Introduction to Statistical Reasoning

Flashcards covering the fundamentals of statistics, sampling methods, study types, and confidence intervals based on Unit 5A.

Statistics (Science)

The science of collecting, organizing, and interpreting data.

Statistics (Data)

The data that describe or summarize something.

Population

The complete set of people or things being studied in a statistical study.

Sample

The subset of the population from which the raw data are actually obtained.

Population parameters

Specific numbers describing the characteristics of the population.

Sample statistics

Numbers describing the characteristics of the sample found by consolidating or summarizing the raw data collected from the sample.

Representative Sample

A sample in which the relevant characteristics of the sample members are generally the same as those of the population.

Simple random sampling

A method where every sample of the same size has an equal chance of being selected.

Systematic sampling

A method where a simple system is used to choose the sample, such as selecting every $n$-th member of the population.

Convenience sampling

A method where a sample is chosen because it is convenient to select or readily available.

Cluster sampling

A method where the population is divided into groups, some clusters are selected at random, and then all members within those selected clusters are chosen.

Stratified sampling

A method where the population is partitioned into at least two strata (subgroups), and a simple random sample is drawn from each.

Bias

A condition occurring if a statistical study's design or conduct tends to favor certain results.

Observational study

A study in which researchers observe or measure characteristics of the sample members but do not attempt to influence or modify them.

Experiment

A study in which researchers apply a treatment to some or all of the sample members and then observe the effects of the treatment.

Treatment group

The group of sample members in an experiment who receive the treatment being tested.

Control group

The group of sample members in an experiment who do not receive the treatment being tested.

Placebo

A substance that lacks active ingredients of the treatment but looks or feels enough like it so participants cannot distinguish it from the real treatment.

Placebo effect

A situation in which patients improve simply because they believe they are receiving a useful treatment.

Single-anonymous / blinding

An experiment in which the participants do not know whether they are in the treatment group or the control group, but the experimenters do know.

Double-anonymous / blinding

An experiment in which neither the participants nor the experimenters know who belongs to the treatment group or the control group.

Retrospective study (case-control study)

An observational study using data from the past in which the sample naturally divides into a group of cases and a group of controls.

Margin of error ($E$)

A value used to describe a confidence interval that is likely to contain the true population parameter.

Confidence interval

An estimate of the true population parameter ranging from $(\text{sample statistic} - \text{margin of error})$ to $(\text{sample statistic} + \text{margin of error})$.