Statistical Reasoning: Basic Terms, Sampling, and Experiments

These vocabulary flashcards cover essential terms in statistical reasoning, including data sources, variables, sampling methods, experimental design, and data visualization techniques based on the lecture transcript.

Individuals

The objects described by a set of data, which may be people, animals, products, or articles.

Variable

A characteristic of an individual that can take different values for different individuals.

Data

The actual measurements recorded for individuals, typically organized in tables with rows as data points and columns as variables.

Continuous Variable

A variable that can take on potentially all values in a range, such as sales, population, or shooting percentage.

Categorical Variable

A variable that can take on a discrete number of categories, such as gender, consumer type, or yes/no outcomes.

Binary Variable

A categorical variable with only two possible outcomes, such as True/False or Yes/No.

Numerical Variable

A variable with numerical values for which arithmetic operations like adding and averaging are meaningful.

Ordinal Variable

A variable whose values must follow a particular order to be meaningful, such as educational levels.

Response Variable

A variable that measures an outcome or result of a study.

Observational Study

A study that observes individuals and measures variables of interest without intervening to influence the responses.

Sample Survey

An observational study that surveys a group of individuals selected because they represent a larger group.

Population

The entire group of individuals about which information is desired in a statistical study.

Sample

The part of the population from which information is actually collected, used to draw conclusions about the whole.

Census

A sample survey that attempts to include the entire population in the sample.

Experiment

A study that deliberately imposes some treatment on individuals to observe their responses and determine if the treatment causes a change.

Bias (Statistical Study)

A design flaw where the study systematically favors certain outcomes.

Convenience Sampling

A sampling method that selects individuals who are easiest to reach.

Voluntary Response Sample

A sample that chooses itself by responding to a general appeal, often attracting those with strong negative opinions.

Survivorship Bias

A bias that occurs when a study focuses on individuals or entities that passed a selection process and overlooks those that did not, such as only studying warplanes that returned from battle.

Simple Random Sample (SRS)

A sample of size $n$ consisting of $n$ individuals from the population chosen such that every individual has an equal chance of being selected.

Parameter

A fixed number that describes a population, whose value is typically unknown in practice.

Statistic

A number that describes a sample; its value is known once a sample is taken but can change from sample to sample.

Bias (Measurement)

Consistent, repeated deviation of the statistic from the parameter in the same direction over many samples.

Variability

A description of how spread out the values of a statistic are when many samples are taken.

Margin of Error (MOE)

A measure of how close an estimate is believed to be to the population parameter; for a $95\%$ confidence level, it is approximately $\frac{1}{\sqrt{n}}$.

Confidence Level

The overall success rate of a procedure in generating confidence intervals that capture the true value of the population parameter.

Confidence Interval

A range of values, calculated as $\text{parameter estimate} \pm \text{MOE}$, which likely contains the true population parameter.

Random Sampling Error

The deviation between the sample statistic and population parameter caused by chance.

Under-coverage

A sampling error where certain groups of the population are left out of the process of choosing the sample.

Non-sampling Errors

Errors not related to the act of sampling, including processing errors, poorly worded questions, response errors, and nonresponse errors.

Stratified Random Sampling

A method that divides the population into smaller subgroups (strata) based on shared attributes and then takes a separate SRS from each stratum.

Snowball Sampling

A method where initial respondents are selected and then asked to identify others who belong to the target population.

Cluster Sampling

A method where the population is divided into clusters, a random sample of clusters is selected, and then an SRS is taken within each chosen cluster.

Explanatory Variable

A variable that a researcher thinks explains or causes changes in a response variable.

Lurking Variable

A variable that has an important effect on the relationship among variables in a study but is not one of the explanatory variables studied.

Confounded Variables

Variables whose effects on a response variable cannot be distinguished from each other.

Statistically Significant

An observed effect of a size that would rarely occur by chance.

Placebo Effect

A favorable response to a treatment due to the subject's expectation of a cure rather than the treatment itself.

Double-Blind Experiment

An experiment in which neither the subjects nor the researchers know which treatment was received.

Matched Pairs Design

An experimental design that compares two treatments by using pairs of subjects that are closely matched and randomizing the treatment within each pair.

Block Design

An experimental design where subjects are divided into blocks (groups similar in some way) and random assignment to treatments is carried out separately within each block.

Instrument

A variable used to reasonably measure an abstract or unobservable concept, such as using years of education as a proxy for ambition.

Predictive Validity

The property of a variable if it can be used to accurately predict another variable.

Exploratory Data Analysis (EDA)

The process of using visualizations and simple calculations to summarize data features, look for patterns, and form hypotheses before main analysis.

Trend

A long-term upward or downward movement in data over time.

Seasonal Variation

A pattern in data that repeats itself at known regular intervals of time.