Notes on sampling for UGC NET Paper 1 Research Aptitude, in 3 short sub-topics. Each one gives the concept, the facts to memorise and the traps examiners set.
3 sub-topics
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3 exam-trap notes
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Topic 13 of 29
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The population (universe) is the complete set of units that the researcher wants to describe; the sampling frame is the actual list from which the sample is drawn; a sample is the subset studied. A parameter describes the population (written with Greek letters, such as μ and σ) and a statistic describes the sample (x̄ and s). Sampling is used because it saves time and cost and is the only possible option when testing is destructive. Sampling error is the difference between a sample statistic and the population parameter that arises by chance because only a part is studied; it falls as the sample grows and can be estimated in probability samples through the standard error (σ/√n). Non-sampling errors, such as non-response, measurement and coverage errors, occur in censuses as well and do not shrink with a larger sample.
Memorise
Parameter = population; statistic = sample.
Standard error = σ/√n; to halve it, the sample must be four times larger.
Census has no sampling error but may have large non-sampling error.
Analyse / traps
A very large but biased sample is still biased; size cannot cure bad selection.
Sample size depends on the variability of the population, the precision (margin of error) required, the confidence level, the number of subgroups to be analysed, the expected response rate and the resources available. For a proportion, a common formula is n = Z²pq / e²; with p = 0.5, 95% confidence (Z = 1.96) and a 5% margin of error it gives about 384. Yamane’s simple formula is n = N / (1 + Ne²). Beyond a moderately large population, the population size matters little; what matters is the absolute sample size. About 30 observations are often cited as the minimum for the central limit theorem to begin to apply.
Memorise
95% confidence → Z = 1.96; 99% → Z = 2.58.
Greater variability or tighter precision → larger sample.
Increasing n reduces sampling error, not bias.
Analyse / traps
Sample size does not need to be a fixed percentage of the population.
3E.3Probability and Non-probability Sampling Methods#
Concept
In simple random sampling each unit has an equal and independent chance, drawn by lottery or random number tables. Systematic sampling picks every k-th unit after a random start, where k = N/n; it is convenient but risky if the list has a hidden pattern. Stratified sampling divides the population into internally homogeneous strata and draws randomly from each, proportionately or disproportionately; it improves precision. Cluster sampling randomly selects whole groups (schools, villages) that are internally heterogeneous, saving cost but usually with higher error than simple random sampling of the same size. Multistage sampling selects in successive stages (state, district, village, household), as national surveys do. Non-probability methods include convenience, purposive (judgemental), quota and snowball sampling; their selection probabilities are unknown, so sampling error cannot be calculated.
Memorise
Stratified: homogeneous within strata. Cluster: heterogeneous within clusters.
Quota = non-random equivalent of stratified; snowball = chain referral for hidden populations.
Sampling with replacement: a unit may be chosen more than once.
Analyse / traps
Stratified draws from every stratum; cluster draws only some clusters and studies all or many units in them.
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