Data on a nominal scale can be sorted, but the intervals between the ranks are not quantifiable or consistent. For ordinal data, while you can determine the median and certain non-parametric statistical tests, you cannot assume equal intervals, which prevents the use of parametric tests like t-tests or standard deviation calculations.
Understanding Categorical, Ordinal, Interval, and Ratio Variables
Temperature in Celsius or Fahrenheit is the classic example: the difference between 10°C and 20°C is the same as between 20°C and 30°C, but 0°C does not mean "no temperature. The interval scale has order, equal intervals, and known differences, but it lacks a true zero point.
A weight of 20 kilograms is exactly twice as heavy as 10 kilograms, and an object with a length of 0 meters has no length. This allows for ratios to be compared meaningfully.
Categorical Ordinal Interval Ratio Variables Explained
The distinction between nominal, ordinal, interval, and ratio scales dictates the types of statistical operations that can be meaningfully applied and determines the nature of the insights that can be derived. You can identify the most common category or calculate percentages, but you cannot logically compute a mean or a standard deviation.
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