Introductory Statistics - Chapter 1: Sampling and Data

Vocabulary terms and definitions covering Chapter 1 (Sampling and Data) of Introductory Statistics.

Descriptive Statistics

The branch of statistics that deals with organizing and summarizing data through numerical summaries, such as averages, or graphical representations.

Inferential Statistics

Formal statistical methods that use probability to draw conclusions from data and determine confidence levels in those conclusions.

Probability

A mathematical tool used to study randomness that evaluates the chance or likelihood of an event occurring.

Population

The complete collection of persons, things, or objects under study in a statistical investigation.

Sample

A portion or subset selected from a larger population to gain information about that population.

Statistic

A numerical characteristic that represents a property of a sample and serves as an estimate of a population parameter.

Parameter

A numerical characteristic that represents a property of an entire population.

Variable

A characteristic of interest for each person or thing in a population, typically represented by capital letters such as $X$ and $Y$.

Numerical Variables

Variables that take on values with equal measurement units, such as weight in pounds or time in hours.

Categorical Variables

Variables that place an individual or object into a specific category, such as political affiliation, eye color, or gender.

Data

The actual values of a variable obtained through sampling, which may consist of numbers or words.

Datum

A single, specific value of a variable.

Qualitative Data

Data resulting from categorizing or describing attributes of a population, such as hair color or blood type.

Quantitative Data

Data consisting always of numbers that result from counting or measuring attributes of a population.

Quantitative Discrete Data

Quantitative data that result from counting and take on only specific numerical values.

Quantitative Continuous Data

Quantitative data that result from measuring attributes, assuming measurement can be done with complete accuracy.

Pie Chart

A display for qualitative data where categories are shown as wedges in a circle proportional to the percentage of individuals in each category.

Bar Graph

A display for qualitative data where vertical or horizontal bars have lengths proportional to the number or percentage of individuals in each category.

Pareto Chart

A specialized bar graph where categories are sorted and displayed in descending order by size.

Simple Random Sample

A sampling method in which every sample of the same size has an equal probability of being selected.

Stratified Sample

A sampling method where the population is divided into subgroups called strata, and a proportionate random sample is drawn from each stratum.

Cluster Sample

A sampling method where the population is divided into groups called clusters, clusters are randomly chosen, and all members from the chosen clusters are included.

Systematic Sample

A sampling method where a starting point is selected at random and every $n\text{th}$ member is selected from a population list.

Convenience Sampling

A non-random sampling method that selects readily available results from a population.

Sampling with Replacement

A sampling procedure in which an individual selected from a population is returned before the next selection, allowing them to be chosen more than once.

Sampling without Replacement

A sampling procedure in which an individual selected from a population is not returned, ensuring they can be chosen only once.

Sampling Error

An error resulting from the actual process of sampling, such as an insufficient sample size.

Nonsampling Error

An error caused by factors independent of the sampling process, such as a defective counting device.

Sampling Bias

A flaw in data collection where certain members of a population are less likely to be selected than others, leading to incorrect conclusions.

Nominal Scale Level

A qualitative level of measurement consisting of unordered categories, names, labels, or yes/no responses.

Ordinal Scale Level

A level of measurement where data can be ordered or ranked, but precise differences between data values cannot be calculated.

Interval Scale Level

A level of measurement with ordered data and meaningful differences between values, but lacking a true zero point.

Ratio Scale Level

A level of measurement with ordered data, meaningful differences, a true zero point, and valid calculated ratios.

Frequency

The number of times a specific data value occurs in a dataset.

Relative Frequency

The fraction or proportion of times a specific data value occurs relative to the total number of outcomes.

Cumulative Relative Frequency

The sum of the relative frequency of a current row and all preceding relative frequencies in a dataset.

Explanatory Variable

The variable manipulated by a researcher in an experiment to cause change in another variable.

Response Variable

The variable measured in an experiment to observe the effects caused by the explanatory variable.

Treatments

The specific conditions or values of the explanatory variable applied in an experiment.

Experimental Unit

A single individual or object measured within an experiment.

Lurking Variables

Uncontrolled additional variables that can obscure or cloud the relationship between the main variables under study.

Control Group

A baseline group in an experiment that receives a placebo treatment to isolate active treatment effects from experimental influence.

Placebo Treatment

An inactive treatment given to a control group that cannot influence the response variable directly.

Blinding

A procedure in an experiment that prevents participants from knowing whether they are receiving an active treatment or a placebo.

Double-Blind Experiment

An experimental setup in which neither the study participants nor the researchers directly interacting with them know who receives active treatments or placebos.

Confounding

A situation in a study where the separate effects of multiple factors on a response variable cannot be distinguished.