| Scenario / Data Type | Number of Samples | Procedure Name | Test Statistic Formula |
|---|---|---|---|
| Categorical (Proportions) | 1 Sample | 1-Prop z-test / interval | z = (p̂ - p₀) / √(p₀(1-p₀)/n) |
| Categorical (Proportions) | 2 Independent Samples | 2-Prop z-test / interval | z = (p̂₁ - p̂₂) / √(p̂c(1-p̂c)(1/n₁ + 1/n₂)) |
| Quantitative (Means) | 1 Sample (σ unknown) | 1-Sample t-test / interval | t = (x̄ - μ₀) / (s / √n), df = n - 1 |
| Quantitative (Paired Data) | 1 Sample of Differences | Matched Pairs t-test | t = (x̄_d - 0) / (s_d / √n), df = n - 1 |
| Categorical Distribution Fit | 1 Categorical Variable | Chi-Square Goodness of Fit | χ² = Σ (O - E)² / E, df = k - 1 |
| LSRL Equation | ŷ = a + bx where slope b = r(sy / sx) and intercept a = ȳ - bx̄ |
| Residual Definition | Residual = Observed y - Predicted ŷ = y - ŷ |
| Coefficient of Determination (r²) | "[r²]% of the variation in [response variable y] is accounted for by the linear relationship with [explanatory variable x]." |
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Key Conceptual Scaffolding & Diagnostic Intuition
Tested Competency: Hypothesis testing & p-value interpretation. In modern competitive exams, questions are engineered to test whether you understand the underlying structural relationship—not just whether you memorized a formula.
Conflating 'fail to reject' with 'accepting' the null hypothesis, or forgetting to check 10% / Normal conditions.
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.
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