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Random sampling is a method where each member of a population has an equal chance of being selected for a study. Researchers use this sampling method to draw samples without bias and ensure they accurately represent the entire population. Since measuring every member of a population is impractical, random sampling provides reliable data while reducing time and cost.

In random sampling, each population member has an equal chance of selection. Probability sampling is similar but differs significantly: each member has a known probability of selection that is not necessarily equal. For example, selecting students from different disciplines with guaranteed representation from each creates unequal but fixed selection chances, exemplifying probability sampling.

Suppose researchers want to determine the average cost of a two-day hospital stay in Massachusetts. They randomly select 100 hospitals across the state using simple random sampling. Each hospital has an equal chance of being chosen, ensuring the sample accurately represents all hospitals in the state and provides reliable cost data.

Equal probability means every member of the population has the same likelihood of being selected. For instance, if a container holds 20 colored balls—five red, five black, five blue, and five green—each color has a 5 out of 20, or one in four, chance of being picked. This equal chance ensures unbiased representation.

Probability sampling assigns each population member a fixed but unequal selection probability based on group characteristics. For example, surveying 100 part-time students across ten disciplines ensures at least one student from each discipline is selected. Students from larger disciplines have higher selection chances, but each has a known, predetermined probability.

Biased sampling produces inaccurate results that do not represent the population. Sampling methods like random sampling ensure each population member has a fair chance of selection, eliminating systematic errors. Unbiased samples provide reliable data that researchers can confidently use to draw conclusions about the entire population.

Sample size determines how well a sample represents the population. Larger samples generally provide more reliable estimates of population characteristics. For example, surveying 25 professors about office books or 100 hospitals about stay costs allows researchers to calculate accurate averages and statistics that reflect the broader population.