Explain the factors that decide sample size and the types of variables used in research.

1. 1 · Open with definitions. Sample size is the number of units studied. A variable is a feature that can take different values.
2. 2 · List the factors deciding sample size.
   • Precision required.
   • Variability of the population.
   • Confidence level.
   • Expected frequency.
   • Number of subgroups.
   • Resources: time, money, staff.
   • Non-response.
3. 3 · Show the formula with an example. n = Z²pq ÷ d². With p = 0.6, d = 0.05, Z = 1.96: n = 369, about 410 with 10% non-response.
4. 4 · Explain variables by role. [Diagram: independent → dependent, with extraneous and confounding variables pointing in from the side]
   • Independent: the cause.
   • Dependent: the outcome.
   • Extraneous: other influences.
   • Confounding: linked to both, gives false links.
5. 5 · Explain variables by measurement. Quantitative (continuous, discrete) vs qualitative (categorical). Add the operational definition.
6. 6 · Nutrition example. Mid-day meal (independent) → child's weight or Hb (dependent); worm infestation (extraneous).
7. 7 · Close in one line. The right sample size and clearly defined variables make the results accurate and believable.

Scoring tip: Draw a box-and-arrow: independent → dependent, with extraneous variables pointing in from the side.