Statistics: Sampling Methods, Experimental Design, and Bias

Simple Random Sample (SRS)

A sample where every individual and every possible group of individuals has an equal chance of being chosen.

Convenience Sample

A sample chosen by selecting individuals who are easiest to reach or contact; often leads to bias.

Voluntary Response Sample

A sample made up of people who choose themselves by responding to a general appeal (like an online poll); tends to overrepresent people with strong opinions.

Stratified Random Sample

The population is divided into groups (strata) based on a shared characteristic, and an SRS is taken from each group.

Cluster Sample

The population is divided into clusters, usually by location, and one or more entire clusters are randomly selected; all individuals in chosen clusters are included in the sample.

Systematic Random Sample

A sample chosen by selecting every kth individual after a random starting point.

Undercoverage

Occurs when some members of the population are left out of the sampling frame and therefore have no chance of being selected.

Non-Response

Occurs when individuals chosen for the sample cannot be contacted or refuse to participate.

Response Bias

Systematic pattern of inaccurate answers due to wording of questions, interviewer behavior, or the respondent's desire to appear a certain way.

Confounding Variables

A variable that is related to both the explanatory and response variables, making it hard to tell which variable causes the observed effect.

Observational Study vs. Experiment

Observational Study: Observes individuals without imposing treatments. Experiment: Deliberately imposes treatments to measure their effects.

Experimental Units

The smallest collection of individuals to which treatments are applied; called subjects when they are human.

Treatments

The specific experimental conditions applied to the units; often a combination of factor levels.

Components of an Experiment

Imposed treatment, Comparison (use at least two treatments), Random Assignment (reduce bias), Control (keep other variables constant), Replication (use enough subjects to reduce chance variation).

Random Assignment

Using chance to assign experimental units to treatments, balancing unknown variables across groups.

Placebo Effect

When participants respond to a fake treatment simply because they believe they are receiving a real one.

Randomized Block Design

Experimental units are divided into blocks of similar individuals, and random assignment is carried out separately within each block.

Matched Pairs Design

Each subject is matched with another similar subject or acts as their own control; used to compare two treatments closely.

Simulation

A model used to imitate real-world processes or situations using random numbers or technology to estimate probabilities or outcomes.

Statistical Significance

When the observed difference in results is too large to be explained by random chance alone.

Purpose of Using a Random Sample

To avoid bias and ensure the sample represents the population, allowing results to be generalized.

Purpose of Using a Random Assignment

To create roughly equivalent groups, ensuring differences in results can be attributed to treatments rather than other factors.