Sample size and variables
Sample size depends on precision, variability and resources. Variables are the measurable features you study: the independent variable is the cause, the dependent is the effect.
What decides sample size
- Precision: the smaller the error you accept, the larger the sample.
- Variability: a mixed population (different incomes, diets) needs a larger sample than a uniform one.
- Confidence level: 95% (Z = 1.96) is usual; 99% needs more people.
- Expected frequency: a rare condition needs a larger sample, because the allowed error must be small compared with p (e.g. ±1 point when p = 5%).
- Design and analysis: more subgroups to compare means a larger sample.
- Resources: time, money and staff set the upper limit.
- Non-response: add about 10% for those who refuse or drop out.
Sample size for an anaemia survey
You want to estimate how common anaemia is among adolescent girls in Chennai schools. Taking the all-India NFHS-5 figure, assume about 60% are anaemic. You want the answer within ±5 percentage points at 95% confidence. How many girls should you test?
- Formula for a proportion: n = Z² × p × q ÷ d²
- Z = 1.96 (95% confidence), p = 0.60, q = 1 − p = 0.40, d = 0.05
- Z² = 1.96 × 1.96 = 3.8416
- Z² × p × q = 3.8416 × 0.60 × 0.40 = 0.9220
- d² = 0.05 × 0.05 = 0.0025
- n = 0.9220 ÷ 0.0025 = 368.8, rounded up to 369
- Allow 10% non-response: 369 ÷ 0.9 = 410
Test about 410 girls (369 before allowing for non-response). Books that round Z² to 4 use n = 4pq ÷ d², which gives 384.
Types of variables by their role (anaemia study)
| Variable | Meaning | Example |
|---|---|---|
| Independent | The cause or factor the researcher changes or compares | Iron intake, or an iron-rich diet given to one group |
| Dependent | The outcome that is measured; it changes with the independent variable | Haemoglobin level |
| Extraneous | Any other factor that can affect the outcome but is not being studied | Worm infestation, heavy menstrual loss |
| Confounding | An extraneous variable linked to both cause and outcome; it can create a false link | Family income: affects both diet and access to health care |
| Intervening | Comes between cause and effect and carries the link | Iron absorbed from the meal, between iron intake and Hb |
Quantitative vs qualitative variables
Ranjit Kumar links these to measurement scales: nominal and ordinal scales for categorical variables, interval and ratio scales for continuous ones.
In a mid-day meal study, the meal is the independent variable and the child's weight, height or Hb is the dependent variable. Illness, worm infestation and home diet are extraneous variables; deworming all children before the study controls one of them.
2 marks: “What is a dependent variable? Give an example.” The outcome that is measured and changes with the independent variable, e.g. haemoglobin level in a study of iron intake.
5 marks: “Explain the factors that decide the sample size of a study.” Precision, variability, confidence level, expected frequency, number of subgroups, resources and non-response, with the formula n = Z²pq ÷ d².
10 marks: “Explain the factors that decide sample size and the types of variables used in research.” Sample-size factors with a worked formula; define variable and operational definition; independent, dependent, extraneous, confounding; quantitative vs qualitative.
Independent = Input, the cause you change. Dependent = Depends on it, the outcome you measure.