Stats

Population

The entire group of individuals that you want to draw conclusions about. (e.g., all 900 high school students).

Sample

A subset or portion of the population that you actually collect data from. (e.g., the 80 surveyed students).

Parameter

A number that describes a characteristic of the population. (e.g., the average income of every household in a city).

Statistic

A number that describes a characteristic of a sample. (e.g., the 60% of students in the sample who prefer music).

Census

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

Simple Random Sample (SRS)

A method where every individual and every possible group of a given size has an equal chance of being selected. This is the gold standard for unbiased sampling.

Systematic Sampling

A method where you select a random starting point and then choose every k-th individual from a list (e.g., every 50th voter).

Stratified Random Sampling

A method where the population is first divided into non-overlapping, homogeneous groups (called strata), and then an SRS is taken from each group. (e.g., splitting students by grade level and randomly sampling freshmen, sophomores, etc.).

Cluster Sampling

A method where the population is divided into groups (called clusters), a random sample of the clusters is chosen, and then every individual within the selected clusters is surveyed. (e.g., randomly selecting 10 dorms and surveying everyone inside them).

Observational Study

• A study where researchers observe subjects and measure variables without assigning treatments or manipulating any variables. They don't interfere.

Experiment

A study where researchers deliberately impose a treatment on subjects to measure a response. This is the only way to determine a cause-and-effect relationship.

Random Selection

The process of randomly choosing participants from a population to be in a study. This is crucial for generalizability (being able to apply the results to the whole population).

Random Assignment

The process of randomly assigning participants to different treatment groups (e.g., a treatment group and a control group) within an experiment. This is crucial for establishing causation.

Confounding Variable

An "extra" variable that you didn't account for that could be influencing the outcome of your study, making it difficult to determine the true cause.

Control

The practice of keeping conditions constant for all subjects in an experiment to isolate the effect of the variable being tested.

Bias

A systematic error in a study's design that favors certain outcomes, making the results unrepresentative of the population. A larger sample size does not fix bias.

Nonresponse Bias

A type of bias that occurs when individuals who decline to participate in a study are systematically different from those who do participate. (e.g., the most stressed people quitting a stress survey).

Response Bias (or Measurement Bias)

A type of bias that occurs when something about the survey design (like a confusing or leading question) or the way a person answers (like lying) influences the responses.