Data Types, Measurement, and Data Collection
Types of Variables
Measurement levels
Variables can be categorical or numerical. Categorical variables are labels or groups, while numerical variables represent counts or measurements. Measurement levels matter because they determine which summaries and models are appropriate.
Common variable types
| Type | Examples | Typical summaries |
|---|---|---|
| Nominal categorical | Blood type, color | Counts, proportions |
| Ordinal categorical | Survey ratings, class rank | Median category, proportions |
| Discrete numerical | Number of defects, children | Mean, variance, count plots |
| Continuous numerical | Height, weight, time | Mean, standard deviation, histograms |
Measurement levels
Why type matters
Treating ordinal ratings as if they were interval measurements can lead to misleading averages and inappropriate model assumptions.
Good data collection practice
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Step 1: Define the target population precisely.
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Step 2: Choose a sampling method aligned with the question.
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Step 3: Standardize measurement procedures to reduce error.
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Step 4: Record missing data and outliers transparently.
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Step 5: Document the context so results can be interpreted correctly.
Which variable is best classified as discrete numerical?
A count like number of pets takes integer values and is discrete.
Correct answer: Number of pets
Why is a true zero important for ratio scales?
Ratio scales support statements involving multiplication and division because zero represents absence of the quantity.
Correct answer: Because it makes ratios meaningful, such as saying one value is twice another.