Game 12 · Testing and estimation
How do you choose who gets studied?
Simple random, systematic, stratified, cluster and non-probability sampling.
Read with: Sampling37 DNB questions
Play
Draw the sample from a district of 400 houses
Each round names a sampling method. Carry it out on the map by clicking houses or villages, or by setting the interval or allocation. Then see your estimate of anaemia prevalence against the true value, and the spread of 300 more samples drawn the same way. Other rounds ask you to name a method from a picture, or work out a design effect. You have three lives.
Loading the first round…
The district, its villages and every prevalence in the game are made up for teaching.
The methods
Probability and non-probability sampling
In a probability sample every unit has a known, non-zero chance of selection. That is what allows the sampling error to be calculated and the result to be generalised. A non-probability sample (convenience, consecutive, purposive, quota, snowball) is quicker, but nobody's chance of selection is known, so the sampling error cannot be calculated.
- Simple random: every unit has the same chance, by lottery, random-number table or computer. It needs a full list.
- Systematic: interval k = N ÷ n, a random start between 1 and k, then every k-th unit. Only the start is random, so a list with a repeating pattern that matches k gives a biased sample.
- Stratified random: split the list into strata that differ (urban and rural), then draw a random sample in each. Proportionate allocation is self-weighting.
- Cluster: pick whole natural groups (villages, schools, wards) at random and study everyone in them. Only a list of groups is needed.
- Multistage: a random pick at every level, for example villages and then households inside each chosen village.
Proportionate allocation: n(h) = n × N(h) ÷ N
- n(h)
- sample size in stratum h
- N(h)
- number of units in stratum h
- N, n
- population size and total sample size
| Feature | Stratified | Cluster |
|---|---|---|
| Groups are | Alike inside, different between strata | Mixed inside, each a mini-population |
| You sample from | Every stratum | A random few clusters |
| List needed | Individuals within each stratum | Only the clusters |
| Main gain | Better precision, every subgroup represented | Lower cost and travel |
| Main cost | Needs stratum information in advance | Less precise, needs a design effect |
Stratified: sample from every group. Cluster: choose some groups and study everyone in them.
Error and bias
A bigger sample shrinks only one kind of error
Sampling error is the chance difference between a sample estimate and the population value. It is present even when the sampling is done correctly, and it becomes smaller as n increases. The histograms in the game show it: every method scatters around the true value, and a larger n narrows the scatter.
Non-sampling error covers selection bias, non-response, a faulty sampling frame and measurement error. It shifts every estimate the same way. In the road round, the road-side sample grew from 10 to 120 houses and stayed away from the true value. In 1936 a magazine poll with about 2.4 million replies predicted the wrong winner of the US election, while Gallup was right with about 50,000.
For the full chapter, with PPS sampling and the allocation methods, read Sampling in the Research Methodology book.
Design effect
Why a cluster sample must be larger
People in one village tend to be alike, so 100 people from 4 villages carry less information than 100 people drawn one by one. The design effect is the factor by which the sample size for a simple random sample is multiplied.
Design effect = 1 + (m − 1) × ICC
- m
- people sampled per cluster
- ICC
- intracluster correlation: how alike people in one cluster are (0 = not at all, 1 = identical)
m = 10, ICC = 0.05 → 1 + 9 × 0.05 = 1.45, so 323 × 1.45 = 468.4 → 469 people
The WHO Expanded Programme on Immunization 30 × 7 cluster survey (Henderson and Sundaresan, 1982) chose 30 clusters and 7 children of the target age in each, 210 in all, starting at a random house and moving to the next nearest. WHO's 2018 reference manual (WHO/IVB/18.09) now recommends probability-based sampling at every stage, because the next-nearest-house rule gives households unequal and unknown chances of selection.
Writing the answer
How to write this in a 10-mark DNB answer
- Define sampling, population, sampling frame, sampling unit, and parameter versus statistic. Say why we sample instead of taking a census.
