層別抽出法

Use stratified sampling when studying a heterogeneous population with large variations in characteristics. This method works well for populations like students across different age groups or geographical regions with varying habitat and soil type. By dividing the population into homogenous strata first, stratified sampling ensures each subgroup is represented proportionately in your sample, reducing bias and improving accuracy.

Strata must be mutually exclusive, meaning each subject belongs to only one stratum. They must also be exhaustive, ensuring all subjects with shared characteristics are included in a single stratum. For example, all red balls must be in one stratum only, and all balls of the same color must be grouped together. These requirements prevent overlap and ensure complete population coverage.

After dividing the population into strata, randomly draw a proportionate number of subjects from each stratum. For instance, if studying college students, number each member within each department, then use random selection to choose proportionate numbers from every department. Combine these randomly selected subjects from all strata to form your final stratified sample.

Stratified sampling applies to election polling, studying life expectancy across populations, analyzing income for different jobs across a nation, and examining people who work overtime hours. Researchers also use it for geographical surveys where regions with similar habitat, elevation, and soil type are grouped into strata. This approach ensures each population segment is adequately represented in findings.

Stratified sampling guarantees representation from each subgroup within a heterogeneous population, whereas simple random sampling may miss or underrepresent certain groups. By organizing subjects into homogenous strata based on shared characteristics, stratified sampling reduces sampling variability and produces more accurate estimates. This structured approach is particularly valuable when population characteristics vary significantly.

Since weight varies greatly among students in different age groups, dividing students into strata by grade level ensures each age group is represented. Randomly selecting students from each stratum and calculating their average weight produces a more accurate population estimate than random sampling alone. This stratified approach accounts for the natural variation in weight across different developmental stages.

Stratified sampling reduces bias by ensuring systematic representation from each stratum rather than relying on chance alone. The sampling method ensures samples are drawn without bias and accurately represent the population by proportionately including all subgroups. This structured approach prevents certain population segments from being accidentally excluded or overrepresented in your sample.