LESSON 29 - SAMPLING: METHODS OF DETERMINING THE SAMPLE SIZE IN QUANTITATIVE RESEARCH

Determining sample size in quantitative research is a balancing act: the sample must be large enough to represent the population and deliver accurate estimates, yet not so large that costs and timelines become unmanageable. Sample size—often abbreviated as “n” or “small m”—refers to the number of respondents used in the study, and it directly affects how confidently researchers can generalize findings from a subset to the full population.

The lesson frames sample size as one of the most consequential decisions in quantitative research because it governs both statistical reliability and practical feasibility. A sample that is too small may fail to capture the population’s variation, weakening representation and inflating uncertainty. A sample that is too large can reduce margins of error, but it can also increase cost and time substantially. The “ideal” sample size therefore depends on several measurable factors, starting with the type of research approach. Quantitative studies rely on statistical methods and aim for representativeness, while qualitative studies typically use judgmental approaches and seek information-rich cases rather than statistical generalization.

Confidence level and precision drive much of the calculation. Confidence level reflects the probability that a population parameter falls within a specified range of values; in social science, 90% and 95% are common, with 99% also used. Higher confidence levels require larger samples. Precision is treated as sampling error: the degree of accuracy around the estimate (often expressed as “plus or minus” percentages). For example, if 85% of students show a positive attitude with a precision of ±5%, the implied range for the population is 80% to 90%. Larger samples improve precision, narrowing the error band.

Population size matters too, particularly when generalization is central, as in quantitative research. Finally, non-response rate can undermine the entire plan. The lesson distinguishes between the number of subjects selected and the number who actually respond correctly; the latter determines the effective sample size. As non-response increases, the risk of a biased sample rises, so researchers should build in strategies to reduce non-response as much as possible.

With those factors in mind, the lesson outlines five practical methods for determining sample size. For very small populations, researchers can use every element (a census), eliminating sampling error. Another approach is borrowing the sample size from a similar prior study, though it risks repeating earlier mistakes. More systematic options include using online sample size calculators, published tables (notably the Krejcie and Morgan table, and the Yamane formula approach referenced with 1967), and mathematical formulas. An example calculation using an online calculator for a population of 500 yields a sample size of 218, while applying the Yamane-style formula with a margin of error of 0.05 produces a sample size around 222. Across these last three methods, results tend to converge, reinforcing that statistical tools and formulas offer more defensible sample-size decisions than ad hoc choices.