- Draw a tree: probability methods (simple random, systematic, stratified, cluster, multistage, PPS) and non-probability methods (convenience, consecutive, purposive, quota, snowball).
- For each method give one line on how it is done, one example from your branch, and one merit and one demerit. Draw small dot diagrams for stratified and cluster sampling.
- Give the formulas: k = N ÷ n for systematic, n × N(h) ÷ N for proportionate allocation, and design effect = 1 + (m − 1) × ICC for cluster sampling.
- Separate sampling error (falls with larger n) from non-sampling error (bias, non-response, which does not).
- If the question is from Community Medicine, add the WHO 30 × 7 survey and the 2018 WHO change to probability sampling at every stage.
The one thing to remember
How you pick matters more than how many you pick.
Past papers
DNB questions this game helps you answer
Questions from NBE theory papers for DNB, DrNB and Diploma courses, most often asked first. The tag after each question is the specialty and the year it was set.
- ×1Enumerate various sampling techniques. Describe indications for each technique with limitations/advantages.
- ×1Epidemiological Investigation of RA (EIRA) study was conducted to investigate the influence of environmental factors on the risk of developing rheumatoid arthritis. 679 patients with rheumatoid arthritis were compared with 847 individuals randomly selected from the population for smoking status. The incidence of RA in current smokers, ex-smokers and ever-smokers, respectively, was compared with that of never-smokers. a) What study design was it? b) What sampling technique would be appropriate for such a study? c) What are the potential biases? d) What is the measure of effect calculated in such a study? e) Enumerate the pros and cons of this study design.
- ×1Quota sampling.
- ×1Random sampling. [2.5]
- ×1Sampling methods in clinical research.
- ×1Significance of sampling in research.
- ×1Describe different type of sampling in psychiatric research. What is the sample size? Describe principle and essential components of sample size calculation for any two types of research designs?
- ×1What are the types of sampling methods in research methodology? Describe them in brief.
- ×1Sampling methods in research.
- ×1Advantages and Disadvantages of Systematic Random Sampling.
- ×1Comment on stratified sampling method.
- ×1Define Sample. Enlist sampling techniques. Describe the procedure of cluster sampling in detail.
- ×1Enumerate various sampling methods.
- ×1Non-probability sampling methods.
- ×1What is sampling bias?
- ×1Methods of sampling.
- ×1What is the impact of sampling errors?
- ×1Explain various types of random sampling techniques with examples.
- ×1Sampling techniques.
- ×1Types of sampling methods.
- ×1What are various methods of sampling?
- ×1What is incidence density sampling? Make a brief protocol of a study to explain it.
- ×1Describe the methodologies of sampling in clinical study population.
- ×1Sampling methods.
- ×1What are the possible sampling techniques that can be used in this study?
- ×1Cluster sampling.
- ×1Enumerate various sampling techniques. Write the unique advantage of each technique with appropriate example.
- ×1Sampling techniques for biomedical research.
- ×1What are sampling and non sampling errors?
- ×1What is sampling?
- ×1Random Sampling
- ×1Different sampling methods followed in clinical trials.
- ×1Sampling techniques in Research Methodology.
- ×1What is sampling? Why do we do sampling? What are the methods of sampling?
- ×1Write in brief about non-random sampling. What is Lot Quality Assurance (LQA) sampling? In which situation such technique apply and how? What are the advantages and disadvantages of LQA sampling?
- ×1Discuss the sampling methodology covering: a) Sample size, b) Adjustment of sample size, c) Sample design, d) Sample selection, and e) Mapping and listing operation, in context of National Family Health Survey (NFHS) Round 3.
- ×1Discuss the sampling methodology covering: a. Sample size, b. Adjustment of sample size, c. Sample design, d. Sample selection, and e. Mapping and listing operation, in context of National Family Health Survey (NFHS) Round 3.
Read next