes and explain why low-count genes move the most

## Lesson: Reading change out of RNA count tables

You treat sequencing output as counts, not measurements. Two samples differ in total reads, and replicates vary far more than coin flip sampling predicts. A normal model gets this wrong, and a Poisson model underfits the extra variance.

You scale counts before you compare anything. A sample sequenced twice as deeply shows roughly twice the counts for every gene, so size factors rescale using the bulk of moderately expressed genes. But scaling has limits: a few huge transcripts can distort every share, and then the constant majority assumption breaks. Diagnostic plots show when count distributions warp after scaling; suspect composition effects and distrust comparisons until the failure is fixed.

**Example.** You see a tenfold rise built from three reads versus zero and feel excited. Then you check the counts and the uncertainty, and the excitement fades. The pipeline models counts with a negative binomial, borrows strength across genes to estimate dispersion, and shrinks your flimsy fold change toward zero.

**Tip.** You read shrunken fold changes as conservative statements of what the data support. Strongly expressed genes barely move, while low count genes move the most because their raw estimates carry the least information. A shrunken value near zero with wide uncertainty means no trustworthy evidence of change.

**Recap.** You scale for depth, you model counts with a negative binomial plus borrowed dispersion, and you trust shrunken changes over raw ratios.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Multiple Regression and Model Diagnostics](https://lightmysky.com/learn/mathematics/multiple-regression-and-model-diagnostics-mt_TUx1tDF0jv)

## Opens up

- [Testing Thousands of Genes at Once: False Discovery Rate and What q Means](https://lightmysky.com/learn/science/testing-thousands-of-genes-at-once-false-discovery-rate-and-what-q-means-mt_mIQ27rphrC)