With vivid examples explain the four scales of measurement with citation
The four scales of measurement are commonly referred to as nominal, ordinal, interval, and ratio. These scales help categorize data and determine the appropriate statistical techniques to be used. Below are vivid examples for each scale of measurement.
1. Nominal Scale: The nominal scale involves categorizing variables into distinct groups or categories. The data at this level is qualitative and cannot be ranked or ordered. An example would be the classification of people into different blood types (e.g. A, B, AB, O). Each blood type is distinctly different, but there is no inherent order or ranking between them (Urdan, 2010).
2. Ordinal Scale: The ordinal scale allows variables to be ranked or ordered based on certain characteristics or attributes. Unlike the nominal scale, the distances between ranks are not uniform. An example could be rating customer satisfaction on a scale of "very dissatisfied," "dissatisfied," "neutral," "satisfied," and "very satisfied." While the ranks are ordered, the difference between "dissatisfied" and "neutral" is not necessarily the same as the difference between "satisfied" and "very satisfied" (Urdan, 2010).
3. Interval Scale: The interval scale preserves the order and has equal intervals between the data points. It allows for comparisons in terms of magnitude and difference, but it lacks a meaningful zero point. For instance, measuring temperature on the Celsius or Fahrenheit scales would be considered an interval scale. The difference between 20°C and 30°C is the same as the difference between 50°C and 60°C, but zero does not indicate the absence of temperature (Agresti & Finlay, 2009).
4. Ratio Scale: The ratio scale possesses all the properties of the interval scale, along with a meaningful zero point. This scale allows for comparisons of magnitude, difference, and ratios. An example of a ratio scale would be measuring the weight of objects in kilograms. Zero kilograms represents the absence of weight, and it is meaningful to say that one object weighs twice as much as another (Agresti & Finlay, 2009).
In conclusion, the four scales of measurement provide a framework for organizing and analyzing data. The nominal scale categorizes variables, the ordinal scale allows for ranking or ordering, the interval scale provides uniform intervals without a meaningful zero, and the ratio scale includes a meaningful zero point allowing for ratio comparisons.
References:
Agresti, A., & Finlay, B. (2009). "Statistical methods for the social sciences" (4th ed.). Pearson.
Urdan, T. (2010). "Statistics in plain English" (3rd ed.). Routledge.