When is a discrete counting model appropriate compared to a continuous measurement model?
Conditions
- The variable is a count of distinct entities.
- The variable is a measurement of a continuous quantity.
Reasoning, step by step
- Determine if the variable is obtained by counting (discrete) or measuring (continuous).
- If counting, check if the possible values form a finite or countable set.
- If measuring, consider if the values are idealized as real numbers in an interval.
- Select the model that matches the nature of the data generation process.
Example
A count within a four-person family has possible values 0,1,2,3,4. Such a finite set of values defines a discrete counting model. Conversely, an idealized continuous amount uses a different model before rounding.
Common misconceptions
- Using a continuous model for small integer counts.
- Ignoring the difference between rounded measurements and idealized continuous variables.
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