| Variable Type | Samples / Groups | Procedure Name | Test Statistic Formula | Critical Assumptions |
|---|---|---|---|---|
| Categorical (Proportions) | 1 Sample | 1-Sample z-test for p | z = (p̂ - p₀) / √(p₀(1-p₀)/n) | Random sample; 10% condition; np₀ ≥ 10 and n(1-p₀) ≥ 10. |
| Categorical (Proportions) | 2 Independent Samples | 2-Sample z-test for p₁ - p₂ | z = (p̂₁ - p̂₂) / √(p̂c(1-p̂c)(1/n₁ + 1/n₂)) | Independent random samples; 10% condition; pooled counts ≥ 10. |
| Quantitative (Means) | 1 Sample (σ unknown) | 1-Sample t-test for μ | t = (x̄ - μ₀) / (s / √n), df = n - 1 | Random sample; 10% condition; Normal population or n ≥ 30 (CLT). |
| Quantitative (Means) | Paired Data (Before/After) | Matched Pairs t-test for μ_d | t = (x̄_d - 0) / (s_d / √n), df = n - 1 | Random paired sample; differences approximately normal or n ≥ 30. |
| Quantitative (Means) | 2 Independent Samples | 2-Sample t-test for μ₁ - μ₂ | t = ((x̄₁ - x̄₂) - 0) / √(s₁²/n₁ + s₂²/n₂) | Independent random samples; both populations normal or n₁, n₂ ≥ 30. |
| Categorical Frequencies | 1 Variable across multiple categories | Chi-Square Goodness of Fit | χ² = Σ (O - E)² / E, df = k - 1 | Random sample; all expected counts E ≥ 5. |
| Two Categorical Variables | Single Sample (Association) | Chi-Square Test of Independence | χ² = Σ (O - E)² / E, df = (r-1)(c-1) | Random sample; two-way table; all expected counts E ≥ 5. |
| Bivariate Quantitative | Paired (x, y) coordinates | Linear Regression t-test for slope β | t = (b - 0) / SE_b, df = n - 2 | LINER conditions: Linear, Independent, Normal residuals, Equal variance, Random. |
Key Conceptual Scaffolding & Diagnostic Intuition
Tested Competency: Core exam competencies, blueprint formulas & diagnostic review. In modern competitive exams, questions are engineered to test whether you understand the underlying structural relationship—not just whether you memorized a formula.
Relying on rote memorization instead of conceptual problem-solving and timed simulation drills.
Always write out your hypotheses and state conditions explicitly before calculating test statistics. Graders award up to 40% of partial credit for proper setup, regardless of arithmetic precision.
Core high-yield entity clusters calibrated for automated vector retrieval, licensing examination standards, and practical field calculations: