Statistics Chapter 1 Key Terms & Definitions

A complete set of glossary terms and definitions covering statistical and critical thinking, types of data, and sampling methods from Chapter 1 of the Stat C1000E course.

Statistics

The science of planning studies and experiments to obtain, organize, summarize, analyze, and interpret data, and draw conclusions based on them.

Data

Collections of observations such as measurements or survey responses.

Population

The complete collection of individuals or objects about which information is desired.

Sample

A subcollection selected from the population that is used for study.

Census

When data are collected from every subject in the population, not just a sample.

Descriptive Statistics

Consists of the collection, summarization, and presentation of data, describing only what is in the data with no generalizations beyond it.

Inferential Statistics

Consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions.

Voluntary Response Sample

A self-selected sample where respondents themselves decide whether to participate, often leading to bias because people with strong opinions are more likely to respond.

Parameter

A measurement describing some characteristic of a population.

Statistic

A measurement describing some characteristic of a sample.

Quantitative Variable

Consists of numbers representing counts or measurements that mean something as amounts.

Qualitative Variable

Consists of names, labels, or categories; even if numbers are used, they serve as labels rather than amounts.

Discrete Data

Quantitative data where the number of possible values is finite or countable.

Continuous Data

Quantitative data resulting from infinitely many possible values on a continuous scale where values cannot all be counted individually.

Nominal Level

Data consisting of names, labels, or categories in which order cannot be meaningfully arranged.

Ordinal Level

Data that can be arranged in some order, but differences between values are not meaningful.

Interval Level

Data that can be arranged in order with meaningful differences, but there is no true zero, meaning $0$ does not indicate none of the quantity.

Ratio Level

Data with meaningful differences and a true zero, where $0$ indicates none of the quantity is present and the word "twice" makes sense.

Ratio Test

A test to distinguish interval from ratio levels by asking "Does the word twice make sense?"

True Zero

A zero value that indicates none of the quantity is present; it is required for ratio level data.

Observational Study

A study where the researcher observes and measures specific characteristics but does not modify or interfere with the individuals being studied.

Experimental Study

A study where the researcher manipulates one or more variables and observes the effects on individuals to prove cause and effect.

Confounding Variable

An uncontrolled variable in an experiment whose effect on the response cannot be separated from the effect of the treatment.

Replication

The repetition of an experiment on more than one individual, requiring a sample size large enough to detect treatment effects.

Blinding

A technique where a subject does not know whether they are receiving a treatment or a placebo, used to prevent the placebo effect.

Double-Blind

A procedure where neither the subjects nor the researchers administering the treatment know who is in the treatment or placebo group.

Placebo Effect

When an untreated subject reports improvement in symptoms because they believe they are receiving a treatment.

Randomization

A process where individuals are assigned to treatment groups via random selection to use chance to create similar groups.

Completely Randomized Design

An experimental design where subjects are assigned to treatment groups entirely through random selection with no grouping or pairing.

Randomized Block Design

A design where subjects with similar characteristics are grouped into blocks first, then randomly assigned to treatments within each block.

Matched Pairs Design

A comparison of two treatment groups using subjects matched in pairs who share similar characteristics, such as twins or before/after tests on the same subject.

Random Sample

A sample where every possible sample of size $n$ has an equal chance of being selected.

Systematic Sample

A sampling method where every $k^{\text{th}}$ element in the population is selected.

Convenience Sample

A sampling method that uses subjects who are easy to access, which typically does not represent the population well.

Stratified Sample

A sampling method where the population is divided into subgroups sharing common characteristics, then a random sample is drawn from each subgroup.

Cluster Sample

A sampling method where the population is divided into clusters, some clusters are randomly selected, and then all members of the chosen clusters are surveyed.

Retrospective Study

A study where data are collected from the past through examination of records or interviews; also called a case-control study.

Cross-Sectional Study

A study where data are observed, measured, and collected at one point in time as a single snapshot.

Prospective Study

A study where data are collected forward in time from groups sharing common factors (cohorts); also called a longitudinal or cohort study.