Biserial & Tetrachoric Correlation — Previous Year Questions
📊 Topic Overview
| Metric | Value |
|---|---|
| Papers Appeared | 9 of 27 (33.3%) |
| Priority | 🟠 HIGH |
| Section Distribution | Sec A: ~2 |
| Most Repeated | "Describe biserial and tetrachoric correlation." |
🎯 Must-Know Concepts
- Biserial correlation (r_b): continuous variable vs artificially dichotomous variable
- Tetrachoric correlation (r_t): two artificially dichotomous variables
- Distinction from point biserial and phi coefficient
- When the dichotomy is "genuine" vs "artificial"
🔥 Most Repeated Question
Common phrasings:
- "Describe biserial and tetrachoric correlation."
- "Describe point biserial correlation and tetrachoric correlation."
- "What is tetrachoric correlation? Compute Kendall's tau for the following data."
Answer (Section B — ~250 words):
When measuring correlation between variables, the measurement scale of each variable determines which correlation coefficient to use. Two important coefficients for situations involving dichotomous variables are biserial and tetrachoric correlations.
Biserial Correlation (r_b):
Biserial correlation is used when one variable is continuous (interval/ratio) and the other is an artificially dichotomised continuous variable (a truly continuous trait that has been split into two groups for practical reasons).
Examples:
- Correlation between intelligence score (continuous) and "high/low IQ" (artificial dichotomy — really a continuous variable)
- Correlation between anxiety score (continuous) and pass/fail (if "fail" is an arbitrary cut-off on a continuous performance variable)
Key distinction from point biserial: Point biserial (r_pb) is used with a genuine dichotomy (truly only two states exist, e.g., alive/dead, male/female). Biserial (r_b) is used with an artificial dichotomy (a continuous variable that has been split).
Property: Biserial r tends to be larger in magnitude than point biserial r for the same data, and can occasionally exceed +1 (which is a limitation).
Tetrachoric Correlation (r_t):
Tetrachoric correlation is used when both variables are artificial dichotomies — i.e., both underlying traits are assumed to be continuous and normally distributed, but have been split into two groups each.
Examples:
- Correlation between pass/fail on Test A and pass/fail on Test B (when both tests measure continuous traits)
- Correlation between "high/low aggression" and "high/low anxiety" when both are natural continuous traits
Procedure: Uses a 2×2 table like phi, but assumes bivariate normal distribution for the underlying traits. The value is estimated from the proportions in the four cells using special tables.
Choosing the Right Correlation:
| X Variable | Y Variable | Correlation |
|---|---|---|
| Continuous | Continuous | Pearson's r |
| Continuous | Genuine dichotomy | Point biserial (r_pb) |
| Continuous | Artificial dichotomy | Biserial (r_b) |
| Genuine dichotomy | Genuine dichotomy | Phi (φ) |
| Artificial dichotomy | Artificial dichotomy | Tetrachoric (r_t) |
🧠 Memory Aid
- Biserial: Both underlying variables continuous; one bisected (artificially cut)
- Tetrachoric: Two artificial cuts; both variables are "two-ified"
📚 Related Content
✅ Self-Assessment
- What is the difference between biserial and point biserial correlation?
- When is tetrachoric correlation used?
- What assumption does tetrachoric correlation make about the underlying distributions?
- Give an example from psychology for biserial correlation.
- Which correlation would you use if both variables are genuinely binary?
💡 Exam Tips
- The full table of correlation types (continuous/dichotomous combinations) is the centrepiece of Section B answers.
- Genuine vs artificial dichotomy is the critical distinction — define both clearly.
- Tetrachoric can be asked as a short note (Section C) — 3–4 lines suffice.
- Often paired with a Kendall's Tau or Pearson's r computation — prepare conceptual and computational answers independently.