Simple Random Sampling: Every member of the population has an equal chance of selection. It requires a sampling frame and uses random number generators to pick individuals.
Systematic Sampling: Members are selected at regular intervals from a list. The interval is calculated as , where is population size and is sample size.
Stratified Sampling: The population is divided into mutually exclusive groups (strata) based on shared characteristics. A random sample is then taken from each stratum proportional to its size in the population.
Quota Sampling: Similar to stratified sampling, the population is divided into groups, but the selection within groups is non-random (e.g., an interviewer stops people until a target number is reached).
Opportunity (Convenience) Sampling: Selecting individuals who are easiest to reach or available at the time of the study. This is the fastest method but often the most biased.
Census vs. Sample: A census observes every member of a population, providing 100% accuracy but at high cost and time. A sample is a subset, which is cheaper and faster but introduces sampling error.
Stratified vs. Quota Sampling: While both use groups, stratified sampling uses random selection within those groups (requiring a sampling frame), whereas quota sampling does not.
| Feature | Stratified | Quota |
|---|---|---|
| Selection | Random | Non-random |
| Sampling Frame | Required | Not required |
| Bias | Low | High (interviewer bias) |
| Cost/Speed | Higher/Slower | Lower/Faster |
Identify Data Types: Always check if data is discrete or continuous before choosing a statistical model. Age is a common trick; it is discrete if measured in years, but continuous if measured as time lived.
Justify Sampling Choices: When asked to recommend a method, consider the availability of a sampling frame. If no list exists, random methods (Simple, Systematic, Stratified) are impossible; Quota or Opportunity must be used.
Calculate Proportions: In stratified sampling questions, ensure the sample size for a group is . Always round to the nearest whole number.
Check for Bias: If a scenario describes a researcher picking people in a specific location (like a shopping mall), identify it as Opportunity or Quota sampling and mention the risk of bias.
Confusing Strata and Quotas: Students often forget that stratified sampling requires a random process (like a random number generator) after the groups are formed.
Sampling Frame Errors: Assuming a random sample can be taken without a list of the population is a common mistake. Without a frame, you cannot assign numbers to individuals for random selection.
Sample Size Fallacy: While larger samples generally reduce error, a large biased sample (e.g., 10,000 people from one specific town to represent a country) is still less accurate than a small random sample.
Probability Distributions: The type of data (discrete vs. continuous) determines whether you use a Binomial/Poisson distribution or a Normal distribution for analysis.
Hypothesis Testing: The validity of a hypothesis test depends entirely on the assumption that the sample was collected randomly and is representative of the population.
Real-world Application: Quality control in manufacturing often uses systematic sampling (testing every 100th item) because it is easier to implement on a production line than simple random sampling.
