Stats chapter 0/1

What is Statistics?

The science of collecting, organizing, analyzing, and interpreting data to make better decisions.

Descriptive Statistics

Summarizes and presents the data you already have (tables, graphs, averages).

Inferential Statistics

Uses sample data to draw conclusions about a population.

DCOVA

Define, Collect, Organize, Visualize, Analyze.

Variable

A characteristic that can take different values.

Categorical (Qualitative) Variable

Places observations into categories or labels (ex: eye color, major).

Numerical (Quantitative) Variable

A variable whose values are numbers.

Discrete Variable

Obtained by counting; only whole numbers (ex: number of employees).

Continuous Variable

Obtained by measuring; can include decimals (ex: height, weight, time).

Nominal Scale

Categories with no meaningful order (ex: eye color, phone carrier).

Ordinal Scale

Categories with a meaningful order but unequal differences (ex: class rank, satisfaction).

Interval Scale

Numerical scale with meaningful differences but no true zero (ex: temperature in °F or °C).

Ratio Scale

Numerical scale with meaningful differences and a true zero (ex: age, income, weight).

Population

The entire group you want to study.

Sample

A portion of the population used for analysis.

Parameter

A numerical value that describes a population.

Statistic

A numerical value that describes a sample.

Simple Random Sample

Every member of the population has an equal chance of being selected.

Convenience Sample

A sample chosen because it is easy to obtain; may not represent the population well.

Judgment Sample

A sample selected by experts or the researcher's judgment.

Systematic Sample

Select every kth individual after a random starting point.

Stratified Sample

Divide the population into groups (strata) and randomly sample from each group.

Cluster Sample

Randomly select entire groups (clusters) and sample everyone or some within those groups.

Observational Study

Researchers observe subjects without assigning treatments.

Designed Experiment

Researchers assign treatments to determine cause-and-effect relationships.

Survey Errors

Coverage Error = some groups excluded; Nonresponse Error = people don't respond; Sampling Error = natural difference between sample and population; Measurement Error = poor questions or inaccurate responses.