Exam Pattern: Allocation Ratio Power Graph for Continuous Outcomes

This note abstracts the normal midterm question where power must be read from a graph as the allocation ratio changes while the total sample size is fixed.

Source Question

  • STA305 Midterm W2026, Question 4

Setup

A two-arm continuous-outcome trial has fixed total sample size, fixed significance level, and a target effect size. The only thing being varied is the allocation ratio

$$ r = \frac{n_1}{n_2}. $$

The graph reports how power changes as $r$ changes.

Workflow

Step 1: Read the power at the proposed ratio

If the question proposes, for example, a heavily unbalanced ratio such as $4:1$, locate that point on the graph and read the corresponding power.

Step 2: Compare with the target

If the graph value is below the required target, the proposed ratio is not acceptable at the fixed total sample size.

Step 3: Give the design recommendation

The general recommendation is to move toward a more balanced design, because for equal per-subject variance a balanced allocation is most efficient at fixed total sample size.

Key Lesson

With everything else fixed, imbalance costs power. A large allocation ratio may be operationally attractive, but it usually reduces efficiency enough that the target power is missed.

Exam Checklist

  • State what the graph is displaying
  • Read the approximate power at the proposed ratio
  • Compare it directly with the target power
  • Recommend a more balanced ratio if the plotted power is too low