• Adaptive sample size;
  • Conditional inference;
  • Contingency table;
  • Fisher's exact test;
  • Nuisance parameter;
  • Test of proportions

Summary Two-by-two tables arise in a number of diverse settings in biomedical research, including analysis of data from a clinical trial with a binary outcome and gating methods in flow cytometry to separate antigen-specific immune responses from general immune responses. These applications offer interesting challenges concerning what we should really be conditioning on—the total number of events, the number of events in the control condition, etc. We give several biostatistics examples to illustrate the complexities of analyzing what appear to be simple data.