Math 183 - Part 1 (Data Collection: Surveys, Experiments, Observational Studies, Meta-Analyses)

Observation

A single subject or unit for which data is collected; each row in a dataset.

Variable

A characteristic or measurement collected for each observation; each column in a dataset.

Numerical Variable

A variable measured in numbers, can be discrete (counts) or continuous (any value in an interval).

Discrete Variable

A numerical variable that takes only specific, separate values (like number of children).

Continuous Variable

A numerical variable that can take any value within a range (like height or weight).

Categorical Variable

A variable whose values are categories or groups, not numerical.

Nominal Variable

Categorical variable with no natural order (e.g., gender, region, marital status).

Ordinal Variable

Categorical variable with a meaningful order or ranking (e.g., education level, income bracket).

Population

The entire group you want to learn about in a study.

Sample

A subset of the population, ideally chosen to represent the population well.

Census

A survey that attempts to collect data from every member of the population.

Sampling

The process of selecting a subset of the population to gather information.

Representative Sample

A sample that accurately reflects the population, allowing generalization.

Bias

Systematic error that causes results to differ from the true population value.

Self-selection Bias

Bias introduced when participants choose themselves, making the sample unrepresentative.

Non-response Bias

Bias introduced when certain groups are less likely to respond to a survey.

Response Bias

Bias introduced by wording, interviewer, or survey method, affecting answers given.

Simple Random Sampling

Every individual in the population has an equal chance of being selected.

Stratified Sampling

Divide the population into groups (strata), then randomly sample within each group.

Cluster Sampling

Divide the population into groups (clusters), randomly select clusters, then survey all or some within those clusters.

Multistage Sampling

Combine two or more sampling methods (e.g., cluster then simple random sampling within clusters).

Systematic Sampling

Select every nth individual from a list or sequence.

Convenience Sampling

Sample individuals who are easiest to reach; usually not representative.

Quota Sampling

Select a fixed number from each group, but not randomly.

Network (Snowball) Sampling

Ask initial subjects to refer others, useful for hard-to-reach populations.

Controlled Experiment

Researchers randomly assign treatments to subjects to study causal effects.

Randomization

Assigning subjects to groups by chance to reduce bias.

Replication

Including multiple subjects in each group to increase reliability.

Blocking

Grouping similar subjects and randomizing within those groups to reduce confounding.

Blinding

Subjects and/or researchers do not know which group a subject is in, preventing bias.

Placebo

A fake treatment used to compare against the real treatment in experiments.

Observational Study

Researchers observe without intervening or assigning treatments; can show association, not causation.

Cohort Study

An observational study following exposed and unexposed groups over time.

Case-Control Study

An observational study comparing those with a condition (cases) to those without (controls), looking back for exposure.

Cross-Sectional Study

A study measuring variables at one point in time.

Confounding Variable

A variable related to both the explanatory and response variables, potentially misleading results.

Association

When two variables tend to change together; does not imply one causes the other.

Causation

One variable produces a change in another; typically established by experiments with randomization.

Natural Experiment

An experiment where randomization occurs by “nature” or outside events, not by researchers.

Meta-Analysis

A study that combines results from multiple studies to increase evidence and power.