The scale that has a true zero point and equal intervals between points is the ratio scale.
A ratio scale is the highest level of measurement and possesses all the characteristics of the other three scales: nominal, ordinal, and interval. In addition to classifying and ordering data, and having equal intervals between points, the ratio scale has a meaningful and non-arbitrary zero point. This allows for meaningful ratios to be calculated.
Here's a breakdown:
- Nominal Scale: Data is categorized (e.g., colors, types of fruit).
- Ordinal Scale: Data is categorized and ordered (e.g., rankings, satisfaction levels).
- Interval Scale: Data is categorized, ordered, and has equal intervals between points, but no true zero (e.g., temperature in Celsius or Fahrenheit).
- Ratio Scale: Data is categorized, ordered, has equal intervals, and a true zero point (e.g., height, weight, age, income).
The existence of a true zero point is the key distinguishing factor of a ratio scale. A true zero indicates the absence of the quantity being measured.
Examples of Ratio Scales:
- Height: A height of zero centimeters means there is no height.
- Weight: A weight of zero kilograms means there is no weight.
- Income: An income of zero dollars means there is no income.
- Age: An age of zero years means birth.
Because ratio scales have a true zero, you can say that one value is a multiple of another. For example, someone who is 2 meters tall is twice as tall as someone who is 1 meter tall. Similarly, someone with an income of $50,000 earns twice as much as someone with an income of $25,000. These types of comparisons are not valid with interval scales.
In summary, the ratio scale is the only scale that allows for all arithmetic operations, including meaningful ratio comparisons, due to its true zero point and equal intervals.
