Tools › Quality › Improvement › Pareto and Root Cause › Example
Agresti Table 3.2: gender by party identification cross-tab (1991 GSS) with X², G² and adjusted residuals
| Tool | Pareto and Root Cause |
| Source | Agresti, A. (2002). Categorical Data Analysis, 2nd ed. Wiley, Hoboken, NJ. Tables 3.2 and 3.3. |
| Level | Undergraduate |
Problem
In the 1991 General Social Survey 980 respondents were classified by gender and party identification (Democrat, Independent, Republican). Test the independence of the two classifications with Pearson's X² and the likelihood-ratio G², and locate the departures with the standardized (adjusted) residuals.
Inputs to Enter
- Records with a count column (paste): Females Democrat 279, Independent 73, Republican 225; Males Democrat 165, Independent 47, Republican 191
- Stratified Pareto with category = party and stratifier = gender
Answers
- X² = 7.01, G² = 7.00, df = 2, P ≈ 0.03; expected Females–Democrat 577 × 444 / 980 = 261.4
- Adjusted residuals (females): Democrat 2.29, Independent 0.46, Republican −2.62 (males with the opposite signs)
- Cramér's V = √(7.01/980)
Notes
Paste the six lines as records with a count column; not in the example selector. The 2000 GSS table of Agresti (2007) gives X² = G² = 30.0 with residuals 4.50, 0.70, −5.32 the same way.