Module 5: Sampling Design

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Learning outcomes

After this module, you should be able to:

• distinguish population and sampling frame;
• apply probability and non-probability sampling methods;
• determine sample size for a study;
• distinguish sampling error from bias and minimise bias.

Prerequisites

Complete Module 4 first. Review its quick-revision section if any term below feels unfamiliar.

Study blocks

Study one block at a time. Work through its example and checkpoint before continuing.

Block	Topic	Suggested time
1	Start here: the simple idea	10-15 minutes
2	Basics: population, sampling frame, sample	10-15 minutes
3	Probability sampling methods (everyone has a known, non-zero chance)	10-15 minutes
4	Non-probability sampling methods (chance unknown or zero)	10-15 minutes
5	Sample size determination	10-15 minutes
6	Sampling errors and bias minimisation	10-15 minutes
7	Estimation: point and interval	10-15 minutes
8	Sampling for quantitative vs qualitative research	10-15 minutes
9	Sampling case studies	10-15 minutes

Start here: the simple idea

You almost never study an entire population; you study a manageable sample and infer to the population. The trick is choosing a sample that faithfully represents the population so your conclusions are trustworthy.

Analogy

Tasting a soup to judge the whole pot: you need a spoonful from everywhere (stir well = randomisation) and a big enough taste (sample size), not just the top (which biases toward the salty surface).

Basics: population, sampling frame, sample

• Population (target): the entire set you want to generalise to (e.g., all full-time MCA students in India).
• Sampling frame: a list you can actually draw from (e.g., student enrolment at one college).
• Sample: the units actually studied.

Sampling frame error = the frame differs from the target population (the classic example: 1936 Gallup poll used car-owners (rich) to predict a president).

Probability sampling methods (everyone has a known, non-zero chance)

Method	How	Use
Simple random	Lottery/random numbers	Baseline
Systematic	Every kth from a list (k = N/n)	Quick; watch periodicity
Stratified	Random within strata (e.g., year)	Increase precision
Cluster	Random groups (classes), then all/some inside	Cheap when frame is group-based
Multi-stage	Cluster, then sub-sample inside	National surveys

Stratified divides by a known characteristic and samples within each; cluster divides into natural groups and samples whole groups.

For our stress study

Population = full-time MCA students at a college. Strata by year (1st, 2nd, 3rd). Within each year, simple random sample of ~30 → stratified sample for precision.

Non-probability sampling methods (chance unknown or zero)

Method	How	Risk
Convenience	Whoever is easy to reach	High selection bias
Purposive	Expert-chosen "information-rich" cases	Not generalisable
Quota	Fill quotas by trait (no random)	Selection bias
Snowball	Referrals from initial participants	Hidden populations only
Judgement	Researcher picks "typical" cases	Subjective bias

Useful for exploratory/qualitative work; avoid for generalisation.

Sample size determination

By precision (estimation)

For a mean: n = (z²·σ²) / d², where:

• z = critical value (1.96 for 95% confidence),
• σ² = variance (from pilot, or a planning value; for proportions use p(1−p), max at p = 0.5),
• d = desired margin of error.

Quick rule for proportions (infinite population)

n = z²·p(1−p)/d². At 95% confidence, ±5% margin, p=0.5 → n ≈ 384.

Finite population correction (FPC)

If the population N is small relative to n, shrink n: n_adj = n / (1 + (n−1)/N) (or n·(N−1)/(N... )). For our college of ~600 students, the correction is small.

For our stress study

Goal: 95% CI for the mean stress change, margin ±3 points, prior SD ≈ 6. n = 1.96²·6² / 3² ≈ 3.84·36/9 = 15.4 → need ~16 per group, but we plan 30 per group for power and attrition.

Rule: for hypothesis testing, also consider power (1 − β, typically 0.80) and effect size; use the larger n.

Sampling errors and bias minimisation

• Sampling error: natural variation between sample and population; shrinks with larger n (∝ 1/√n). Cannot be eliminated, only reduced.
• Sampling bias (selection bias): systematic over/under-representation. Can and must be eliminated by proper sampling design.

Bias minimisation tactics:

• Use a proper frame (no missing groups).
• Randomise selection and assignment.
• Stratify on known important factors.
• Avoid convenience/snowball for quantitative claims.
• Account for non-response (follow-up, weighting).

