Sampling and Inference
Sampling and Inference
A population is the entire group under study. A sample is a subset selected from the population. Because surveying an entire population is often impractical, samples are used to make inferences about population characteristics — with awareness of what can and cannot be concluded.
Types of Sampling
| Method | Description | Key feature |
|---|---|---|
| Random sampling | Every member of the population has an equal chance of selection | Unbiased |
| Stratified sampling | Population divided into subgroups; sample drawn from each in proportion | Representative structure |
| Systematic sampling | Every \( n \)th member selected from a list | Simple, may introduce pattern bias |
| Convenience sampling | Easiest-to-reach members selected | Likely biased |
Bias in Sampling
A sample is biased if certain members of the population are systematically more or less likely to be selected. Bias leads to unreliable inferences. Common sources of bias include: surveying only one location, using a self-selected sample, asking leading questions.
Making Inferences
A sample statistic (e.g. sample mean, sample proportion) is used to estimate the corresponding population parameter. The larger and more representative the sample, the more reliable the inference — but uncertainty always remains. Always state that conclusions are estimates, not certainties.
Key Takeaways
- Population = everyone/everything under study. Sample = a subset used to make inferences.
- Random sampling is unbiased — each member equally likely to be chosen.
- Stratified sampling preserves the proportions of subgroups in the population.
- Larger, unbiased samples give more reliable inferences.
- Inferences from samples are estimates — they carry uncertainty.