Data Types & Data Collection (Quick Review)

Population of interest: adults; parameter is the true proportion $p$ .
Sample statistic for proportion: $\hat{p} = \dfrac{x}{n}$
Distinguish: population parameter vs sample statistic; use proportion for population context (not the mean).

Data collection types: surveys, experiments, observational studies.
Survey = observational study.
Experiment = active manipulation (controls or intervention) to study effects.
Example concept: future-oriented observational study (e.g., teacher retention over the next five years).

Data categories: Categorical vs Numerical.
Numerical data splits: Discrete vs Continuous.
Categorical data splits: Nominal vs Ordinal.
Numerical data splits: Interval vs Ratio.
Key distinction:
- Interval: differences meaningful, no true zero.
- Ratio: differences meaningful, true zero exists.

Discrete data (countable):
- Number of students in a class; number of marbles in a jar.
Continuous data (infinite values):
- Height, weight, length (can take decimals).
Nominal (categorical, no order):
- Yelp/Amazon/Netflix category labels (non-ordered).
Ordinal (categorical, ordered):
- Course grades (A, B, C, D); educational level (Freshman, Sophomore, Junior, Senior).
Interval data (numerical, no true zero):
- SAT scores, temperature in Celsius/Fahrenheit (differences meaningful, zero is not absolute).
Ratio data (numerical, true zero):
- Height, weight, length; number of children; class duration (when zero means none).
Note on zeros:
- Interval: zero is arbitrary (no true zero).
- Ratio: zero is meaningful (represents none).
Class duration can be either discrete or continuous depending on measurement, and it can be analyzed as ratio data if zero is meaningful.

Always classify data first: categorical vs numerical; then refine (nominal/ordinal or interval/ratio).
For numerical data, identify whether a true zero exists to choose interval vs ratio.
Surveys are observational; experiments involve active intervention; both produce data of varying types.