AP Statistics Unit 3 Notes: How to Collect Data with Good Samples

Population

The entire group you want to learn about in a study (the group your question is targeting).

Sample

The subset of the population from which you actually collect data.

Parameter

A numerical summary of a population (usually unknown), such as the true population proportion or mean.

Statistic

A numerical summary computed from a sample (known after data collection), used to estimate a parameter.

Census

A data collection that measures every member of the population; can still be inaccurate if measurement is poor.

Sampling Frame

The list or mechanism that identifies all units you can realistically sample from; mismatches with the population can cause bias.

Generalizability

The ability to use results from a sample to draw conclusions about the population (who you can talk about).

Random Sampling

Selecting a sample by a chance process that gives population units a known (often equal) chance of being chosen; supports generalizing to the population.

Random Assignment

Assigning treatments to individuals by chance in an experiment; supports cause-and-effect conclusions (not generalizability).

Bias

A systematic tendency for a sampling or measurement process to overrepresent/underrepresent certain outcomes, leading to consistently off-target estimates.

Variability

Natural random fluctuation in results from sample to sample; not the same as bias.

Simple Random Sample (SRS)

A sample of size n from a population of size N where every possible group of n individuals has an equal chance of being selected.

Strata

Non-overlapping groups in a population that are similar within themselves on an important variable; used in stratified sampling.

Stratified Random Sample

A sample made by dividing the population into strata, randomly sampling within each stratum (often by SRS), and combining the results.

Proportional Stratification

A stratified design where the number sampled from each stratum is proportional to that stratum’s size in the population.

Cluster Sample

A sample made by dividing the population into clusters that are mini-versions of the population, randomly selecting clusters, and including all individuals in chosen clusters.

Systematic Sample

A sample chosen by randomly selecting a starting point and then taking every k-th unit from an ordered list.

Step Size (k)

In systematic sampling, the interval between selected units, often computed as k = N/n.

Periodicity

A risk in systematic sampling where a repeating pattern in the list aligns with k, causing a biased sample.

Undercoverage

Bias that occurs when some members of the population are left out of the sampling frame or are very unlikely to be selected.

Nonresponse Bias

Bias that occurs when selected individuals can’t be contacted or refuse to participate and nonresponders differ from responders.

Response Bias

Bias that occurs when respondents give systematically inaccurate answers (e.g., due to social desirability or interviewer effects).

Leading Question (Wording Bias)

A question worded in a way that encourages a particular response, creating systematic error in survey results.

Voluntary Response Sample

A sample made of people who self-select into participating (often those with strong opinions); typically highly biased.

Convenience Sample

A sample chosen because it is easy to obtain (e.g., friends, one class); often unrepresentative and weak for generalization.