Ch. 1 STAT2013

General terminology and foundational concepts for Chapter 1: Introduction to Statistics.

Statistics

The science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data.

Variable

A characteristic or attribute that can assume different values, such as age, hair color, or GPA.

Data

The values that a variable can assume.

Population

Consists of all subjects (human or otherwise) that are studied.

Census

Data collected from an entire population.

Sample

A subset of the population.

Descriptive Statistics

Consists of the collection, organization, summarization, and presentation of data, such as averages and demographics.

Inferential Statistics

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

Probability

The chance of an event occurring.

Inference

A conclusion reached on the basis of evidence and reasoning.

Qualitative Variables

Variables that have distinct categories according to some characteristic or attribute; categorical and non-numeric.

Quantitative Variables

Variables that can be calculated or measured.

Discrete Variables

Quantitative variables that assume values that can be counted.

Continuous Variables

Variables obtained by measuring that can assume an infinite number of values between any two specific values, often including fractions or decimals.

Boundary

Defined as a class in which a data value would be placed before the data value was rounded; written as $72.5-73.5$ for a recorded value of $73$.

Nominal Level of Measurement

Classifies data into mutually exclusive categories in which no order or ranking can be imposed, such as eye color or political affiliation.

Ordinal Level of Measurement

Classifies data into categories that can be ranked, but precise differences between ranks do not exist, such as movie ratings or student classifications.

Interval Level of Measurement

Ranks data where precise differences between units exist, but there is no meaningful zero, such as temperature ($^{\circ}F$) or IQ scores.

Ratio Level of Measurement

Possesses all characteristics of interval measurement and has a true zero, such as height, weight, or salary.

Random Sample

A sampling technique where all members of the population have an equal chance of being selected.

Systematic Sample

Obtained by selecting every $k^{th}$ member of the population where $k$ is a counting number.

Stratified Sample

Obtained by dividing the population into subgroups (strata) based on a relevant characteristic and then randomly selecting subjects from each subgroup.

Cluster Sample

Obtained by dividing the population into sections (clusters) and then selecting one or more clusters and using all members within them.

Convenience Sample

A sampling technique where the researcher uses subjects who are convenient, such as mall surveys or internet sampling.

Sampling Error

The difference between result obtained from a sample and the results obtained from the population from which the sample was selected.

Non-Sampling Error

Occurs when data are obtained erroneously or the sample is biased (non-representative).

Observational Study

A study where the researcher draws conclusions based on observation and imposes no control.

Cross-Sectional Study

An observational study where all data is collected at one time.

Retrospective Study

An observational study where data is collected using records from the past.

Longitudinal Study

An observational study where data is collected over a long period of time.

Experimental Study

A study where the researcher manipulates one variable to determine how it influences other variables, involving a design and researcher control.

Independent Variable

The variable being manipulated by the researcher in an experimental study; also called the explanatory variable.

Dependent Variable

The resultant variable in an experimental study; also called the outcome variable.

Treatment Group

A group in an experimental study that receives special instructions or a special treatment.

Control Group

A group in an experimental study that receives no special instruction or special treatment.

Confounding Variable

A variable that influences the dependent or outcome variable but was not separated from the independent variable.

Hawthorne Effect

Occurs when subjects used in a study respond favorably or show improvement simply because they have been selected for the study.

Blinding

A method used to minimize the Hawthorne Effect in statistical experiments.

Suspect Samples

A misuse of statistics involving small samples or biased sampling methods.

Ambiguous Averages

A misuse where different interpretations of 'average' (mode, median, or mean) are used to mislead.

Changing the Subject

A misuse of statistics involving the use of percentages instead of actual numbers.

Detached Statistics

A statistical statement involving a comparison that lacks a reference to what or who the comparison is being made against.

Implied Connections

A misuse of statistics using qualifying words like 'suggest' or 'some studies show' to imply a relationship.

Misleading Graphs

The practice of labeling axes in a way that changes the visual appearance of data on a graph.

Faulty Survey Questions

The use of tricky or lengthy wording for questions that can be misleading or manipulative.