Introduction to Statistics and Levels of Measurement

Statistics: The study of how to collect, organize, analyze, and interpret data.
Data: A collection of numbers, measurements, or observations.
Descriptive Statistics: Procedures used to summarize and describe the primary characteristics of a set of measurements.
Inferential Statistics: Procedures used to draw conclusions or inferences about a population based on sample data.

Qualitative Data: Non-numerical observations representing attributes or characteristics (e.g., gender, eye color, yes/no responses).
Quantitative Data: Numerical measurements or counts accompanied by units (e.g., height, weight, length, width).
Population: The complete set of all measurements or observations of interest.
Sample: A subset drawn from a population.

Sampling: Drawing subsets from an entire population.
Experiments: Observing outcomes after applying specific conditions or treatments.
Simulation: Using a model or facsimile to reproduce real-world phenomena.
Census: Collecting measurements from every member of the population (indicated by keywords such as each, all, or every).
Survey: Gathering information by asking respondents questions.

Reliability (Precision): The degree to which a test or measurement procedure yields consistent results upon repetition.
Validity (Accuracy): The extent to which a measurement process is logically correct and agrees with an accepted true value.

Nominal: Data organized into categories, names, or labels without numerical order, typically not intended for mathematical calculations.
Ordinal: Data that can be arranged in relative order or rank, though exact quantitative differences between ranks cannot be determined (e.g., ratings of good, better, best).
Interval: Ordered data where differences between values are meaningful, but no true starting zero point exists (e.g., temperature in $\text{degrees Celsius}$ or $\text{degrees Fahrenheit}$ ).
Ratio: The highest level of measurement; data can be ordered with meaningful differences and possesses a true zero point, enabling valid quantitative comparisons (e.g., core temperature in $\text{Kelvin}$ , length, weight, age, salary).