Unit 3: Collecting Data

Population

The entire group of individuals or objects that you want information about.

Sample

A subset of the population that you actually measure or observe.

Census

Collecting data from every individual in the population.

Parameter

A numerical value that describes a population (usually unknown).

Statistic

A numerical value computed from a sample (known once the sample is taken).

Sampling frame

The list or method used to identify and select the individuals who can be included in the sample.

Representative sample

A sample that reflects the population well, without systematically over- or under-representing certain groups.

Random sampling

Selecting a sample using a known chance process so individuals (or groups) have known probabilities of selection.

Generalization

Using results from a sample to draw conclusions about the larger population; strongest when based on random sampling from an appropriate sampling frame.

Undercoverage

Bias that occurs when some groups in the population are left out of the sampling frame or are less likely to be included.

Nonresponse bias

Bias that occurs when selected individuals do not respond and nonresponders differ systematically from responders.

Response bias

Bias that occurs when respondents give inaccurate answers due to factors like social desirability, sensitive topics, interviewer influence, or poor question design.

Voluntary response sample

A sample where individuals choose themselves to participate; tends to overrepresent people with strong opinions.

Convenience sample

A sample chosen because individuals are easy to reach; usually does not support generalization to the population.

Question wording bias

Bias caused by leading, loaded, ambiguous, or double-barreled wording (or question order) that pushes respondents toward certain answers.

Sampling bias

Systematic error from a sampling method (or frame) that consistently produces unrepresentative samples; a property of the method, not one particular sample.

Sampling variability (sampling error)

Natural random fluctuation in sample results from sample to sample, even when using a good random sampling method.

Accuracy vs. precision

Accuracy: results centered near the true value (low bias). Precision: low spread from sample to sample (low variability).

Simple random sample (SRS)

A sample of size n chosen so that every possible group of n individuals has an equal chance of being selected.

Stratified random sample

A probability sample that divides the population into homogeneous strata and takes an SRS within each stratum, then combines results.

Cluster sample

A probability sample that divides the population into clusters (ideally mini-versions of the population), randomly selects clusters, and includes all individuals in selected clusters.

Systematic sampling

Selecting individuals by choosing a random start on an ordered list and then taking every k-th individual.

Periodicity

A risk in systematic sampling when the list has a repeating pattern that lines up with the sampling interval, causing bias.

Pilot study

A small trial run of a survey or data-collection process used to detect confusing wording, poor answer choices, or logistical problems.

Observational study

A study that observes individuals and measures variables without assigning treatments; can show association but not cause-and-effect.

Retrospective vs. prospective study

Retrospective: looks back using past records or memories. Prospective: follows individuals forward in time to observe outcomes.

Explanatory variable

A variable that may help explain or influence changes in another variable.

Response variable

The outcome variable measured in a study; the variable that may be influenced by the explanatory variable.

Confounding variable

A variable related to both the explanatory and response variables that can create a misleading association, especially in observational studies.

Lurking variable

A variable not included in the study that affects the interpretation of the relationship among variables (often similar in use to confounding on AP).

Experiment

A study that deliberately imposes treatments on experimental units and compares responses; can support cause-and-effect if well designed.

Random assignment

Using chance to assign experimental units to treatments; helps balance known and unknown variables across treatment groups.

Cause-and-effect conclusion

A conclusion that a treatment causes a change in the response; justified primarily by random assignment in an experiment (not by random sampling).

Experimental unit

The individual or object on which a treatment is imposed (called a subject when the unit is a person).

Treatment

A specific experimental condition applied to experimental units (including a placebo or standard treatment, if used).

Factor

An explanatory variable in an experiment that the researcher controls (e.g., dosage, type of diet).

Level

A specific value of a factor in an experiment (e.g., 0, 1, or 2 hours of exercise).

Control group

A treatment group used as a baseline comparison (may receive no treatment, a placebo, or the current standard treatment).

Placebo

An inactive treatment made to look like an active one, used to help control for expectations in experiments.

Blinding

A procedure in which subjects do not know which treatment they are receiving, reducing expectation-related effects.

Double-blinding

A procedure in which neither the subjects nor the people evaluating responses (or interacting with subjects about outcomes) know who received which treatment.

Replication (experimental design)

Using enough experimental units in each treatment group to reduce chance variation and make effects easier to detect.

Completely randomized design

An experimental design that assigns all experimental units to treatments purely by chance, with no additional grouping structure.

Randomized block design

An experimental design that groups units into blocks based on a variable expected to affect the response, then randomizes treatments within each block.

Matched pairs design

A special randomized block design with blocks of size 2, done by pairing similar subjects or having each subject receive both treatments in random order.

Noncompliance

When subjects do not follow their assigned treatment; weakens the clean comparison created by random assignment.

Dropouts

When subjects leave a study; can bias results if dropout is related to the response or treatment (similar in spirit to nonresponse).

Statistical significance

A result so unlikely to occur by random chance alone (if there were no real effect) that it suggests a real difference or effect exists.

Internal validity

How well an experiment supports a cause-and-effect conclusion for the subjects studied (strengthened by random assignment, control, and replication).

External validity

How well results generalize to a broader population; strengthened by random sampling and a good match between sampling frame and population.