Principles of Sampling & Sample Size Estimation of Proportion

sampling

process of selecting a subset of individuals from a larger population to make generalizations or inferences about the entire population.

Because conducting a census (collecting data from the entire population) is often expensive, time-consuming, and impractical for large populations.

Why do we use sampling instead of a full census?

census

collects data from all units of a population, ensuring complete accuracy but requiring high cost, time, and resources.

sample survey

collects data from a subset of the population, making it cheaper, faster, and more practical than a census.

population

The entire group of interest in a study.

target population

The group for which we want to make inferences

sampling population

The group from which the sample is drawn.

sampling unit

The unit selected in the sampling process.

sampling frame

A list of all sampling units available for selection.

elementary unit

The smallest unit of analysis in the study.

representativeness

should reflect the characteristics of the population.

efficiency

Should provide reliable results with minimal cost and effort.

practicability

Should be simple, large enough, and easy to implement.

economy

Should maximize information while minimizing cost.

measure reliability

Should allow measurement of accuracy and precision.

probability sampling

A method where every unit in the population has a known, nonzero probability of being selected.

Simple Random Sampling (SRS)

• Each unit has an equal chance of being selected.

• Requires a sampling frame (list of all units).

• Advantage: Easy to understand and analyze.

• Disadvantage: Not cost-efficient for large, dispersed populations.

Systematic Random Sampling (SyS)

• Selects individuals at regular intervals (e.g., every kth unit).

• Advantage: Easy to implement and reduces clustering.

• Disadvantage: May be biased if there is a hidden pattern in the data.

Stratified Random Sampling (StrRS)

• The population is divided into mutually exclusive groups (strata).

• Random samples are drawn independently from each stratum.

• Advantage: More representative and precise.

• Disadvantage: Requires a detailed sampling frame for each stratum.

Cluster Sampling

• The population is divided into clusters, and entire clusters are randomly selected.

• Advantage: More cost-effective than simple random sampling.

• Disadvantage: Clusters may not fully represent the population.

Multi-Stage Sampling

• A complex method combining multiple sampling techniques (e.g., stratified + cluster).

• Advantage: Increases representativeness while reducing costs.

• Disadvantage: More complex analysis and requires a larger sample size.

non-probability sampling

A method where some members of the population have zero or unknown probability of selection.

Haphazard Sampling

Also called convenience sampling, where researchers select subjects based on availability.

Judgmental Sampling

Also called purposive sampling, where experts select participants based on specific criteria.

Quota Sampling

Selecting samples to match a predetermined proportion (e.g., 50% male, 50% female).

Snowball Sampling

Used for hard-to-reach populations where participants refer others for the study (e.g., HIV patients).

To ensure the sample is large enough to accurately estimate population characteristics with a given level of precision.

Why do we compute for sample size?

We adjust the sample size

What happens if we expect non-response in our sample?

Precision

Smaller errors require larger samples.

Confidence Level

Higher confidence increases sample size.

Proportion

If unknown, use p = 0.5 for the largest required sample.

OpenEpi

A free online tool for statistical calculations, including sample size estimation.

Precision (d)
Confidence Level (Z)
Proportion (p)

What factors affect sample size?

0.5

What is the default p-value used when no prior data is available?

Higher precision (lower d) increases the required sample size

How does increasing precision affect sample size?

95% (Z = 1.96)

What is the recommended confidence level for medical research?