Estimation: point and interval

• Point estimate: a single best guess (e.g., sample mean x̄ for population mean μ).
• Interval estimate: a range with a confidence level (e.g., 95% CI). For a mean with unknown σ: x̄ ± t·(s/√n).

Example: 30 students' stress change mean = 5.2, SD = 6.0. 95% CI ≈ 5.2 ± 2.045·(6/√30) ≈ 5.2 ± 2.23 ≈ [2.97, 7.43].

Sampling for quantitative vs qualitative research

• Quantitative: probability sampling (representative, generalisable), sample-size by power/precision.
• Qualitative: non-probability (purposive/criterion/maximum variation), sample-size by saturation (keep going until no new themes emerge).

Sampling case studies

1. National health survey — multi-stage probability (select districts, then households, then individuals).
2. Exploratory interview study — purposive sampling of "expert developers."
3. Political poll — stratified by state/demographic + margin of error ±3%.
4. Clinic quality audit — convenience sample (patients seen this month) — quick but not generalisable.

PDF-aligned additions

Sampling and sample-size planning

Define the population, sampling unit, sampling frame, selection method, and target sample size before collecting data. A sample-size decision depends on the study goal:

• Estimation: desired confidence level, margin of error, variability, and population size.
• Comparison: expected effect size, significance level alpha, desired power, number of groups, and variability.

Power is the probability of detecting a real effect. A common target is 80%. Plan for non-response or dropout by increasing the recruitment target. A larger sample cannot repair a biased sampling frame.

Sampling errors

Sampling error is random variation caused by studying a sample. Bias is systematic error from undercoverage, non-response, convenience selection, or measurement. Probability sampling supports known selection probabilities; convenience and purposive sampling may be appropriate for qualitative or hard-to-reach groups but limit statistical generalisation.

Common mistakes

• Forgetting that non-response is a source of bias, not just noise.
• Using a convenience sample and then claiming population generalisation.
• Ignoring the finite population when the sample is a large fraction of N.
• Using p = 0.5 when you have local pilot data (over-samples).

Memory rules

• Population ≠ sampling frame; the gap is frame error.
• Probability = known non-zero chance (random/stratified/cluster); Non-probability = convenience/purposive/snowball.
• n = z²σ²/d²; for proportions p(0.5) maximises n; FPC shrinks n when n/N is large.
• Sampling error ↓ with √n; sampling bias is a design flaw, not luck.
• Point = single number; Interval = range with confidence.
• Quantitative → probability + size by power; Qualitative → purposive + size by saturation.

Check your understanding

1. Give one probability and one non-probability sampling method.
2. What is sampling bias, and how is it different from sampling error?
3. For ±5% margin at 95% confidence (p unknown), what sample size per the rule?
4. When is a cluster sample better than a stratified sample?

Answers

Reveal answers after attempting the questions

1. e.g. simple random (probability) vs convenience (non-probability).
2. Bias = systematic error (design flaw); error = random variation (shrinks with n).
3. ~384 (using p = 0.5).
4. When you lack a complete frame of individuals but have easy access to natural groups (e.g., schools, villages) — cluster is cheaper then.

Quick revision box

• Population (target), sampling frame (list), sample (studied); frame ≠ target → frame error.
• Probability: random, systematic, stratified, cluster, multi-stage — known non-zero chance.
• Non-probability: convenience, purposive, quota, snowball, judgment — for exploration.
• Sample size: n=z²σ²/d²; proportions use p(0.5) max; FPC for small populations.
• Sampling error ∝ 1/√n (reduce); sampling bias (eliminate via design, randomise, stratify).
• Point estimate vs interval (CI). Quantitative → power+precision; Qualitative → saturation.

Exam guidance

Define the method, justify why it fits the research question, apply it to the running study, and mention one limitation or ethical consideration.

Practice ladder

1. Easy - Recall: Define the module's central idea in one or two sentences.
2. Easy - Recognize: Identify the correct method for a small example and explain why it fits.
3. Medium - Apply: Work through one representative problem without copying the example.
4. Medium - Compare: Contrast two methods or concepts from the module.
5. Hard - Integrate: Solve a university-style scenario and justify every major step.

Reveal self-evaluation guide

A complete response uses correct terminology, shows intermediate steps, connects the result to the scenario, and states one assumption or limitation.

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