Population and Sampling Techniques

• Population refers to the entire group under study.
• A sample is a subset of a population obtained through random or non-random sampling.
• Random sampling ensures each element of the population has an equal chance of selection.

Types of Random Sampling Techniques

• Lottery Sampling: Each member has an equal chance, such as names drawn from a hat.
• Systematic Sampling: Samples are selected from a list at regular intervals (e.g., every nth item).
• Stratified Random Sampling: Population is divided into homogeneous groups, then sampled.
• Cluster Sampling: Area sampling done geographically (e.g., provinces, then cities, then households).
• Multi-Stage Sampling: Combines different techniques, like lottery and stratified methods.
• Non-random sampling doesn't give each population member an equal chance; it's used for quick, non-confidential responses.

Types of Non-Random Sampling

• Accidental Sampling: Includes those the researcher happens to meet.
• Quota Sampling: Includes a specific number of people from certain categories.
• Convenience Sampling: Uses the most accessible means (e.g., phone, internet).
• Purposive Sampling: Used for small samples, like selecting experts or managers.

Parameter and Statistics

• A parameter is a descriptive measure of a population’s characteristics.
• Statistics describe a sample and can be directly calculated.
• Sampling Distribution of the Sample Means formula is 𝑁𝐶𝑛, determining the number of ways to take n objects from N.

Additional Definitions

• In modern statistics, a sample is a portion of data analyzed, while a population is the entire data set.
• Census: Recording information of an entire population.
• Survey: Systematically gathering information.
• Sample Survey: Systematically gathering information on a population segment to infer quantitative descriptors.
• Sampling: Process of selecting a population section.
• Random means outcome is based on chance.
• Random Sampling: Method for choosing an equally distributed subset from a larger population.
• Statistical Inference: Concluding population parameters using sample statistics.
• Probability Sampling: Each member has an equal chance of being selected.

Basic Types of Probability Sampling

• Simple Random Sampling (SRS): Each sample has an equal chance. Selection can be with or without replacement. Requires a sampling frame.
• Stratified Sampling: Extension of SRS for different homogeneous groups (strata). SRS is used within each stratum to get proportional sample sizes.
• Systematic Sampling: Elements selected at uniform intervals (time, order, space). First, determine desired sample size n, divide the N units into groups of k units, where k=N/n. One unit is randomly selected from the first group, with every kth unit thereafter also selected.
• Cluster Sampling: Population is divided into clusters, a random sample of clusters is selected, and then every member of the selected clusters is included.

Basic Types of Non-Probability Sampling

• Haphazard/Accidental Sampling: Unsystematic selection of sample units.
• Convenience Sampling: Easily accessible sample units are taken.
• Volunteer Sampling: Participants volunteer in studies.
• Purposive Sampling: Expert selects a representative sample based on subjective judgment.
• In Quota Sampling: Sample units are picked for convenience but certain quotas are given to interviewers, mainly used in market research.
• Snowball Sampling: Participants refer other potential participants, useful for rare topics or populations.

Central Limit Theorem

• As sample sizes increase, the sampling distribution of the mean becomes normal, even if the original data are not normally distributed. This justifies the use of the formula for z-values.
• Standard error of the mean measures the sample mean's accuracy in estimating the population mean 𝜇.
• A larger n leads to a smaller standard error and a better estimate of 𝜇. For a sufficiently large n, the estimate of 𝜇 is good.
• Regardless of the population distribution, the sampling distribution of the mean approaches a normal distribution as n increases.
• A sample that is sufficiently large is approximately normal whenever n is greater or equal to 30.
• If the population distribution is normal, the sampling distribution will always have a normal curve, regardless of sample size.