Tools › Statistics › Surveys and Sampling › Survey Analysis › Example
Fisher's tea-tasting experiment: exact test on a 2 × 2 table
| Tool | Survey Analysis |
| Source | Agresti, A. (2007). An Introduction to Categorical Data Analysis, 2nd ed. Wiley, Hoboken, NJ. Section 2.6.1, Table 2.8. |
| Level | Undergraduate |
Problem
A colleague of Fisher claimed she could tell whether milk or tea was poured first. Of four cups with milk first she identified three correctly, and of four with tea first, three. Compute Fisher's exact one- and two-sided P-values, the odds ratio and the ordinary and Yates-corrected χ².
Inputs to Enter
- Data layout 'Cross-tab of counts'
- poured, milk first, tea first / guess milk, 3, 1 / guess tea, 1, 3
Answers
- P(observed table) = C(4,3) C(4,1)/C(8,4) = 16/70; one-sided P = 17/70 = 0.2429, two-sided P = 34/70 = 0.4857
- Odds ratio 9; φ = 0.5, Cramér's V = 0.5
- X² = N φ² = 2.0; Yates-corrected X² = 0.5
Notes
Paste the 2 × 2 table in the cross-tab layout; the exact test appears automatically for a 2 × 2 table. Not the default case.