Sample: A sample is a subset of a population selected for measurement, observation, or questioning, to provide statistical information about the population.
Purpose:
To gather data that can be used to make inferences about the entire population.
To save time and resources by studying a smaller group rather than the entire population.
Simple Random Sample (SRS)
Simple Random Sample (SRS): A sampling method where every member of the population has an equal chance of being selected.
Characteristics:
Equal probability of selection for all individuals.
Typically achieved using random number generators or other randomization methods.
Minimizes bias in sample selection, ensuring that every individual is equally likely to be chosen.
Advantages:
Unbiased: Reduces the risk of bias in sample selection.
Representative: In large samples, SRS tends to produce a sample that is representative of the population.
Disadvantages:
Not Always Practical: Requires a complete list of the population, which may not always be available.
Sampling Error: There’s still a possibility that the sample might not represent the population perfectly, especially with small sample sizes.
Representative Sample
Representative Sample: A sample that accurately reflects the characteristics of the population from which it is drawn.
Characteristics:
Proportional Representation: The sample mirrors the population in key characteristics such as age, gender, income, etc.
Low Bias: Selection methods are designed to reduce bias, ensuring that no subgroup is over- or under-represented.
Importance:
Generalizability: Conclusions drawn from a representative sample are more likely to apply to the population as a whole.
Accuracy: The more representative the sample, the more accurate the results and inferences will be.
Achieving a Representative Sample:
Stratified Sampling: Dividing the population into subgroups (strata) and sampling from each subgroup to ensure all key characteristics are represented.
Quota Sampling: Ensuring that the sample meets certain quotas for different subgroups to reflect the population accurately.
Key Differences Between SRS and Representative Samples
Simple Random Sample (SRS) is a method of selection, while Representative Sample is a quality or characteristic of a sample.
An SRS might not always be representative if the population has significant subgroups, but it is often used as a way to achieve a representative sample.
Related Concepts
Sampling Bias: Occurs when some members of the population are more likely to be selected than others, leading to a non-representative sample.
Sampling Frame: The list of individuals from which a sample is actually drawn. The accuracy of this list impacts the representativeness of the sample.
Sampling Error: The difference between the characteristics of the sample and those of the population. Can be minimized with larger and more representative samples.